Survey of the Indoor Availability of the GPS

Transcription

A Study of the Availability of Signals from a Global Navigation Satellite System in
an Indoor Environment
Bachelor’s thesis in Electrical Engineering, Engineering Physics and Computer Science
VIKTOR AHLQVIST
BOJAN DRVENICA
BJÖRN HERDER
KEVIN LAM
MALIN OLOFSSON
Department of Signals and Systems
Communication systems, Information theory and Antennas
CHALMERS UNIVERSITY OF TECHNOLOGY
Gothenburg, Sweden 2013
Bachelor’s thesis SSYX02-13-33
BACHELOR’S THESIS IN ELECTRICAL ENGINEERING, ENGINEERING PHYSICS AND
COMPUTER SCIENCE
A Study of the Availability of Signals from a Global Navigation Satellite System in an Indoor
Environment
VIKTOR AHLQVIST
BOJAN DRVENICA
BJÖRN HERDER
KEVIN LAM
MALIN OLOFSSON
CHALMERS UNIVERSITY OF TECHNOLOGY
Environment
VIKTOR AHLQVIST
BOJAN DRVENICA
BJÖRN HERDER
KEVIN LAM
MALIN OLOFSSON
© VIKTOR AHLQVIST, BOJAN DRVENICA, BJÖRN HERDER, KEVIN LAM, MALIN OLOFSSON,
2013
Bachelor’s thesis SSYX02-13-33
ISSN 1654-4676
Chalmers University of Technology
SE-412 96 Gothenburg
Sweden
Telephone: +46 (0)31-772 1000
Cover:
Heatmat plot showing the mean number of available space vehicles
Typeset with LATEX using fonts from the Linux Libertine family
Environment
Bachelor’s thesis in Electrical Engineering, Engineering Physics and Computer Science
VIKTOR AHLQVIST
BOJAN DRVENICA
BJÖRN HERDER
KEVIN LAM
MALIN OLOFSSON
Chalmers University of Technology
Abstract
Reliable navigational systems have always been of great interest and while the most commonly
used navigational system today, the Global Positioning System (gps), works good outdoors, the
high frequency signals are attenuated when penetrating walls or roofs.
There is much research being done on the different ways of constructing an Indoor Navigational
System (ins). A system that can combine both outdoor and indoor navigation would be of great
interest in many fields and everything from airports to emergency services would benefit from
such a system. Furthermore, since the gps receivers are featured in almost all smartphones
there is a huge market for a ins based on, or used in combination with, the gps.
This thesis deals with measurements of the gps availability on one floor of an office building at
Chalmers University of Technology. Measurements have been done on two metres equidistantly
spaced measurement points both in offices, lecture halls and corridors. The hardware used
during the measurements were U-blox 6 receivers and measured data includes among other
Dilution of Precision (dop)-values, Signal-to-noise ratio (snr), satellite availability and accuracy
of positioning. The data was then analysed and visualised using a program written in Matlab.
Results show that even though more than the needed four satellites where available in most
places indoors, other factors, such as snr, made the accuracy to low to be usable to get accurate
position. It was also found that different measures of quality for the gps indoors and outdoors
are necessary, since the satellite constellation alone does not give much information about how
the signals propagate indoors.
Keywords: Global Positioning System, Satellite navigation systems, GPS, measure, position,
signal, system
i
Sammanfattning
Det har alltid funnits ett intresse och behov av precisa och tillförlitliga navigationssystem som
fungerar över stora områden och mycket forskning och resurser har lagts på att konstruera
sådana. Det idag mest använda satellitbaserade systemet, Global Positioning System (gps),
fungerar bra utomhus men den korta våglängden och den låga effekten på radiosignalerna
medför att signalerna propagerar dåligt inomhus.
Det finns olika tekniker för hur ett navigationssystem för inomhusbruk, ett Indoor Navigational
System (ins), kan konstrueras, men de flesta kräver utbyggd infrastruktur. Ett system som kan
kombinera den globala räckvidden av ett satellitbaserat system med tillförlitlig positionering
inomhus har tillämpningar inom allt från flygplatser till räddningstjänst. Vidare medför den
ökade spridningen av gps-mottagare i smarttelefoner att ett möjligt stort tillämpningsområde
är navigering för privatpersoner på till exempel en mässa eller i en kontorsbyggnad.
Det här arbetet behandlar mätningar av tillgängligheten av gps inomhus i en kontorsbyggnad
på Chalmers tekniska högskola i Göteborg. Mätningar har gjorts på mätpunkter placerade
med två meters mellanrum i en byggnad som innehåller både kontor, föreläsningssalar och
korridorer. Mätningarna genomfördes med U-blox 6 mottagare och mätdatan inkluderar bland
annat Dilution of Precision (dop)-värden, signal-brusförhållanden, satelliternas tillgänglighet
och tillförlitlighet i positionen. Mätdatan är sedan analyserad och visualiserad med ett program
skrivet i Matlab.
Resultaten visar att även om fler än de fyra nödvändiga satelliterna som krävs för positionsbestämning var tillgängliga på de flesta platserna inomhus så påverkade andra faktorer, som
signal-brusförhållandet, att tillförlitligheten av positionsbestämningen var låg. Resultaten visar
vidare att samma kvalitetsmått för mätningarna inte kan användas inomhus och utomhus, då
till exempel satellitkonstellationen inte ger någon information om hur signalerna propagerar
inomhus.
iii
Acknowledgements
We would like to extend our gratitude to Henk Wymeersch and Gabriel Garcia, our supervisors
throughout this project, for their help and support whenever we had questions and also for
supplying the materials needed to make this project possible.
We would also like to thank everyone in the Department of Signals and System and Department
of Computer Science and Engineering for letting us disturb them and do measurements in their
offices.
Lastly, we would like to thank the cleaning staff of Chalmers University of Technology for
putting up with the little tape markers we placed all over the building.
v
Nomenclature
BDS
Beidou Satellite Navigation System, also known as compass, is a Global Navigation Satellite System owned and
operated by the People’s Republic of China.
DGPS
Differential Global Positioning System is a method to
reduce systematic errors using known reference points,
which transmits correction data over radio. This requires
special receivers and nearby reference points.
DOP
Dilution of Precision, a value that describes the quality of
positioning. A value under 5 is considered good and values above 20 are considered poor and give an inaccurate
position.
Galileo
Galileo is a Global Navigation Satellite System currently
under development by the European Space Agency and
the European Union. The goal is to provide a high precision navigation system for European Union.
GDOP
Geometric Dilution of Precision, see dop.
GLONASS
Globalnaya Navigatsionnaya Sputnikovaya Sistema, a
Global Navigation Satellite System owned and operated by Voyska Vozdushno-Kosmicheskoy Oborony, the
Russian Aerospace Defence Forces and the Russian
Federation.
GNSS
Global Navigation Satellite System is a term used to describe satellite navigation systems with global coverage,
such as navstar gps.
GPS
Global Positioning System, see navstar gps.
vii
viii
HA-NDGPS
High Accuracy Nationwide Differential Global Positioning System, a system similar to Differential Global Positioning System that is currently under development in
the United States.
HDOP
Horizontal Dilution of Precision, see dop.
INS
Indoor Navigational System.
NAVSTAR GPS
Navigation Satellite Time and Ranging Global Positioning
System, more commonly known as the gps, is a gnss
operated by United States Department of Defence.
NMEA
National Marine Electronics Association is an organisation that maintains the nmea protocol which is commonly
used in the gps recievers and marine electronics.
NV
Navigational Message, a message containing data about
currently active satellites, clock corrections, ephemeris
and similar data about the satellite constellation.
PDOP
Positional Dilution of Precision, see dop.
PRN
Pseudo-Random Noise is a deterministic sequence that is
mixed with the signal which allows multiple satellites to
send in the same frequency and still be identified by the
receiver.
Pseudo-range
Pseudo-range is the calculated distance between satellite and receiver. The distance is calculated through time
elapsed between sending and receiving the signal multiplied with speed of light.
SNR
Signal-to-Noise ratio is the ratio between signal and noise.
It is used to compare the signal power to the background
noise.
SV
Space Vehicle is a term describing any vehicle, space craft
or satellite that is used in space. In a Global Navigational
Satellite System, Space Vehicle refers to the navigation
satellites.
TDOP
Time Dilution of Precision, see dop.
VDOP
Vertical Dilution of Precision, see dop.
ix
Contents
1. Introduction
1
1.1. Background and motivation of thesis . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2. Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.3. Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.4. Report structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2. Theoretical background
5
2.1. The gps system segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2.2. Gps positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
2.3. Measurement errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
2.4. National Marine Electronics Association (nmea) protocol . . . . . . . . . . . . . .
16
3. Method
18
3.1. Equipment and preparations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
3.2. The building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
3.3. Measurement specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
3.4. Minor indoor campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
3.5. Major indoor campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
3.6. Description of collected measurements . . . . . . . . . . . . . . . . . . . . . . . .
23
4. Results
26
4.1. Outdoor campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
4.2. Minor campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
4.3. Major indoor campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
4.4. Time validity of measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
4.5. The code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
xi
5. Discussion
39
5.1. Minor indoor campaign and measurement methodology . . . . . . . . . . . . . . .
39
5.2. Results of the major indoor campaign . . . . . . . . . . . . . . . . . . . . . . . . .
40
5.3. Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
6. Conclusion
44
Bibliography
45
A. Available data
49
B. The antenna
51
C. Data log
52
D. Checklist for measurements
54
D.1. Pre measurement preparation of software (U-blox) . . . . . . . . . . . . . . . . . .
54
D.2. During measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
E. Photos for references
55
E.1. Outdoor campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
E.2. edit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
E.3. Major measurement campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
F. Swedish summary
59
F.1. Inledning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
F.2. Metod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
F.3. Sammandrag av resultat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
F.4. Diskussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
F.5. Slutsats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
xii
1. Introduction
This introduction presents the research and provides a background to the project as well as the
purpose of the thesis. Related work within the field is also described.
Imagine a group of firefighters arriving at the scene of a fire in a large-scale building. Their
first objective is to find out if there are people still inside the building and before sending in the
firefighters the blueprints needs to be acquired. In an ideal world, the firefighters will be guided
perfectly through the building. However, there are a lot of things that can and will go wrong, as
they are dependant on the communication between the man reading the blueprints and the men
inside. The firefighters also need to correctly report back what they see, even though the room might
be completely filled with smoke.
Imagine how much simpler, safer and efficient it could be if the firemen were able to use a precise
navigational system and work their own way through the building. Currently this is not a possibility
as there is no navigation system comprehensive enough to work indoors on this scale. However, the
Global Positioning System ( gps) could be a part of the solution to their problem, but there is not
enough information about how the gps actually behaves in an indoor environment.
1.1. Background and motivation of thesis
The Global Positioning System (gps) is a technology which has been developed for usage
outdoors and it functions well while in its intended environment. However, a major problem
with the gps, or any other Global Navigation Satellite System (gnss), is that they normally
do not work indoors. This is mainly due to the signals being fairly weak and that the high
frequencies used have very little penetration through objects such as walls or roofs. Other
electrical equipment using similar frequencies might also interfere with the signals.
There are several different actors who are searching for alternatives for an indoor environment,
but there is little research being done concerning the actual performance and availability of the
gps indoors.
An accurate research of the gps availability could be used to validate the construction of a
gps-based Indoor Navigational System (ins), a technology which could be used within a great
number of fields. One example is the firemen above, but it could also be used for example within
emergency services, airports, shipping companies and the military.
1
1. Introduction
1.2. Purpose
The purpose of this project is to explore, document and visualise the availability of the gps
signals in a typical indoor environment. Measurements will be conducted on one floor of the
edit building at Chalmers University of Technology.
Measured data will include information about availability in terms of Signal-to-noise ratio (snr),
satellite availability, Dilution of Precision (dop)-values and quality of the positioning.
