IN
DEGREE PROJECT CIVIL ENGINEERING AND URBAN MANAGEMENT,
SECOND CYCLE, 30 CREDITS STOCKHOLM SWEDEN 2021,
Analysis of Positional Precision when Using Ground Control Points with Supported INS in GNSS-Free Environments
LINUS BÄCKSTRÖM PATRIK GRENERT
KTH ROYAL INSTITUTE OF TECHNOLOGY
SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT
Acknowledgements
Milan Horemuz, KTH Division of Geoinformatics, supervisor. For helping us when we got stuck, always being available to meet and for reading our drafts and giving feedback.
Peter Östrand, WSP, supervisor. For giving us concrete ideas of what to research, being open to meet when we needed it and explaining WSPs mobile mapping process for us.
Johan Vium Andersson, WSP, supervisor. For explaining the more technical aspects of the geodetic applications and requirements that are important for our work.
Martin Brandin, WSP. For helping us with the used data as well as for explaining how to use the softwares that were utilized throughout the thesis.
WSP. For offering us the possibility to work on this topic as well as for supplying us with the required data.
Title
Authors Department TRITA number Supervisors Keywords
Analysis of Positional Precision when Using Ground Control Points with Supported INS in GNSS-Free Environments
Linus Bäckström and Patrik Grenert Real Estate and Construction Management TRITA-ABE-MBT-21377
Milan Horemuz, Johan Vium Andersson and Peter Östrand Track maintenance, GNSS, INS, GCP, GNSS-free environments, Railway positioning
Abstract
Railway traffic is one of the most used transportation methods in today's society both for freight transports and transportation of people. A necessity for this to function is that the tracks upon which the trains travel are functional. This includes both that the tracks have been constructed correctly and that the tracks have not experienced wear and tear to the level that their functionality is in jeopardy.
This requires that the tracks are thoroughly maintained and thus a continuous knowledge about the state of the tracks is required.
One way to obtain knowledge about the current track geometry is to measure the tracks using laser scanners to establish the tracks geographical position. This in turn leads to the possibility to notice changes in the tracks. These laser scanners can be mounted on trains or modified vehicles where they scan the tracks while the vehicle is moving along the tracks. However, the scanned points also have to be precisely located in a coordinate system so that they can be compared to the scanned geometry of the initial tracks. The precise locations can be acquired by using Global Navigation Satellite Systems (GNSS) along with Inertial Measurement Systems (INS) and odometers, which are then used as input in a Kalman filter. The GNSS and INS complement each other in a good way since INS have very high positional accuracy and a large temporal error while GNSS has an acceptable positional accuracy and no temporal error. In locations where there is sufficient GNSS availability, this method reaches positional accuracies around the low cm level.
The aforementioned method does however struggle when there is subpar GNSS availability, for example in tunnels or in dense forests. This necessitates the use of additional data, and in this work the use of ground control points (GCP) have been examined. The GCPs have been implemented in simulated GNSS-free areas where a temporal distance of 2, 5, 10, 20 and 40 seconds between GCPs has been used.
Based on these experiments, an estimated positional accuracy from 0.5 cm to 30 cm in GNSS-free environments has been acquired depending on the distance between points. The authors recommend an implementation of GCPs in a tightly coupled approach every 5-10 seconds to achieve a reliable positional precision on the mm-cm level.
The disadvantages of GCPs are quite large since they have to be established and maintained, which costs a fair amount of money and time. It is therefore of utmost importance to minimize the need for GCPs.
This can be accomplished either by using alternative solutions such as implementations of track alignment in the Kalman filter, but also by increasing the efficiency of the GCPs. The way that this thesis recommends this to be researched is to use the same GCPs multiple times by either using more advanced sensors for locating the GCPs or by increasing the number of sensors as well as spreading them out across the vehicle.
Titel Undersökning av positionsprecision vid utnyttjande av kända punkter tillsammans med INS i områden utan GNSS
Författare Linus Bäckström och Patrik Grenert Institution Fastigheter och Byggande
TRITA nummer Handledare
TRITA-ABE-MBT-21377
Milan Horemuz, Johan Vium Andersson och Peter Östrand Nyckelord Rälsunderhåll, GNSS, INS, Kända punkter, Avsaknad av GNSS,
Positionering på räls Sammanfattning
Tågtrafik är ett av de mest använda transportsätten idag vare sig det gäller godstransporter eller persontransporter. En nödvändighet för att detta ska fungera är att rälsen som tågen färdas på är funktionella. Detta inkluderar att rälsen är korrekt konstruerad, men även att rälsen inte har blivit skadade av bland annat kontinuerlig användning. Därmed behöver rälsen underhållas, och för att kunna göra det krävs kunskap om i vilket skick rälsen är.
Ett sätt att införskaffa kunskap om rälsens skick är att mäta rälsen med hjälp av laserskanners. Dessa laserskanners kan monteras på tåg eller rälsanpassade fordon så att de kan mäta in rälsen samtidigt som fordonet färdas längs med rälsen. De inmätta punkterna måste emellertid även vara kända i ett koordinatsystem så att de kan jämföras med punkterna som mättes in när rälsen initialt skannades. Den precisa platsinformationen som krävs för detta kan införskaffas genom att använda Global Navigation Satellite Systems (GNSS) samt Inertial Measurement Systems (INS) och odometer, som sedan används som input i ett Kalmanfilter. GNSS och INS kompletterar varandra på ett bra vis eftersom INS har en väldigt hög platsnoggrannhet samt ett högt tidsberoende fel medan GNSS har relativt hög platsnoggrannhet och inget tidsberoende fel. Denna metod kan därmed nå noggrannheter runt cm- nivån när det är bra GNSS-förutsättningar.