Outdoor measurements will also be conducted to study how the gps should behave in a normal
setting and to serve as reference measurements.
1.3. Related work
The general focus of creating an ins lies on developing a completely new system or using other
systems than the gps as it is assumed that it does not work. However, there are a few teams
whom are still investigating the possibilities of an ins based on the gps.
Research and measurements of the gps availability indoors have been conducted by the Department of Computer Science at the Aarhus University and the Alexandra Institute in Denmark
[1]. They have been experimenting with state-of-the-art gps receivers as well as receivers
within mobile phones which are of less accuracy. The measurements were done within smaller
buildings of specific materials such as wood or concrete. The positions had been distributed
with one point per room. The researchers also conducted measurements within a shopping mall
where the measured points were somewhat evenly distributed according to a grid.
Their results show that the accuracy was below five metres within the designated wooden
structures and below ten metres within most of the buildings that were made out of bricks and
concrete. They concluded that the gps can be used to a certain extent in an indoor environment.
However, the time it takes to get a fix towards a satellite (up to a few minutes) and an accuracy
down to tens of metres are not satisfactory within certain applications such as emergency
services.
Gustavo López-Risueño and colleagues have also performed measurements within a so-called
medium error building, a building where the signals transmitted by the satellites reach the
receiver through either windows or one external wall [2]. The measurements were conducted
using a one-shot high-sensitive gnss receiver. These receivers require less time to fix on to
the satellites. They also make it impossible for the messages received to become distorted
within high-attenuation environments. They found that the receiver is likely to always detect a
minimum of five satellites with a respective snr above 20 dB Hz.
2
1. Introduction
1.3.1. Existing wireless solutions
There are several different solutions competing for the spot as the ins of the future, some of
them aim for a broader area of application, while others are more specialised to giving a high
accuracy within a smaller area. There are also differences between systems that are used to
pinpoint a position and systems designed to locate specific objects.
There are several different aspects that need to be taken into consideration, regardless of the area
of application, such as the cost, accuracy, precision, usability, robustness, complexity, scalability
and whether or not it is possible to use already existing technology [3].
Wireless solutions consists of two hardware aspects, a transmitter and a receiver or a combination
with a transceiver where the receiver or transceiver generally contains the intelligence for
performing calculations. While developing an ins it is possible to either develop a new system
or to change and improve an already existing one. A new system has the benefits of being
tailored to the developer’s specification and area of application, while it is possible to save a lot
of time and money by using an already existing system.
This report will not discuss the different technologies and aspects to develop an ins, since
this is beyond the scope of the report. To mention some work on ins, there is a system being
developed by Google using cellphone base stations and Wi-Fi hotspots called My Location,
which is intended to work with the gps [4]. Another company that has developed ins is Nokia,
using Bluetooth hotspots [5].
1.4. Report structure
The structure of the report is presented to make it easier for the reader to find the relevant
information and to know what to expect from the different sections.
1. Introduction
This part introduces the research and provides a background as well as presents the
purpose of the thesis.
The theoretical background aims at explaining and clarifying how the gps works in depth
and to explain important terms that will be used in the thesis.
A reader with experience within the gps field might want to skip this section.
3. Method
The method contains a description of how the measurements were planned and carried
out. It also describes the how the data was handled.
4. Results
This part presents the results of the work conducted during this project including a brief
description of the code written.
3
1. Introduction
5. Discussion
The discussion will draw conclusions from the achieved results and it will also discuss
important choices made within the method.
6. Conclusion
This part presents the conclusions drawn from the thesis with regards to the purpose,
theoretical background, method, results and the discussion.
7. Appendix
The appendix contains additional material such as a detailed description of the antenna,
checklist for the measurements, a datalog and a description of the different datatypes. It
also contains a Swedish summary of the project which is a requirement of the Engineering
Physics section of Chalmers University of Technology.
4
The theoretical background aims at explaining and clarifying how the gps works in depth and to
explain important terms that will be used in the thesis. A reader with experience within the gps
field might want to skip this section.
Determining an exact position has always been of great interest and the applications of such
systems are almost endless. Early sailors used the stars for navigation when landmarks were
nowhere to be seen and with the invention of radio transmission that provided a good way
of determine position in large areas. To get good coverage over the whole world the radio
transmitters were moved to space, into a gnss.
Navigation Satellite Time and Ranging Global Positioning System (navstar gps), or the gps as
it is more commonly known, is such a gnss which is operated by the United States Department
of Defence. It was the first operational gnss and although several other systems exist it is still
the most commonly used one.
Other gnss that either are in use or currently under development are the Russian system
Globalnaya Navigatsionnaya Sputnikovaya Sistema (glonass), the European Galileo and the
Chinese Beidou Satellite Navigation System (bds).
2.1. The gps system segments
The gps can be divided into three system segments: space, control and user.
2.1.1. The space segment
The space segment consists of at least 24 satellites, called Space Vehicle (sv), divided into six
orbital planes with four satellites in each. The planes are tilted 55 degrees with respect to the
equator and the sv are located at an altitude of 20 200 kilometres [6]. This configuration ensures
that at least four sv are always visible, which is enough to determine an accurate position in
the three spatial dimensions. In 2011 three of these planes were expanded with an extra sv to
provide better coverage for large parts of the world. Apart from these 27 sv, 4 extra sv and 3 to
4 decommissioned sv are part of the gps [6].
The satellites take 11 hours 58 minutes to make one revolution around the Earth and the whole
configuration is therefore reset after 23 hours 56 minutes [7]. This orbit time is deliberately
chosen because it equals the time for a full rotation of the Earth relative fix stars, also known
5
as a sidereal day [7]. The gps also has to correct for effects of general relativity because of the
difference in the gravitational field at the surface of the Earth and at the orbit of the satellites
[8], [9].
2.1.2. Signal
The satellites transmit radio signals consisting of a carrier wave with modulated Pseudo-Random
Noise (prn). Pseudo-random means that the sequence is not truly random but is instead
generated by an algorithm.
Three carrier frequencies are used: L1 (1 575.42 MHz), L2 (1 227.60 MHz) and L5 (1 176.45 MHz).
Frequency L1 and L2 are transmitted by all satellites, but L2 is a military frequency that is not
available for civilian use [10]. L5 is only transmitted by the newest satellites [11].
Each satellite broadcasts three types of code [10]:
• The coarse acquisition code, C/A
• The encrypted military precision code, P(Y)
• The Navigational Message (nv)
The ranging code consists of a prn-code which is unique to each satellite. The code is modulated by phase-modulation on the carrier wave, which makes it possible to have all satellites
transmitting on the same frequency. The ranging code differ between the C/A-code on the L1
frequency for civilian uses and the P(Y)-code transmitted on both L1 and L2 for military uses
[6]. The P(Y) code is precision code (P) with a much higher resolution than the C/A-code [11],
[12]. To prevent tampering with the signal the P-code is encrypted with a W-code to create the
P(Y)-code [12].
The third code modulated on the carrier wave is the nv, which contains the navigation data [12].
The message includes information about the satellite constellation, which of satellites that are
currently active, clock correction for these satellites, ionosphere data, the ephemeris (position
and velocity of satellites) and an almanac message [12]. The ephemeris– and almanac-parts
contain roughly the same data, but while the ephemeris contains highly detailed information
about the location and velocities, almanac contains more general information [12]. Due to this,
the ephemeris data is only valid for four hours while almanac is valid for 180 days. The almanac
is therefore used to determine which satellites that are relevant during startup of the receiver in
order to download the ephemeris data. The ephemeris data contains orbit parameters according
to the wgs-84 system which is a geocentric coordinate system with Cartesian coordinates.
6
2.1.3. The control segment
This segment consists of a network of control stations, monitor stations and ground based
antennas [12]. The control stations are used to generate navigational messages and determine
the accuracy of the satellites. They are also used in order to make sure that the sv are in the
correct constellation and other system maintenance [12]. To track the satellites positions, a
network of 16 monitor stations are used, which report the passings back to a control station
[12]. A system of ground antennas is used to communicate with the sv [12].
2.1.4. The user segment
The gps is a free and open global information structure that serves a broad variety of users. Some
of the uses for the gps are navigation, timing and positioning. For this project the gps-receivers
and software program constitute a part of the users segment as a means for positioning and
navigation indoors [6].
2.1.5. Ground based stations
While not being defined as a segment of the gps, ground based stations are used in Differential
gps (dgps) and High Accuracy Nationwide dgps (ha-ndgps). These enhancements to the gps
uses these ground stations to get a higher accuracy without having the need for large antennas
[13]. The positions of the ground stations in dgps are well known, which makes it possible
to compute corrections for the pseudo-range measurements at that station. These corrections
are then transmitted to the gps units, which can use these corrections to get better position
accuracy. These systems require stations that are relatively close to the user, the distance to
the stations can not be more than a couple of dozen of kilometres [13]. The nationwide dgps
system in Sweden is called Swepos. An version of dgps called ha-ndgps is being developed
in the United States and aims at providing a position with an accuracy error of less than 10
centimetres in the horizontal plane [13], [14].
2.2. Gps positioning
This section describes the basics components and calculations for the gps positioning
2.2.1. Pseudo-range
A pseudo-range is the range from satellite to receiver with the clock bias and noise included
[7], [15]. The satellite transmits a signal that reaches a receiver and gets recorded at the time
of arrival [7]. Autocorrelation is used to determine the time delay. This technique compares
the received wave from the satellite with an exact replica that is created in the receiver. Such
7
a replica can be created since the receiver knows exactly how the satellite’s signals look at
any given point in time [7], [15]. The replica is made in synchronisation with the receivers
own clock. The pseudo-range is calculated by multiplying the time delay with the propagation
velocity of the signal, which is equal to the speed of light [7].
A simplified version of the pseudo-range can be written as
𝑃𭑠 = (𝑇 − 𝑇𭑠 )𝑐
(2.1)
where 𝑃𭑠 is the pseudo-range, (𝑇 − 𝑇𭑠 ) is the time difference and 𝑐 is the speed of light,
299 792 458 m/s. The subscript 𝑠 denotes satellite. 𝑇 is the time of arrival at the receiver and 𝑇𭑠
is the transmission time from the satellite.
The simplified model in (2.1) does not take the clock bias into account. This bias, which is
present in both the satellite and receiver clocks contributes to the error in the pseudo-range
calculation.
With the clock bias taken into account the times 𝑇 and 𝑇𭑠 can instead be written as
𝑇 =𝑡+𝜏
𝑇𭑠 = 𝑡𭑠 + 𝜏𭑠 .
(2.2)
Where 𝑡 is the true time and 𝜏 is the clock bias. A more advanced model of the pseudo-range
function then becomes dependent on the true time the signal was received:
𝑃(𝑡) = ((𝑡 + 𝜏) − (𝑡𭑠 + 𝜏𭑠 ))𝑐 = (𝑡 − 𝑡𭑠 )𝑐 + 𝜏𝑐 − 𝜏𭑠 𝑐
𝑃(𝑡) = 𝜌(𝑡, 𝑡𭑠 ) + 𝜏𝑐 − 𝜏𭑠 𝑐.
(2.3)
In (2.3) 𝜌(𝑡, 𝑡𭑠 ) is the range from the receiver, at receive time, to the satellite at transmit time. It
is still a simplified model, because the relativistic effects are ignored, but it can still be used to
describe how pseudo-ranges are calculated. With Pythagoras theorem, 𝜌(𝑡, 𝑡𭑠 ) can be written
as:
2
2
2
𝜌(𝑡, 𝑡𭑠 ) = √[(𝑥(𝑡𭑠 ) − 𝑥(𝑡)] + [𝑦(𝑡𭑠 ) − 𝑦(𝑡)] + [𝑧(𝑡𭑠 ) − 𝑧(𝑡)] .
(2.4)
The nv makes it possible to calculate the satellite position (𝑥𭑠 , 𝑦𭑠 , 𝑧𭑠 ) and the satellite clock bias
𝜏𭑠 . This leaves the pseudo-range model with four unknown parameters: the receiver position
(𝑥, 𝑦, 𝑧) and the receiver clock bias 𝜏 [7], [15].
It is important to use the correct transmission time of the message to be able to calculate a good
pseudo-range value. This data is not transmitted with the nv but is instead calculated by an
iterative algorithm known as the light time algorithm. The calculation starts with the receive
time and the iteration is stopped once the value converges. The light time algorithm looks as
follows:
8
𝑡𭑠 (0) = 𝑡 − (𝑇 − 𝜏)
𝜌 (𝑡, 𝑡𭑠 (0))
𝑡𭑠 (1) = 𝑡 − 𭑠
𝑐
𝜌𭑠 (𝑡, 𝑡𭑠 (1))
𝑡𭑠 (2) = 𝑡 −
𝑐
⋮
𝜌 (𝑡, 𝑡𭑠 (𝑛 − 1))
𝑡𭑠 (𝑛) = 𝑡 − 𭑠
.
𝑐
(2.5)
The algorithm starts with the true receiver time which usually is not known in advance. For
most receivers an error does not get larger than a few milliseconds, but even an error as low as
one microsecond will cause a range error of 300 metres [16].
Normally at least four pseudo-range observations are needed to solve the equation system with
four unknown parameters 𝑥, 𝑦, 𝑧, 𝜏. The equation system can be written as follows:
𝑃1 = √(𝑥1 − 𝑥)2 + (𝑦1 − 𝑦)2 + (𝑧1 − 𝑧)2 + 𝜏𝑐 − 𝜏1 𝑐
𝑃2 = √(𝑥2 − 𝑥)2 + (𝑦2 − 𝑦)2 + (𝑧2 − 𝑧)2 + 𝜏𝑐 − 𝜏2 𝑐
𝑃3 = √(𝑥3 − 𝑥)2 + (𝑦3 − 𝑦)2 + (𝑧3 − 𝑧)2 + 𝜏𝑐 − 𝜏3 𝑐
𝑃4 = √(𝑥4 − 𝑥)2 + (𝑦4 − 𝑦)2 + (𝑧4 − 𝑧)2 + 𝜏𝑐 − 𝜏4 𝑐.
(2.6)
(2.7)
(2.8)
(2.9)
2.2.2. Mathematical description of the gps positioning
For a full mathematical description, see Basics of the GPS Technique: Observation Equations by
Geoffrey Blewitt [7].
Based on the pseudo-range measurements and the ephemeris information, the position of a
receiver unit can be calculated using a linearised model [7].
Because of different types of noise, which will be discussed later on in the text, the pseudorange values will have different amounts of noise in them. A way of reducing the error in
position is to use more than the needed four satellites, which will make the system of equations
overdetermined and the use of the least-squares method a necessity. The first step in making a
least-squares estimate is to model the pseudo-range observations as a sum of an unperturbed
term following the model and a noise term:
𝑃observed = 𝑃model + noise = 𝑃(𝑥, 𝑦, 𝑧, 𝑡) + 𝜈.
(2.10)
From this model the unperturbed model 𝑃model can be linearized by applying Taylor’s theorem
and neglecting terms of orders higher than one. The equations can be rewritten on matrix form
and then a least-squares solution can be calculated. By analysing the variance between the
solution and the individual pseudorange values, the covariance matrix, which is the building
stone for the computation of the dop-values, can be explained.
9
2.2.3. Linearizing the pseudo-range
Four provisional parameter values, one for each of the observation parameters, are chosen and
denoted as 𝑥0 , 𝑦0 , 𝑧0 and 𝜏0 . In application, these provisional values would be changed for
every iteration of the least-squares computation to minimise the residuals of the solution. The
iteration begins with the receiver making a guess of the clock bias and its own position. From
this it constructs a provisional solution 𝒙.̂ Linearizing 𝑃model around the provisional values
gives
𝜕𝑃
𝜕𝑃
𝜕𝑃
𝜕𝑃
+ (𝑦 − 𝑦0 )
+ (𝑧 − 𝑧0 )
+ (𝜏 − 𝜏0 )
𝜕𝑥
𝜕𝑦
𝜕𝑧
𝜕𝜏
𝜕𝑃
𝜕𝑃
𝜕𝑃
𝜕𝑃
= 𝑃computed +
𝛥𝑥 +
𝛥𝑦 +
𝛥𝑧 +
𝛥𝜏
𝜕𝑥
𝜕𝑦
𝜕𝑧
𝜕𝜏
(2.11)
𝑃(𝑥, 𝑦, 𝑧, 𝜏) ≅ 𝑃(𝑥0 , 𝑦0 , 𝑧0 , 𝜏0 ) + (𝑥 − 𝑥0 )
where the partial derivates are also computed using the provisional values.
2.2.4. Matrix form
The residual observation is defined as the difference between the measured and the above
computed values and is denoted as 𝛥𝑃.
𝛥𝑃 = 𝑃observed − 𝑃computed =
which can be written on matrix form as
𝜕𝑃
𝛥𝑃 = (
𝜕𝑥
𝜕𝑃
𝜕𝑃
𝜕𝑃
𝜕𝑃
𝛥𝑥 +
𝛥𝑦 +
𝛥𝑧 +
𝛥𝜏 + 𝜈
𝜕𝑥
𝜕𝑦
𝜕𝑧
𝜕𝜏
𝜕𝑃
𝜕𝑦
𝜕𝑃
𝜕𝑧
𝛥𝑥
⎛ ⎞
⎟
𝜕𝑃 ⎜
𝛥𝑦
⎜
⎟
⎟
)⎜
⎜
⎟ + 𝜈.
⎜
𝛥𝑧
𝜕𝜏 ⎜ ⎟
⎟
⎝𝛥𝜏 ⎠
(2.12)
(2.13)
For 𝑚 satellites, the following system of equations can be obtained
𝜕𝑃1
⎛
⎜
𝜕𝑥
⎜
⎜
⎜
𝜕𝑃
𝛥𝑃1
⎜
2
⎜
⎛
⎞
⎜
⎜
⎟
⎜
𝛥𝑃
⎜
⎟
𝜕𝑥
2
⎜
⎜
⎟
⎜
⎟ ⎜
⎜
𝜕𝑃3
𝛥𝑃3 ⎟
=⎜
⎜
⎟
⎜
⎜
⎟
⎜
⎜
⎟
⎜
⎜
⎟
⎜
⋮
𝜕𝑥
⎜
⎟ ⎜
⎜ ⋮
⎝𝛥𝑃𭑚 ⎠ ⎜
⎜
⎜
⎜
⎜ 𝜕𝑃𭑚
⎝ 𝜕𝑥
𝜕𝑃1
𝜕𝑦
𝜕𝑃2
𝜕𝑦
𝜕𝑃3
𝜕𝑦
⋮
𝜕𝑃𭑚
𝜕𝑦
𝜕𝑃1
𝜕𝑧
𝜕𝑃2
𝜕𝑧
𝜕𝑃3
𝜕𝑧
⋮
𝜕𝑃𭑚
𝜕𝑧
𝜕𝑃1
⎞
𝜕𝜏 ⎟
⎟
⎟
𝜕𝑃2 ⎟
⎟
⎟
⎟ ⎛ 𝛥𝑥 ⎞ ⎛ 𝜈1 ⎞
𝜕𝜏 ⎟
⎟⎜
⎜
𝛥𝑦 ⎟
⎜
⎟
⎜ 𝜈2 ⎟
⎟
⎟
⎜
⎟
⎟
𝜕𝑃3 ⎟
+⎜
⎜
⎟
⎟
⎜
⎟
⎜
⎟
⎟
𝛥𝑧 ⎟ ⎜
⋮ ⎟
⎜
⎜
⎟
⎟
𝜕𝜏 ⎟
⎟
𝛥𝜏
𝜈
⎟
⎝ ⎠ ⎝ 𭑚⎠
⋮ ⎟
⎟
⎟
⎟
𝜕𝑃𭑚 ⎟
𝜕𝜏 ⎠
(2.14)
where the index 1, 2, … , 𝑚 denote which values are associated to a specific satellite. The matrices
in the above expression can be written as
𝒃 = 𝑨𝒙 + 𝒗.
10
(2.15)
2.2.5. The least-squares solution
To find a solution for the linearised observation, (2.15) can be rewritten to
𝒗̂ = 𝒃 − 𝑨𝒙 ̂
(2.16)
𝐽(𝒙) ≡ ∑ 𝑣𭑖2 = 𝒗𭑇 𝒗 = (𝒃 − 𝑨𝒙)𭑇 (𝒃 − 𝑨𝒙).
(2.17)
𝒙 ̂ = (𝑨𭑇 𝑨)−1 𝑨𭑇 𝒃.
(2.18)
where 𝒗̂ is the estimated residuals and 𝒙 ̂ is the solution for the linearised observation equation.
To find the 𝒙 ̂ that is the least-squares solution, the function 𝐽(𝒙) needs to be minimised
𭑚
𭑖=1
Assuming that an inverse to 𝑨𭑇 𝑨 exists, the solution 𝒙 ̂ is given by
After this step, a new estimate is given and the iterative process can begin its next iteration.
2.2.6. Range residuals
The range residuals frequently used through out the thesis refers to how much the individual
pseudo-range varies from the estimated solution and these values have the unit of metre.
2.2.7. The covariance matrix
Because of interference and error in the computation of the pseudo-range, the model and the
observations will differ from each other leading to a non-zero 𝒗̂ vector in equation (2.16). If, as
is always the case in real world applications, there is an error in the observations they will map
into the least-squares solution. If the errors are denoted in the least-squares solution by 𝑣𭑥 then
an error from the observations will map into the solution as
𝑣𭑥 = (𝑨𭑇 𝑨)−1 𝑨𭑇 𝒗.
(2.19)
Assuming that there is an expected value for errors in the input data, which in the case of the
gps could be calculated from the almanac or ephermis information, the expected errors in the
spatial coordinates can be computed. The covariance matrix is defined as
with elements given by
𝑪 ≡ 𝐸(𝒗𝒗𭑇 )
𝑪𝒊𝒋 ≡ 𝐸(𝝂𝒊 𝝂𝒋 )
(2.20)
(2.21)
where 𝐸(𝝂𝒊 ) is the expected error for parameter 𝑖. The elements 𝑪𝒊𝒋 are called variances and of
note is that the diagonal elements of the covariance matrix (𝑖 = 𝑗) are equal to the square of the
11
standard deviation 𝜎𭑖 2 of the parameters. The covariance matrix of the least squares solution is
given by
𝜎𭑥2 𝜎𭑥𭑦 𝜎𭑥𭑧 𝜎𭑥𭜏
⎛
⎞
⎜
⎟
⎜
𝜎
𭑦𭑥 𝜎𭑦2 𝜎𭑦𭑧 𝜎𭑦𭜏 ⎟
⎜
⎟
𭑇
−1
2
⎟
𝑪𭑥 = (𝑨 𝑨) = 𝜎 ⎜
(2.22)
⎜
⎟.
⎜
𝜎
𝜎
𝜎
𝜎
2
𭑧𭑦
𭑧𭜏 ⎟
𭑧
⎜ 𭑧𭑥
⎟
⎝𝜎𭜏𭑥 𝜎𭜏𭑦 𝜎𭜏𭑧 𝜎𭜏 2 ⎠
The non-diagonal elements (𝑖 ≠ 𝑗) describe how large the correlation between parameters is.
The sign of the elements indicate if an error in one parameter will give a positive or negative
term to the error in another and the value indicates how large the addition to the error will
be.
2.2.8. Transformation to local coordinates
Most navigational solutions use a local coordinate system for positioning and an example of
such a coordinate system chosen by Blewitt is a Cartesian coordinate system. This system is the
north-east-height over geodid topological system and a small vector in the geocentric system
(denoted as 𝑳) transforms into a local topological system as:
𝛥𝑳 = 𝑮𝛥𝑿
𝛥𝑛
− sin 𝜑 cos 𝜆 − sin 𝜑 sin 𝜆 cos 𝜑
⎛
⎞
⎛
⎞
⎜
⎟
⎜
⎜
⎟
⎜
⎟
𝛥𝑒
cos 𝜆
0 ⎟
=
⎜ ⎟ ⎜ − sin 𝜆
⎟.
cos 𝜑 sin 𝜆 sin 𝜑 ⎠
⎝𝛥ℎ⎠ ⎝ cos 𝜑 cos 𝜆
(2.23)
(2.24)
In the above equations 𝜑 is the latitude and 𝜆 the longitude in the geocentric system. Using the
laws of error propagation the covariance matrix for the local system is given by
and explicitly
𝑪𭐿 = 𝑮𝑪 𭑥 𝑮𭑇
𝜎𭑛 2 𝜎𭑛𭑒 𝜎𭑛ℎ
⎛
⎞
⎜
2 𝜎 ⎟
𝑪𭐿 = 𝜎 2 = ⎜
𭑒ℎ ⎟
⎜ 𝜎𭑒𭑛 𝜎𭑒
⎟.
2
⎝ 𝜎ℎ𭑛 𝜎ℎ𭑒 𝜎ℎ ⎠
(2.25)
(2.26)
2.2.9. Computation of dop values
The results from the transformation made in the previous calculations can be used to define
the dop values. These values are functions of the variances 𝜎𭑛 , 𝜎𭑒 , 𝜎ℎ and 𝜎𭜏 which are all
found in the 𝑪𭐿 matrix except from the 𝜎𭜏 from the geoid covariance matrix. The values are a
measure of the quality of the measurements being made and indicate how favourable the gps
sv constellation is at the moment of measurement. The range of the dop-values are from one
to infinity and the classifications can be found in Table 2.1. The five different dop-values for
the local coordinate system are Geometric Dilution of Precision (gdop), Positional Dilution of
12
Precision (pdop), Horizontal Dilution of Precision (hdop), Vertical Dilution of Precision (vdop)
and Time Dilution of Precision (tdop) are defined as following
GDOP ≡ √𝜎𭑛 2 + 𝜎𭑒 2 + 𝜎ℎ 2 + 𝜎𭜏 2
(2.27)
PDOP ≡ √𝜎𭑛 2 + 𝜎𭑒 2 + 𝜎ℎ 2
HDOP ≡ √𝜎𭑛 2 + 𝜎𭑒 2
VDOP ≡ 𝜎ℎ
TDOP ≡ 𝜎𭜏
(2.28)
(2.29)
.
(2.30)
(2.31)
Table 2.1.: Interpretation of dop-values [17], [18].
dop-value Rating
Description
<1
2–4
4–6
6–8
8 – 20
20 – ∞
Ideal
Excellent
Good
Moderate
Fair
Poor
Considered good enough for navigation.
Could be discarded due to low confidence.
Could be discarded due to low confidence.
2.3. Measurement errors
There are several different aspects of the gps that can cause measurement errors. Typical
sources of errors are the satellite clocks, the receiver clock, the ionosphere, the troposphere,
multipathing, the satellite orbits and the measurement noise [19]. Some of these errors are so
minimal that they generally do not cause a problem outdoors. The error is only of a few metres,
but indoors a small error can cause the user to end up in a completely different room. Table 2.2
later in the section will be giving an overview of the average and maximal error distances of
the different error sources mentioned in this section.
2.3.1. Satellite clock
Due to the calculations of the pseudo-range, as described in section 2.2.1, a very slight offset of
the atomic clock can therefore cause a range error of several hundred metres [19], which has
also been previously stated in the bottom of section 2.2.1.
2.3.2. Receiver clock
The receiver clock normally consists of a quartz oscillator which is very inaccurate compared
to the atomic clocks within the satellites [20]. For example, if the receiver clock has not been
13
readjusted for a week, the offset will be so substantial that the calculated position will be located
in space somewhere further away than the Moon instead of on the Earth [21]. Unless the
receiver clock is constantly corrected the error it causes will increase to infinity.
2.3.3. Ionosphere
The ionosphere is a part of the Earth’s atmosphere and it contains a lot of ionised molecules
and free electrons [22]. These conditions slow down the signals and therefor causes an offset in
the pseudo-range. The offset is smaller if the satellites are located above the receiver as this
reduces the distance the signal waves need to travel through the ionosphere, but as previously
stated in section 2.2.9, satellites clustered closely together causes a weak geometry and a high
dop value which causes insecure measurements. If the satellites are at a wider angle the signals
need to travel further in the ionosphere and the delay is greater, but instead this constellation
gives a better dop value.
2.3.4. Troposphere
The troposphere does not contain any ionised or charged molecules like the ionosphere. Instead
it contains neutral atoms that affect the electromagnetic gps signals. This effect is called
tropospheric delay [23], [24]. Similarly to the ionosphere, the tropospheric delay is smaller if
the satellites are close overhead the receiver and more substantial if they are further away close
to the horizon.
2.3.5. Multipathing
Multipath errors are caused by the gps signals that are reflected of another surface before
reaching the receiver’s antenna. This is a very commonly occurring problem indoors, as the
receiver rarely is in line of sight of all the satellites. In some cases, reflected signals that have
traveled a longer distance, can be discarded by the receiver. Short distance signals, however, are
much more difficult to filter as they interfere with the true signals and causes errors that are
almost impossible to distinguish from other errors such as atmospheric delay. The effects are
not as severe when the antenna is moving as the reflected signals become easier to distinguish
[25].
2.3.6. Satellite orbit
Generally the satellite orbits are very precise, but the gravitation of the Earth and the Moon
may have a slight influence which, on its own could have a big effect on the measurement
accuracy. Fortunately, the orbit data is controlled and corrected in regular intervals. This
information is then sent to the gps receivers as a part of the epidermis data package so that it
can be automatically compensated for [26].
14
2.3.7. Measurement noise
The measurement noise is created by the electronics of the gps receiver. It generally causes a
very low position offset, but it is completely dependent on the quality of the gps. Outdoors the
effect is so small that it does not matter, but indoors it may cause slight problems [27].
Table 2.2.: Average and maximum range error distances measured in metres for the different error
sources [19].
Error source
Average Maximum
Satellite clock
Receiver clock bias
Ionosphere
Troposphere
Multipath
Satellite orbit
Measurement noise
Variable
10 m – 10 000 m
2 m – 30 m
2 m – 20 m
0 m – 10 m
5 m – 20 m
0.1 m – 3 m
300 000 m
Unlimited
150 m
20 m
300 m
30 m
5m
2.3.8. Consequences for the project
The main concern with the measurement errors is that a very slight error can cause a positional error of several meters and there are already other factors that cause issues with indoor
positioning, such as weak signals.
The errors caused by the different attributes stated above will generally be corrected by software
within the gps receivers, but the quality of these corrections vary between receivers.
2.3.9. Error correction
There are, however, several different ways of dealing the error sources listed above. The satellite
clock will be corrected by the systems onboard the satellite [28]. The receiver clock will be
routinely corrected, by comparing it to other more exact systems on Earth, in order to minimise
the errors it causes [27].
The ionosphere and troposphere errors are corrected by statistically estimating the range of the
errors they cause. This is achievable due to the large amounts of atmospheric data that have
been gathered over time [22].
If the receiver is advanced enough and if the different signals are not interfering with each
other, the multipath error can be corrected by having the receiver determine whether or not the
signal has bounced before being picked up by the receiver [25].
15
The error caused by incorrect satellite orbits, as previously disclosed, can be corrected by using
the data sent within the ephemeris data package containing, amongst other things, the position
of the satellite.
The measurement noise can be dealt with, to some extent, by allowing the receiver to perform a
self-diagnostic test, but generally the easiest way is to utilise a better receiver, as these create
less noise [27].
2.4. National Marine Electronics Association (nmea) protocol
nmea is an organisation that sets the standard for communication between marine electronics
and the protocol is called nmea 0183 which is commonly used in all gnss. The gps receiver used
in this study (U-blox 6) utilises messages based on nmea 0183 version 2.30 and the supported
messages for this receiver are shown below in Table 2.3 [29].
Table 2.3.: Description of the nmea messages received from U-blox.
Message Description
gbs
gga
gll
grs
gsa
gst
gsv
rmc
vtg
zda
gnss satellite fault detection
gps fix data
Latitude and longitude, with time of position fix and status
gnss range residuals
gnss dop and active satellites
gnss pseudo-range error statistics
gnss satellites in view
Recommended minimum data
Course over ground and ground speed
Time and date
Messages that are common for all gnss are: gga, ggl, gsa, gsv, rmc, vtg and zda [29].
Messages relevant for this study are:
GGA This message contains information about time and position among other parameters.
Interesting information from this message is number of satellites in use, presented in the range
zero to twelve.
GRS grs provides range residuals in metres of the satellites in use. Theory about range
residuals are described section 2.2.6.
GSA gsa is another message that contains information about the quality of the gps position.
Focus for this study is pdop, hdop and vdop.
16
GST This message contains information about pseudo-range error statistics and important
information this message provide are the rms value of the standard deviation of the pseudo-range,
standard deviation in longitude, latitude and altitude.
GSV gsv provides information about the satellites. Relevant information for this study are
snr in the range 0 dB Hz to 99 dB Hz and satellites in view.
2.4.1. ubx protocol
The nmea standard allows the manufacturer to add their own proprietary specific messages
and the non standard messages from U-blox are called ubx [29]. The ubx protocol provides
data that is presented in binary format which will need further processing in contrast to nmea
messages which outputs the information in text format. All messages will however need further
processing and the ubx messages received in the measurements in this study are shown in
Table 2.4 below.
Table 2.4.: ubx proprietary messages received from U-blox.
Proprietary message Description
ubx,00
ubx,03
ubx,04
Latitude and longitude position data
Satellite status
Time of day and clock information
Relevant information derived from the massages:
ubx,00 : Provides dop values. Interesting information in this case is tdop which can be used to
calculate gdop which is not provided by the U-blox device.
ubx,03 : Provides snr in the range 0 dB Hz to 55 dB Hz, which can be compared with the snr
value from gsv message described earlier.
ubx,04 : Provides information about utc time and date, receiver clock bias and clock drift.
17
3. Method
This section contains an account of how the measurements were conducted, specifications of the
equipment used and a detailed description of how the data was handled.
3.1. Equipment and preparations
For the measurements two computer connected gps-receivers were used for conducting surveys
of the gps availability both outdoors and indoors.
3.1.1. Hardware
The gps-receivers used were the evk-6t: U-blox 6 Evaluation Kit with Precision Timing from
U-blox which are based on the neo-6t gps module. The evk-6t Evaluation Kit is based on the
lea-6t series of gps modules [30], the data sheet for it can be found at the manufacturers website
at www.u-blox.com. Further specification for the antenna can be found in Appendix B. The
evk-6t is designed to be able to produce precise timing pulses for use in applications were
high precision timing is required. However, this feature is not used in the surveys. It should be
noted that the module does not support dgps information [30] and it also does not include any
dead reckoning features. Dead reckoning is the term for a navigational estimate using a former
position fix and information regarding direction, speed and time elapsed since the position fix
was made [31]. To be able to retrieve and store the gps data the receivers were connected to a
computer.
3.1.2. U-center
U-blox own software for logging and evaluating the gps signals is called U-center and it was used
for initialising and logging measurement data. The software is also capable of communicating
with the receiver and in the survey it was used to configure the information sent and later
collected from the device.
18
3. Method
3.2. The building
The building chosen for the measurements is named edit after the four different engineering
programs which are based in the building: Elektro (Electrical Engineering), Data (Computer
Science Engineering) and it (Computer Science). The building is located on Campus Johanneberg
of Chalmers University of Technology in Gothenburg and it is surrounded by a parking lot to
the north-east, buildings of similar height to the north and lower buildings to the west and
south. The sixth floor, shown in Figure 3.1, was chosen partly because it houses the Department
of Signals and Systems (S2) which is responsible for the thesis. It was also chosen because the
building has a mixture of different architectural styles as it is originally a collection of buildings
that have been joined and expanded. As can be seen from the floor plans, the rooms at different
parts of the building have different sizes ranging from small offices to larger lecture rooms.
Important for the results is that the sky was visible from all windows of the building and there
were few higher obstructions in the vicinity of the building.
Office
6103A
Office
6105
Office
6106
Office Office Office Office Office
6108 6109 6110A 6111 6112A
Office
6113
Office Office Office
6115 6116 6117
Office
6465
Office
6466
Office
6467
Server
6470A
Office
6469
Pause-room
6471
E
E
Sem-room
6128
Office Office Office Office Office
6127 6126 6125A 6124A 6122
Office
6120A
Office
6199
Lib/pause
6461A
Storage
6455B
G-room
5217
Office
6472
Office
6455
Office
6474
Office
6475
Office
6453
G-room
5215
Comp-room
6220
G-room
5213
Sto-room
6224
Office
6452
Office
6476
Office
6451A
Office
6478
Office
6479
Office
6449
G-room
5211
Office
6480
Office
6481
Comp-room
6225
G-room
5209
Office
6447
Office
6482
Office
6446
Office
6483
G-room
5207
E
Edu-room
6606
G-room
5202
Edu-Room
6607
Edu-room
6608
Office
6407
Office
6439
E
Office
6438
Office
6408
Office
6409
Office
6410
Edu-room
6233
Office
6436
Office
6435A
Office
6411
Office
6413
Comp-room
6360
Serv-room
6358
Office
6414
Edu-room
6363
Pause-room
6430
Office
6416
Office
6417
Copy
6429
Comp-room
6355
Office
6418
E
Office
6310
Stor
6311
Office Office
6312 6313
Lab
6345
Office
6343
Office
6342
Office
6315
Stor
6317
Office Copy
6318 6319
Library
6320
Office
6323
Office
6325
Meet-room
6331
Office Office
6330 6329
E
Semi-room
6421
Comp-room
6352
Office
6348
G-room
6346
Office
6340
Office
6339
Office
6337
Office
6335
Office
6333
Figure 3.1.: Floorplan showing the sixth floor of the edit building located on Chalmers University
of Technology Campus Johanneberg.
19
3. Method
3.2.1. Linsen
The centre part of the building is called Linsen, the Swedish word for lens, because of its shape.
It is made out of modern materials such as glass and steel, and joins together two sides of the
building which is otherwise built with bricks. In the survey, it was the part of the building most
different from the others considering the used building materials. For reference photos, see
Appendix E.
3.3. Measurement specifications
Measurements were done both indoors and outdoors. The measurement requirements include
specifications for the measurement equipment and the measurement methodology for surveying
both the gps signals and the locations for the measurement points indoors.
3.3.1. Equipment
The measurement equipment consisted of a computer with U-center installed, a U-blox 6 device
with usb connection and a receiver antenna which was laid upon one of two trolleys. Both
trolleys had approximately the same height, 70 centimetres. Figure 3.2 shows the equipment
and one of the trolleys during measurements.
Figure 3.2.: The measuring equipment during measurements of one point.
20
3. Method
For indoor measurements the receiver was sometimes positioned on other objects because the
trolley could not be used in certain spaces, for example, because furniture was in the way. The
accuracy of the positioning of the receiver was in turn at standard height when it is placed on
the trolley but it could deviate a few centimetres on the horizontal plane but also in the vertical
plane if the trolley was not used.
Before starting the measurement process the U-blox 6 measurement equipment was calibrated
and all the right conditions were preset, these can be found in the Appendix D. The same settings
schedule was followed before every start-up of the U-blox 6 program and set as a standard
for the measurements so that the data was recorded uniformly and thus did not differ from
previous measurements. This makes it possible to reproduce the results. The calibration is done
by following the settings schedule in the Appendix D and letting the receiver be outside the
window for 20 minutes. The calibration is done because it updates the almanac information
which in turn gives a quicker lock on the satellites. By calibrating before the measurements, the
measurements will be done in a state of warm start. It means that the almanac and ephemeris
data is stored in the receivers in comparison to a cold start where the receivers have no data at
the start of the measurement.
3.3.2. Marking the measurement points
The equipment used to position the receiver accurately in an indoor environment was a tape
measure with millimetre grading. The acquisition of the positions for the measurement points
was not very accurate and they may therefore deviate a couple of centimetres.
A map of the sixth floor where the measurement points were marked was used in order to
locate the points within that floor. Once a point had been located, it was marked as a reference
for the measurement and used to find the subsequent points.
3.4. Minor indoor campaign
For this campaign, measurements were done both indoors and outdoors. The minor indoor
campaign was conducted in order to find the proper spacing between the measurement points
for the coming major indoor campaign. This was found by analysing the snr from the minor
indoor measurements. The campaign was also done in order to establish a good time span
for the measurements. All of the available nmea and ubx messages were collected during the
measurements.
3.4.1. Outdoor measurements
The outdoor measurements were made with intention to simulate a typical outdoor positioning
scenario so that the collected data could be analysed and then used as a reference or comparison
to the results from the indoor gps positioning. The outdoor measurements were made on two
21
3. Method
unobstructed different positions, Deltaparken and the parking lot at the campus of Chalmers
University of Technology. Each measurement lasted for at least three minutes.
3.4.2. Indoor measurements
The indoor measurements were done inside the edit building, on the fifth floor, at rooms 5209,
5211 and in the corridor next to them which can be seen in Figure 3.3. The spacing between
the measurement points was set to be one and a half metres and every measurement lasted
for a minimum of three minutes. The grid of points with one and a half metre distance is
demarcated by the walls, which means that every grid of equally distant points is independent
from other surrounding spaces bounded by the walls. This is different from the major indoor
campaign where an entire floor of the building is a part of a single coordinate system with an
equal distance set between the points.
Figure 3.3.: This map shows the minor indoor measurement area inside the red box. The measurement points are denoted A, B or C in the rooms for each line along the corridor, where
A is closest to the window and C closest to the wall. The two lines in the corridor are
named cA and cB. Every point along the line is numbered 1, 2, 3 etc. beginning at the
bottom of the map.
3.5. Major indoor campaign
The major indoor campaign was conducted on the sixth floor in the edit-building as previously
stated in section 3.2.
22
3. Method
After reviewing the minor measurement campaign the final measurement resolution was chosen
to be two metres equidistantly between the measurement points since the signal strength did
not vary too much on a one and a half metre distance and a uniform grid and coordinate system
were also used on the whole floor. The measurements of the major campaign were measured in
one row at a time. In this study two receivers were used in parallel for the measurements.
After evaluation of the minor campaign, the time of measurement of the major campaign was
chosen to be at least three minutes and the measurement specifications were the same as the
minor campaign. These specification were the receiver placement, calibration of receiver, the
use of trolleys and tape. Deviations and excluded measurement points were also recorded in a
data log which is attached in Appendix C. Since there were a lot of measurements points, the
measurement campaign was divided into sessions with two individuals measuring per session.
The final number of measurement points became 879 points.
3.6. Description of collected measurements
In the following paragraphs, the definition and computation of different types of measures included
in the survey will be presented.
3.6.1. Availability of the gps
When conducting a survey, it is necessary establish which parameters are to be examined to
be able to quantify the measurement data. In the case of the gps availability there are several
parameters that can be measured, however there is no single definition of what availability
is. For example, in an indoor environment one might get signals from as many satellites as
outdoors but will not be able to get a good positioning fix because of multipathing and other
issues. Then the availability may therefore be defined as how good a positioning fix can be made,
but this is not relevant if one is to use the the gps information for timing purposes or for other
reasons can settle for fewer satellites than needed for a position fix. Therefore, several different
parameters are analysed and presented in this survey and different definitions of availability
will be made.
3.6.2. Measure of positioning error
To give a measure on the quality of the positioning, the computed longitudes and latitudes are
paired together for every location fix. From these values a mean position is calculated using the
mean of the two different values. From this mean position the distances to every location fix is
calculated to metres using a mapping from the wgs-84 system to a local Cartesian coordinate
system. These distances are thereafter averaged to give a scalar value.
23
3. Method
Mathematically the operations is as follows. For position 𝑛 there is a vector with two values
denoted as 𝑥𭑛 . The average is computed as
1
∑ 𝑥 = 𝑚(𝑋).
𝑛 𭑛𭑖
(3.1)
The Euclidean distance from this mean position to every position fix is calculated and averaged
according to
1
∑ ∣𝑥 − 𝑚(𝑋)∣.
(3.2)
𝑛 𭑛𭑖
The above computation gives the absolute deviation of the positioning fix [32]. From the
absolute deviation, one can find the standard deviation for different types of distribution by
multiplying the absolute deviation with a constant value specific for each distribution [32].
3.6.3. Available satellites
The satellites used in the position fix are given by the receiver in the gga nmea sentence as
described in section 2.4. This information is averaged (mean) over the whole measurement time
to give a measure of how many satellites were typically used for positioning in each point of
the grid.
3.6.4. gst computaion
The gts computation gives the total rms of the range residuals. The computation of this value
is not described in the nmea description from the manufacturer. It is also highly dependent on
the amount of satellites used. The implication is that the value does not reflect how good the
quality of the pseudo-range is and gives less information than the grs computations.
3.6.5. snr
The snr of each satellite is provided in the raw data as well as the gsv message and it is likely,
but not confirmed by the manufacturer, to be ordered after rising prn-number. The mean snr
to each satellite is computed for the measurement time and is sorted into different categories.
These categories are presented by themselves to give a meaningful measure of how many
satellites with a certain snr were available. The unit is decibelHertz (dB Hz).
24
3. Method
3.6.6. dop-values
The dop values described in section 2.2.9 are measured. Outdoors they give a measure of the
quality of the satellite constellation and therefor a low dop indicates a good measurement in
accordance to what has been described in section 2.3.3. Indoors however, the dop values give
little information regarding how good the measurement is. This is because they are only based
on the constellation of available sv as retrieved from the almanac/ephermis data and error
sources do not have an effect on these values.
3.6.7. Receiver computed standard deviations
The receiver in it self provides some basic calculations of the signals. Some of these computations
are used in positing, others are merely calculated for the user. Examples of these computations
are the standard deviation of the latitude, longitude and altitude. Standard deviation is a measure
of how spread the probability distribution is around its peak or centre [33].
3.6.8. Additional measures
Aside from the measures used, more information can be given from the computations made
by the receiver. Examples of these are the expected values of latitude, longitude and altitude.
gst is computed after a solution for the least-squares has been found. It can measure how
much the individual pseudo-range differs from the found solution. A large deviation indicates
that something has happened to the signals and can provide a measure of how effected the
measurement point is of multipath issues. This is because signals are reflected before reaching
the receiver travel a longer distance, which will lead to a longer calculated pseudo-range, see
section 2.3.5. As the exact computation of the GST information has not been disclosed by U-blox,
in this study the range residuals are taken from the GSV messages.
25
4. Results
This part presents the results of the work conducted during this project. The results are impartial
and will be evaluated in the discussion. It also contains further information about the code used to
analyse the data, including a flowchart of the program.
4.1. Outdoor campaign
For reference to the measurements conducted indoors, measurements were also made outdoors.
One measurement point was located at Deltaparken on the same altitude as the building, while
the other was located on a parking spot in a shallow valley on the campus of Chalmers University
of Technology. The measured data are provided in Table 4.1 and photographs of measurement
points can be seen in appendix E.
Table 4.1.: Results from the outdoor campaign
Measure
Mean of the range residuals
Mean number of sv
Mean pdop
Mean hdop
Mean vdop
Mean rms of range residuals
Mean standard deviation of latitude
Mean standard deviation of longitude
Mean standard deviation of altitude
Highest mean of snr
26
Deltaparken
Parking
2.3446 m
9.1137
2.0011
0.8815
1.7969
3.8792 m
0.5185 m
0.3521 m
1.0020 m
48.0902 dB Hz
0.9054 m
9.8109
1.8092
0.8136
1.6162
8.7607 m
0.4649 m
0.3030 m
0.8681 m
48.8036 dB Hz
4. Results
4.2. Minor campaign
The results from the minor indoor campaign are illustrated by five histograms. Each histogram
represents the mean snr of each sv. The five histograms were chosen to correspond to a sample
line of measurement points from the windows in to the corridor because it shows how the
snr varies the longer away from the windows the measurement points get. In Figure 4.1a,
Figure 4.1b and Figure 4.1c it can be seen that the snr does not vary much with the spacing
of one and a half metre between the measurement points. The difference is however larger
between Figure 4.1a and Figure 4.1e. This result was important for determining a reasonable
spacing between measurement points for the major indoor campaign. The analysis of the minor
campaign was based on several sample lines like this. An interesting observation for this sample
line is that the number of sv were higher in the measurement points in the corridor compared
to points in the room near the window.
27
4. Results
(a) Mean values for the snr for different sv in point
A1.
(b) Mean values for the snr for different sv in point
B1
(c) Mean values for the snr for different satellites in
point C1.
(d) Mean values for the snr for different sv in point
cA1.
(e) Mean values for the snr for different sv in point
cB1.
Figure 4.1.: Mean values for the snr for different sv for different points in the minor campaign.
The location of each point can be seen on the map in Figure 3.3
28
4. Results
4.3. Major indoor campaign
Results from the major campaign will be presented here accompanied with heat maps of the different
parameters.
4.3.1. Number of satellites used by the receiver
Figure 4.2 shows the mean number of visible satellites used by the receiver. This should not be
confused with the total number of visible satellites which generally is higher, see discussion
section 5.2. The availability of satellites in the building is fairly good with an availability of four
or more satellites in the majority of places on the floor, except places with exceptionally bad
coverage. These exceptions involve areas close to stairwells and elevators which lack windows,
but also at the middle of the building which is built with large glass windows at all sides. For
the suspected reason, see discussion section 5.3. For reference, the number of visible satellites
outdoors is in the range of nine to ten satellites used by the receiver. White points in the figure
are points where measurements have not been done or could not been calculated.
Figure 4.2.: Heat map plot showing the total number of visible satellites used. The range is from 0
to 12 sv. There are generally more than four satellites available throughout the floor.
29
4. Results
4.3.2. Absolute mean of range residuals
The absolute mean of the range residuals is computed and shown in Figure 4.3. One can see that
the grs message is not available for all measurement points. With higher values of the absolute
mean of the range residuals, the individual ranges differ more and more from the computed
solution and therefore also from each other. Of note is that the ranges are compered to the
computed position and not to an absolute position.
Figure 4.3.: Heat map plot showing the mean of range residuals in the range of 0 to 30 metres. This
gives an indication of how large the errors in the pseudo-ranges are from effects such
as multipath or other signal delays.
4.3.3. Snr
The snr of the sv are divided into five categories for each measurement point. The first category,
which includes all satellites with a snr value of 1 dB Hz or higher, one can see that the number
of satellites available satellites are almost the same throughout the whole floor. One can also see
that it at some points differ from the available satellites figure, this is because satellites which
are not in view for the whole measurement time are included as well. This is because of the
algorithm used.
For the second category, satellites with a mean snr value of 11 dB Hz or higher are included.
This figure more closely resembles the figure over the number of available satellites.
In the figure over the third category, which counts the number of satellites with a mean snr of
21 dB Hz or higher, the likelihood of having satellites with higher snr values are higher near
the outer walls than in the corridors.
Looking at the fourth category, this shows the satellites with an snr value of 31 or higher, the
trend described in the third category is strengthened. There is almost no satellites seen in the
corridors with the higher value of the snr.
30
4. Results
Finally, at the highest category showing snr above 41 dB Hz, sv are found only at or near
windows, with the exception of the windows in Linsen.
4.3.4. dop-values
Figure 4.5a, Figure 4.5b and Figure 4.5c contain the mean vdop, hdop and pdop values measured
within the building. They are almost identical, but with some minor variations. This is due to
fact that the calculations of the different dop values are similar which can be seen in section
section 2.2.9. By comparing the results to the means of which the dop-values have been
computed, it is possible to see that the pdop which requires more variables has the worst values.
However, the differences between the hdop and vdop values are almost indistinguishable. The
values in the figures Figure 4.5a to Figure 4.5c have been normalised with a maximum value
of 10 as anything above this is considered to be of to poor quality. This makes it possible to
better distinguish the different values from one another. The dop values are generally within
the “Excellent” range and this is because they are based on the satellite constellation. If one
compares the values to the availability in Figure 4.2 it is possible to see that these correspond to
each other.
4.3.5. Positioning
To get position data with latitude, longitude and altitude, signals from at least four satellites
are needed. As shown in Figure 4.2, the number of satellites are higher than that on most
measurement points.
Figure 4.6 shows the mean standard deviation in longitude, latitude and altitude. The scale is
normalised to eight metres to make it easier to spot changes and that a deviation of more than
eight metres would make the data unsuitable for navigational purposes. The mean standard
deviation for latitude, longitude was mostly below five metres. Near windows the deviation
was below two to three metres in most of the measurement points. For altitude the deviation
was over eight metres over large parts on the floor.
4.4. Time validity of measurements
The measurements were conducted during office hours between the 24th March 2013 to the 8th
May 2013. The satellites visible and during which hours are presented in Figure 4.7. The times
are compensated for the fact that the time for the constellation to reset is not 24 hours which is
compensated by subtracting four minutes in the measurement time stamp for each day from
the start day. From this data it is seen that the measurements were all conducted close eleven to
twelve o’clock.
31
4. Results
32
(a) Heat map plot showing the number of sv with a
snr of 1 dB Hz or higher.
(b) Heat map plot showing the number of sv with a
(c) Heat map plot showing the number of sv with a
(d) Heat map plot showing the number of sv with a
(e) Heat map plot showing the number of sv with a snr of 41 dB Hz or
higher.
Figure 4.4.: Heat map plots showing the number of sv sorted into categories after snr value. It
shows how the snr value decreases further in to the building. The scales of the heat
maps are adjusted to the maximum number of satellites in the category.
4. Results
(a) Heat map plot showing the pdop values. Maximum
is set to 10.
(b) Heat map plot showing the hdop values. Maximum
is set to 10.
(c) Heat map plot showing the vdop values. Maximum is set to 10.
Figure 4.5.: Heat maps showing the dop values. The figures barely differ from each other, but a
slight distinction can be made due to different methods of calculation. Most of the
positions are within the excellent range.
33
4. Results
(a) Standard deviation of longitude measured in
metres.
(b) Standard deviation of latitude measured in metres.
The data is fairly similar to the standard deviation
of longitude with only minor differences.
(c) Standard deviation of altitude measured in metres. The standard
deviation in altitude is higher than in latitude and longitude.
Figure 4.6.: Standard deviation of longitude, latitude and altitude. The scale is normalised to eight
metre to make it easier to spot changes and since a deviation of more than eight metres
would make the data unsuitable for positioning. The standard deviation of the altitude
is much greater than that of the longitude and latitude.
34
4. Results
Figure 4.7.: This plot show which satellites were seen at any measurement point at a certain time.
The scale is normed, and shows the relative occurance of the satellite during a specific
time.
4.4.1. Accounting for the time dependency of the gps
Modelling of the time dependency can be constructed out of two parts. The first part is based
on a spatial part extracted from the measurement data. This part describes which planes are
visible and is combined with data of when the satellites of these planes are in the visible parts
of their orbit. The first part is measured and information regarding the sv-number, azimuth
and elevation is coupled with information about which planes the observed satellites belong to.
The satellites are assumed to be sending their signals with the same signal strength and that
constellation is periodic with the sidereal day. The other part is time dependent and can be
constructed out of the almanac information.
35
4. Results
(a) Time 7-8
(b) Time 11-12
(c) Time 15-16
Figure 4.8.: Figures illustrating the time dependency of the measurements. Here the sv that were
not available at the time specified in the figures were removed. It shows how the sv
constellation changes with time.
36
4. Results
4.5. The code
As described earlier, the data is collected and saved as binary .ubx files. To make this process
manageable a graphical interface was written in Matlab along with functions to extract and
analyse the data and visualise it on heat map plots.
The functions can be divided into four main groups; input/output, analyse, user interface and
utilities.
Input/output As shown in fig. 4.9 the first thing that needs to be done is loading the binary
files, decode the data and sort it into something that can easily be used in Matlab.
The function LoadData and several functions from the GoGPS project1 loads the binary data
and decodes and calculate the different messages in it.
This process takes much time and to make it easier to continue analysing the data the functions SaveVariable and LoadVariable are used to save the decoded data in Matlab’s own
formatted data format (.mat).
Analyse After the information is decoded from the binary files the nmea messages still consists
of string of text messages.
The analyse functions consists of functions that will extract the relevant values from these text
strings and do the relevant calculations to obtain data that can be analysed and presented.
User interface To make data handling easier a custom graphical user interface was written.
This makes it possible to do batch operations on several files at once and provides an easy
and convenient way of visualising one or several measurement points in a heat map style plot.
These heat maps can also be saved as images to make it possible to use them for presentation
purposes within this report.
Utilities Apart from the three groups above there are also several functions that extends
functionality or provides replacement for Matlab’s inbuilt functions.
The code is licensed under GNU General Public License and can be downloaded from http:
//web.student.chalmers.se/~vikahl/.
1
GoGPS is an open source project “designed to improve the positioning accuracy of low-cost (single-frequency) gps
devices by rtk technique and with the aid of a dtm” and can be found at http://www.gogps-project.org/.
37
4. Results
Binary data
Load and
decode measure data
LoadData.m
DecodeUI.m
Sort the NMEA
messages
NMEASorter.m
Analyse data
AnalyseUI.m
Extract the
values from
NMEA messages
One decoder
for each
message type
Calculate the
statistical data
needed for
visualisations
Save or load
variable to disk
MainAnalyser.m
Visualise
the data
PlotUI.m
Output as image
Figure 4.9.: Flowchart representation of how the code works.
38
GoGPS decode
functions
5. Discussion
The discussion will draw conclusions from the achieved results and it will also discuss important
choices made within the Method. It is concluded by presenting how the project may be expanded.
The aim of the study was to map the availability of signals of the whole sixth floor of the edit
building at Chalmers University of Technology. While not every room of the floor was mapped
due to them being inaccessible at the time of measurements, the majority of all points on the
floor were measured. With 879 measurement points indoors and additional test and reference
measurements, the mapping has been quite extensive and should give a good picture of how
the availability is indoors.
At the beginning of the study, different types of software was evaluated but the U-blox own
software was later chosen. The main feature that was used was its ability to the logging of data
and its ability to communicate directly to the receiver.
Working with proprietary equipment and software has its drawbacks, as U-blox has not provided
information regarding the computations of certain values. For the scientific community it therefore should be more appropriate to use software which openly presents how the computations
are made.
For analytical purposes, it would be to an advantage to only log the raw data from the receivers
at a high sampling frequency and then use post processing tools to analyse measurements.
However, to write software which can handle the processes needed for a gps receiver is no
small feat and given the time available, it was never an option. A fully customised software for
logging and processing data would be very favourable to a measurement campaign.
5.1. Minor indoor campaign and measurement methodology
The main objective for the minor indoor campaign was to test measurement procedures and to
give a preview of which results were to be expected from the major campaign. Measurement
planning of the major campaign were to be adjusted to these results. During the campaign it
could be seen that the snr decreased for measurement points further in the building, compared
to points near the window. The changes were not large between two adjacent measurement
points, but a more noticeable difference could be seen between points further away from each
other. It was briefly mentioned in section 4.2 that during the analysis of the minor indoor
campaign it was found that the number of sv were sometimes higher in the corridor compared
to inside a room near the windows. This lead to a hypothesis that in the corridors, signals would
39
5. Discussion
reach the receiver from all directions and not only the ones visible at one side of the building.
This hypothesis was rejected after the results from the major campaign did not validate the
results from the minor campaign.
After the minor measurement campaign had been analysed, the specifications for measurement
resolution, time and methodology in the major campaign were made. As mentioned, the snr
did not vary much with the one and a half metre resolution. Subsequently the resolution of
measurements was set to two metres. As this reduced the number of measurement points, it
also reduced the time required for the measurement campaign. The measurement grid was laid
out as a single uniform coordinate system which made it easier to manage the data as well as
making the visualisations more informative.
Before the start of the campaign, there was an idea about collecting all messages sent from
the sv including the nv at each measuring point. This was found to be unnecessary, as the
information in the almanac is valid for months forward in time. By calibrating the receivers
twenty minutes before each session it could be made certain that the receivers were always
using the latest almanac data. Also, if the time for each individual measurement point had been
twelve minutes the whole floor could not have been measured because of time constraints in
the project. All data is received with one message per second and with a measurement time of
three minutes there was enough data to eliminate disturbances to the measurement.
For the major campaign it was decided that the measurements should be made in rows from
one face of the building to the opposite side resulting in rows of approximately 8 measurement
points. This was because it was deemed more relevant to measure how the availability for a
given constellation changed from one side of the building to the other. The results from the
major campaign should be viewed with this in mind.
5.2. Results of the major indoor campaign
The definition of what constitutes availability of the gps signals is not unambiguous and several
measures were therefore created to quantify the measurements. The availability in terms of the
number of available sv, snr, dop-values and quality of positioning were factors chosen to be
investigated as these were factors which could be quantified and evaluated against reference
measurements.
The number of visible sv used by the receiver were analysed by calculating a mean of these
value from each message. The total number of satellites in view is generally higher than the
satellite in use since a good fixation and other criteria are needed for the receiver in order to use
the specific satellite. The number of satellites used will also vary throughout the measurement
because of fluctuations and fixation variations of the satellite, this is, however, compensated by
calculating a mean of all samples.
The number of visible sv were categorised into five categories after their snr. This categorisation
is useful because it shows how the signals are attenuated in different parts of the building.
40
5. Discussion
Another observation is that even though the number of visible sv is as high as outdoors in most
points, the snr-values are less favourable indoors.
The figures in section 4.3.4 shows that the dop-values are mostly of excellent quality. As
dop-values are generally used as a measure on how good the position data is outdoors it is
easy to believe that it could also be applied to the dop-values indoors. As previously stated in
section 2.2.9, the dop-values are based on the position and number of the satellites. As shown
earlier, satellite availability is not a problem indoors as the signals generally reach the receiver.
This will result in a good dop-value even though the signals are heavily affected by factors such
as multipath attenuation. A low dop-value should therefore not be used as a quality measure
for indoor use. However, a high dop-value could be an indicator of bad positioning.
For the positioning data, the absolute deviation was chosen because of its independency of
which statistical distribution the measurement has. From Figure 4.6 it can be seen that the mean
standard deviation for latitude and longitude was below five metres for most of the measured
points. It is important to note that the values are adjusted with a maximum of eight metres
since everything above that was deemed equally bad for navigation purposes. Values up to
12 000 metres occurred, and even though they only occurred once or twice they would have a
drastic effect on the capability of indoor navigation. The standard deviation of the altitude was
generally above eight metres and is partly due to the lower exactitude of height measurements
in the gps system. These high deviation of altitude would also have a large impact on the
capabilities of positioning indoors, since it would be hard to distinguish on which floor the
receiver is located.
The mean standard deviation for the same parameters had smaller deviation near windows
which was probably due to direct line-of-sight of the sv, which meant affect of multipath was
minimal. The snr was also higher in these points, probably due to the same reason.
The absolute mean of the range residuals are of interest because they give a measure of how
much the pseudo-ranges vary from each other. If the variations are large it indicates that there
are large errors in the pseudo-ranges and these errors will make the positioning more uncertain.
The absolute mean of the range residuals are the parameter which shows how affected a location
in the building is from multipath issues and it is seen clearly in the results that some parts of
the building are heavily effected by errors.
The satellites which can be seen from different parts of the building will not be the same and
the time window when they can be seen will vary. For example, a window frame, will work as a
boundary for the signals effectively creating an elevation and azimuth mask reducing the time
that a sv is visible at that point. Besides the window frame, other objects in the room might
also mask and result in no line-of-sight for specific times.
The time dependency of the gps have been lowered after the addition of an extra satellite in
three planes in 2011. This has reduced the spacings between satellites and resulted in more
satellites being visible at the same time. The result is that even if the availability will be time
dependent, the fluctuations will be smaller than for a system with fever satellites.
41
5. Discussion
Even though measurements have not been conducted during the night, the availability should
not differ much from the measured values. There is, however, no confirming data for this in the
thesis. The combination of different gnss in the future could further decrease the fluctuations
in the time dependency in availability since the number of sv would be increased and their
spacing would probably be reduced.
A solution to the time dependency problem is to do a full 24 hour measurement, since it will
result in data from all sv constellations and thus minimising the time dependancy of the result.
Even without such measurements the data can be extrapolated for a 24-hour period with the
help of information about the sv constellation, as provided in the almanac/ephemeris messages
as well as on online services.
5.3. Future work
There are several parts from the work in this thesis that could be expanded in future research.
How radio signals propagate through different materials is a well studied field and a lot of
research has been done. It would be of interest to combine the measurements done in this thesis
with structural data about the building to see how the materials affect the signal. For example,
it was obvious that the reception was lower in Linsen and it was believed to be due to the large
glass windows.
The measurements in the thesis were done with one type of receiver and it would be of interest
to do further measurements with receivers from different product segments and with different
antennas. For example the gps receivers within mobile phones have smaller antennas which
means that they might not detect as many sv and also will get lower snr on the received
signals.
Furthermore, measurements could be done with receivers for different gnss, such as Galileo or
glonass, in order to see if the position could be determined better with these systems. There are
also receivers that combine signals from these different gnss in order to provide better position
data when more satellites are available.
All measurements where made during office hours due to restrictions in access to the rooms. It
would be if interest to do measurements at all times of the day in order to provide measurement
data with less time dependency and to get measurements with all sv constellation statuses. It
would also be of interest to do longer measurements to provide more data of how the availability
changes with the sv constellation.
5.3.1. Applications of the results
The gps by itself might not be sufficient to support ins, but the signals are sufficiently useful to
be used with a complementary technology. The gps sv could for example be used to update an
ins based on dead reckoning.
42
5. Discussion
There are several ways to improve the accuracy of positioning of the gps by combining different
techniques such as dgps or by using additional gnss. Future gps-assisted ins will probably use
several of these different techniques.
43
6. Conclusion
This part presents the conclusions drawn from the thesis.
The purpose of this project has been to measure, document and visualise the gps availability
within an indoor environment. The large number of measurements achieves a higher statistical
validity as the amount of random errors is reduced.
The average number of satellites available indoors was almost as many as could be expected to
be found outdoors. However, the signals from most of these satellites were effected by aspects
such as multipath and attenuation. This is reflected in that the snr decreases for locations
further into the building.
The dop-values, which are considered a good benchmark for confirming the quality of a position
outdoors, was found to be of less importance in an indoor environment because of the way that
they are normally computed today.
Due to these results, it is possible to conclude that the gps alone is not suitable for indoor
navigation. However, as there are signals available indoors these could possibly be used to
assist an ins and further investigation in this direction is warranted.
44
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47
A. Available data
In this appendix, all measurement data that were recorded are presented
Data
Unit
Source
Expected error in latitude
Expected error in longitude
Expected error in altitude
Latitude
Longitude
N/S Indicator
E/W indicator
Satellites used
hdop
msl altitude
Geoid separation
utc time
Data validity
m
m
m
Degrees + minutes
Degrees + minutes
N = north or S = south
E = east or W = west
Range 0 to 12
unitless
m
m
hh mm ss.ss
V/A
nmea gbs
nmea gbs
nmea gbs
nmea gga / gll
nmea gga / gll
nmea gga / gll
nmea gga / gll
nmea gga
nmea gga
nmea gga
nmea gga
gll / gga / gbs
nmea gll
Range residuals for sv used in
navigation
pdop
hdop
vdop
rms value of the standard deviation of the ranges
Standard deviation of latitude
Standard deviation of longitude
Standard deviation of altitude
Satellites in view
Elevation
Azimuth
C/N0
m
nmea grs
unitless
unitless
unitless
m
nmea gsa
nmea gsa
nmea gsa
nmea gst
m
m
m
unitless
0° – 90°
0° – 359°
0 dB Hz – 99 dB Hz
nmea gst
nmea gst
nmea gst
nmea gsv
nmea gsv
nmea gsv
nmea gsv
Speed over ground
Course over ground
Date
knot/s
°
ddmmyy
nmea rmc
nmea rmc
nmea rmc
Comments
Current time
V = Data invalid/receiver warning, A
= Data valid
Null when
tracking
49
not
A. Available data
Speed over ground
Speed over ground
utc
utc
utc
utc
pseudo-range
knot/s
km/h
s
day range 01-31
month range 01-12
4 digit year
m
nmea vtg
nmea vtg
nmea zda
nmea zda
nmea zda
nmea zda
Raw data
gps time
gps week
Doppler
Phase
snr
Ephemeris
s
week
Hz
cycles
dB Hz
N/A
Raw data
Raw data
Raw data
Raw data
Raw data
Raw data
50
Update frequency
1 Hz
B. The antenna
The data in this section was taken from the ann product summary [34]. The type of antenna
used in the measurements was the ann-ms high performance active gps antenna. The antenna
incorporates an integrated low-noise amplifier. The characteristics of the antenna can be seen
in the table below.
Table B.1.: Antenna characteristics, taken from product summary
Frequency
(1 575 ± 3) MHz
vswr
Max. 2
Bandwidth
Min. 10 MHz
Impedance
50 Ω
Peak gain
Min. 4 dBiC
Gain coverage ≥ 4 dBiC
Polarisation
rhcp
The characteristics of the integrated amplifier is shown in the table below.
Table B.2.: Amplifier characteristics, taken from product summary
Gain without cable Typical 27 dB
Noise figure
Maximum 1.8 dB
Output vwsr
Maximum 2.0
51
C. Data log
This appendix describes all anomalies in the measured points and is therefore only relevant in
combination with the measured data.
52
Measurement point
Description
3305–3308
1902
1403–1408
1003
1503
0302–0303
6309
0905
1005
0906
1006
0101–0131
0406–0407
0713
0716
2533
0720
0721
0723
0623
0523
0224
0427
1030
2333
2336
0628
0331
0431
2036, 2136
2135
2132
10 cm to 20 cm off their location due to a wall.
Last two seconds measured at new point.
Height difference, measured on a chair.
Behind raffle.
Approximately 18 cm to 20 cm off due obstacle, painting
37 cm off due obstacle, locker
225 cm difference in height
Open door
Closed sun blinds
Closed sun blinds
Open elevator doors
Curtains
Curtains
Closed curtains by the wall
On sofa
Covers in the room
Excluded due closet
Movement after 3 cm
Excluded due to obstacle
People walked into the trolley
Antenna switch.
On chair.
Measured on bicycle.
10 cm off.
Against wall not by window.
Bookshelf 40 cm difference in height.
10 cm off in height, bookshelf.
C. Data log
4008
3603
4202
4109
4033
4035
4031
3332
3330
3131
3230
2930
2735
Covers in the room, master thesis room.
Covers in the room, master thesis room.
Open elevator door.
On ping pong board.
On sofa.
Few cm off.
Few cm off.
40 cm off.
Curtains.
Few cm off.
Curtains.
Curtains.
Few cm off.
53
D. Checklist for measurements
D.1. Pre measurement preparation of software (U-blox)
1. Enable nmea messages (Under message view)
2. Enable ubx messages (Under message view)
3. Close message view window (Important to save the settings and to get gst)
4. Check that nmea messages (Especially gst) and U-blox messages are received under “text
console”.
5. Baud rate 9 600 (default setting)
6. Enable U-blox 6, under receiver -> Generation (default setting)
7. Calibrate the receiver at least 20 min outside of window to lock in satellites
8. If the computer goes in “sleep mode” it is important to check the settings again!
D.2. During measurements
• Use walls as references. Look at where the wall ends on the windows.
• Measure one row at a time.
• Two metres between measurement points
• Take notes if something differs in the measurements
• Measure three minutes per point
54
Figure E.1.: A Google Maps photo of the edit building at Chalmers University of Technology. The
coordinates for the building are 57.687924N, 11.978766E. [35]
E.1. Outdoor campaign
Figure E.2.: Photograph of the first outdoor reference point. In the background is the edit building.
55
Figure E.3.: Photograph of the first outdoor reference point. View towards the south.
Figure E.4.: Photograph of the first outdoor reference point. View towards the east
Figure E.5.: Photograph of the second outdoor reference point. The building with the antennas on
the roof is the edit building.
56
Figure E.6.: Photograph of the second outdoor reference point. View towards the south
E.2. edit
Figure E.7.: Photograph of the Linsen building. Here it is seen how the different buildings are joined.
E.3. Major measurement campaign
Figure E.8.: Photograph illustrating a measurement in an office at the the Department of Computer
Science and Engineering.
57
Figure E.9.: Photograph of a computer lab in Linsen.
58
F. Swedish summary
Below is a Swedish summary of the thesis, which is a requirement of the Engineering Physics
program.
F.1. Inledning
Det har alltid funnits ett intresse och behov av precisa och stabila navigationssystem som
fungerar över stora områden. När radiotekniken blev vanlig började positionsbestämning
ske med triangulering av radiosignaler. För att få bättre täckning över hela världen flyttades
sändarna till satelliter, i ett globalt satellitnavigeringssystem, Global Navigation Satellite System
(gnss).
Navigation Satellite Time and Ranging Global Positioning System (navstar gps), eller Global
Positioning System (gps) som det vanligtvis benämns, är ett sådant gnss som har skapats för att
användas primärt utomhus, och fungerar bra till just detta. Det uppstår dock problem när man
försöker använda detta för positionsbestämning inomhus, då den korta våglängden och låga
effekten på radiosignalerna medför att de propagerar dåligt inomhus.
Ett navigationssystem för inomhusbruk, ett Indoor Navigational System (ins), kan konstrueras
på olika sätt och det finns flera olika, konkurrerande, tekniker i användning. Dessa kräver dock
utbyggd infrastruktur och det är därför önskvärt i att någon omfattning använda gps, eventuellt
i kombination med andra tekniker.
En kartläggning för tillgängligheten av gps-signaler inomhus är därför av intresse för att klargöra
till vilken del gps kan användas och i vilken del andra tekniker måste tas till.
F.1.1. Syfte
Syftet med det här arbetet är att kartlägga och dokumentera tillgängligheten av gps-signaler i en
typisk inomhusmiljö. Mätningar ska genomföras på ett våningsplan i edit-huset på Chalmers
tekniska högskola.
Mätdata ska innehålla information om tillgängligheten i signal-brusförhållande, Signal-to-noise
ratio (snr), antalet satelliter, Dilution of Precision (dop) och positionsbestämningens kvalité.
Utomhusmätningar ska genomföras för att studera hur gps beter sig vid god tillgänglighet och
som att användas som referensmätningar.
59
F. Swedish summary
Slutgiltigt ska ett ramverk tas fram i Matlab för att bedöma och visualisera tillgängligheten
inomhus.
F.2. Metod
Metod delen innefattar hur mätningarna gjordes, specifikationer för mätningarna och hur
datainsamlingen hanterades.
F.2.1. Hårdvara
Mätningarna gjordes med två gps mottagare kopplade till var sin dator. gps mottagarna som
användes var evk-6t: U-blox Evaluation Kit with Precision and Timing från U-blox. Den är
baserad på neo-6t modulen. U-center är U-blox egna mjukvara för att logga och utvärdera data.
Programmet kom till användning för att logga data från alla mätningarna och för uppstart av
själva mätprocessen. Den användes också för att bestämma vilken information som ska skickas
och tas emot av gps-mottagaren.
F.2.2. Plats för mätningar
Mätningarna gjordes vid Chalmers tekniska högskola i edit-huset, där mätningar gjordes över
hela våning sex. Våningen valdes för att det var lättare att få åtkomst till kontoren eftersom
avdelningen för Signaler och System, som är ansvariga för arbetet, har sina kontor där.
F.2.3. Mätningsspecifikationer
gps mottagare kopplades till en dator och placerades på en vagn innan mätningarna utfördes.
Båda vagnarna som användes hade en höjd på cirka 70 cm och användes för att mätningarna
skulle genomföras under samma förutsättningar. Innan varje mätning så kalibreras U-blox 6 och
speciella inställningar hos mottagaren ställs in. Samma rutin för inställning följdes inför varje
mätningstillfälle för att få samma typ av data och för att kunna reproducera dem i efterhand.
För att kunna göra korrekta mätningar i edit-huset så sattes mätpunkterna ut på en karta över
våningen som mätningarna skulle göras på. Detta användes som en referens för att kunna hitta
mätpunkternas position i huset. När en referenspunkt hittades så användes ett måttband för att
mäta ut resterande mätpunkter vid varje mättillfälle.
60
F. Swedish summary
F.2.4. Test- och referensmätningar
Testmätningar gjordes både utomhus och inomhus för att kunna bestämma ett bra avstånd
mellan mätpunkterna och för att kunna bestämma en lämplig mättid för varje mätpunkt. Detta
bestämdes genom att analysera signalstyrkan från testmätningarna. Dessa resultat användes
till mätkampanjen.
F.2.5. Mätkampanjen
För mätkampanjen utformades ett rutnät över våning 6 i edit-huset med två meters avstånd
mellan alla mätpunkter. Mätningstiden sattes till tre minuter för varje mätpunkt.
F.2.6. Hantering av mätdata
För att kunna utföra mätningarna så valdes vilka parametrar som ska undersökas. I detta fallet
så fanns det olika parametrar som kunde undersökas men det finns ingen enskild definition på
tillgänglighet eftersom gps-signaler kan användas till olika syften, och parametrarna får på så
sätt annorlunda innebörd utifrån dessa. Därför kommer olika parametrar att väljas och sättas i
relation till olika beskrivningar på tillgänglighet.
Mätdata hanterades med hjälp av ett specialdesignat program som utvecklades i Matlab och för
att enkelt ha möjligheten att presentera samtliga resultat så visualiserades de med hjälp av så
kallade “heat maps”. Ett exempel på en sådan kan ses nedan och den beskriver satellittillgängligheten på sjätte våningen i edit huset.
Figure F.1.: Heat map som visar antalet tillgängliga satelliter på sjätte våningen i edit huset.
Intervallet är mellan 0 till 12.
61
F. Swedish summary
F.3. Sammandrag av resultat
För att kunna sätta mätningarna gjorda inomhus i perspektiv, utfördes mätningar utomhus.
Dessa mätningar gjordes på två ställen, en på samma höjd som byggnaden och en på en
parkeringsplats. Resultatet från dessa referensmätningar var att medelvärdet på avstånds
residualerna var runt 2,3 meter för platsen på samma höjd som edit huset men med byggnader
och annat som blockerade vissa delar av himmeln. Även andra parametrar mättes under
mätkampanjen utomhus. En mindre mätkampanj genomfördes inomhus för att testa olika
mätprocedurer som skulle ingå i den större mätkampanjen. Resultatet från denna kampanj
var att en mättid på 3 min skulle medföra tillräckligt med data, och att mätningarna skulle få
en robusthet gentemot yttre störkällor. Ett annat resultat var att ett ekvidistant avstånd på 2
meter skulle användas. Slutligen gjordes även en större mätkampanj där tillgängligheten för i
stort sett hela våningsplanet kartlades. Resultatet var att inomhus miljön är mycket drabbad
av felkällor så som reflektion och dämpning. Ett oväntat resultat var att antalet tillgängliga
satelliter i stort sett är lika många inomhus som utomhus, med skillnaden att signalerna är
mycket dämpade och innehåller stora fel. Det visade sig även att det kvalitetsvärde som används
för att uppskatta en mätnings tillförlitlighet inte säger något om kvalitén inomhus. Ursprunget
till detta var att det specifika kvalitetsvärdet inte tog hänsyn till mätfel, utan endast vilka
satelliter som syntes och deras konstellation. Ett annat resultat är att positionerna inomhus med
en traditionell gps mottagare inte är möjligt vilket ses tydligt i resultatet för arbetet. Slutligen
formulerades en struktur för hur tillgänglighetens tidsberoende kan modelleras för en godtycklig
inomhusmiljö.
F.4. Diskussion
Här diskuteras de resultat som erhölls efter mätningarna, val av mätmetodologi, den använda
utrustning och dess begränsningar, vad studien kan användas till samt vad som är intressant att
undersöka ytterligare. Det diskuteras även vad som kan förbättras till framtida undersökningar
och vilka lärdomar som erhållits under arbetets gång. En del av diskussionen ägnas åt att
diskutera olika lösningar för navigationslösningar inomhus, både under tillämpningar av resultat
och under ett eget stycke.
De mest intressanta resultaten som har uppnåtts under projekted är värdena för satellittillgängligheten, dop-värdena och avstånds residualerna. Den goda satellittillgängligheten var intressant eftersom den förväntades vara nära obefintlig, men det visade sig att de flesta signaler når
mottagaren, trotts att de försvagas och påverkas av flervägsfel. Detta ledde till nästa intressanta
resultat, vilket var hur dop-värdena ser ut inomhus. Som nämns så är dessa värden oftast ett
bra mått på hur tillförlitliga de beräknade positionsvärdena är och enligt resultaten som kan ses
i rapporten, så är dop-värdena oftast av utmärkt kvalitet. För en inomhusmiljö är dock dessa
värden endast missvisande och det kan påvisas av resultaten för avstånds residualerna. Dessa
varierar kraftigt mellan allt från fem till över 30 meter.
62
F. Swedish summary
F.5. Slutsats
Slutsatsen som dras är att gps signaler från flertalet satelliter är tillgängliga på de flesta platser på
våningsplanet, men att en positionerna med tillräckligt hög noggrannhet ej är möjlig inomhus
med mottagare byggda för utomhusbruk. Signalstyrkan relativt brus hos signalerna var som
störst nära yttre väggar, och speciellt nära fönster. Slutligen är tillgängligheten på gps väldigt
beroende av hur omgivningen ser ut. Det finns många satellitsignaler tillgängliga och om alla
dessa var användbara, ökar möjligheterna för att bygga en gps baserad navigationslösning för
inomhusbruk.
63

Survey of the Indoor Availability of the GPS

Transcription

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