Metoden som beskrevs ovan fungerar emellertid inte bra när det är dåliga GNSS-förutsättningar, till exempel i tunnlar eller i täta skogar. Då behövs det annan data, och i detta arbete har användningen av kända punkter analyserats. De kända punkterna har implementerats under en sträcka med simulerad avsaknad av GNSS där ett tidsbaserat avstånd på 2, 5, 10, 20 och 40 sekunder mellan kända punkter har använts. Baserat på dessa experiment har en precision på 0,5 cm till 30 cm uppnåtts beroende på avståndet mellan de kända punkterna. Författarna rekommenderar att kända punkter ska implementeras i en tightly coupled beräkningsmetod var 5-10 sekund för att nå en noggrannhet på mm- cm nivå.
Nackdelarna med kända punkter är däremot flertaliga eftersom de måste etableras och underhållas, vilket kräver både tid och pengar. Det är därför viktigt att minimera behovet av kända punkter. Det kan åstadkommas genom att till exempel implementera rälsdata i Kalmanfiltret, men även genom att öka effektiviteten i användandet av de kända punkterna. I det här arbetet rekommenderas det att undersöka hur det går att använda samma kända punkt flertalet gånger. Detta genom att antingen använda mer avancerade sensorer för att lokalisera de kända punkterna eller genom att öka antalet sensorer samt att sprida ut dem över fordonet.
Terms and Abbreviations
DR = Dead Reckoning. A process of calculating the current position of a vehicle by using previous known positions.
GCP = Ground Control Point. Point that has been established and measured so that its coordinates in a certain coordinate system is known.
GNSS = Global Navigation Satellite Systems. An umbrella term used for satellite-based position and navigation systems such as GPS, GLONASS, Galileo and Beidou.
INS = Inertial Navigation System. A system that uses a computer, accelerometers and gyroscopes to calculate acceleration, velocity and orientation of its host vehicle.
IMU = Inertial Measurement Unit. A unit consisting of accelerometers and gyroscopes that measures the host vehicle's acceleration, velocity and orientation.
LC = Loose Coupling/Loosely Coupled. A decentralized integration method where the individual systems are individually computed and then combined.
MLSS = Mobile Laser Scanning System. A laser scanning system mounted on a moving vehicle.
MMS = Mobile Mapping System. A combination of navigation tools and remote sensing tools used to collect and georeference data.
TC = Tight Coupling/Tightly Coupled. A centralized integration method where the individual systems raw data are computed with each other in a filter.
WS = Week Seconds. A week measured in seconds, goes from 0-604800 seconds.
WSP= Williams Sale Partnership Limited. A global consulting company within engineering and infrastructure.
ZUPT= Zero Velocity Update. A method consisting of having zero velocity to eliminate errors in INS drift.
Table of Contents
Acknowledgements ... 1
Abstract ... 2
Sammanfattning ... 3
Terms and Abbreviations ... 4
1 Introduction ... 10
1.1 Background ... 10
1.2 Objectives ... 11
1.3 Limitations ... 11
2 Literature Study ... 12
2.1 Inertial Navigation ... 12
2.2 Supported INS ... 12
2.3 Acquisition of GCPs ... 14
2.4 Train Positioning ... 15
2.4.1 GNSS-free environments ... 16
2.4.2 Environments with GNSS ... 17
2.5 Track Monitoring ... 17
3 Study Areas and Data Description ... 18
3.1 INS Specifications ... 18
3.2 GCP Specifications ... 19
3.3 File formats ... 19
3.3.1 .GTT ... 19
3.3.2 .PVA ... 19
3.4 Lidingöbanan ...20
3.5 Nockebybanan ...20
3.6 Roslagsbanan ...20
3.7 Saltsjöbanan ...20
4 Methodology ... 21
4.1 Inertial Explorer ... 21
4.2 Mobile Mapping Toolbox ... 21
4.3 Data Collection ... 21
4.4 Preparations ... 22
4.5 Computations ... 23
4.5.1 Loosely Coupled ... 23
4.5.2 Tightly Coupled ... 23
4.5.3 Applying GCP ... 23
5 Results ... 25
5.1 Lidingöbanan ... 25
5.1.1 Comparison Between LC and TC ... 26
5.1.2 Simulated GCPs for Lidingöbanan ... 29
5.2 Nockebybanan ... 31
5.3 Roslagsbanan ... 35
5.3.1 Simulated GCPs for Roslagsbanan ... 36
5.3.2 Measured GCPs for Roslagsbanan ... 39
5.4 Saltsjöbanan ... 41
5.4.1 Simulated GCPs for Saltsjöbanan... 42
6 Discussion ... 45
6.1 Errors from GNSS ... 45
6.2 Errors from INS ... 46
6.3 Problematic areas regarding GNSS/INS integration ... 46
6.4 Spacing of GCP ... 47
6.5 Diminishing returns on increased accuracy ... 48
6.6 Increased efficiency in the use of GCP ... 49
7 Conclusions ... 50
8 Future Work ... 51
References ... 52
Table of Figures
Figure 1 Example of a LC supported INS (Gianluca, Marco and Gianluca 2017) ...14
Figure 2 Example of a TC supported INS (Gianluca, Marco and Gianluca 2017) ...14
Figure 3 Visual representation of camera GCP acquisition. (Chu and Chiang 2016) ...15
Figure 4 GCP target established along Roslagsbanan (WSP 2020) ...19
Figure 5 MLSS mounted on small vehicle used by WSP to scan tracks (WSP 2020) ...21
Figure 6 MLSS mounted on a train used by WSP to scan tracks (WSP 2020) ...22
Figure 7 Estimated precision for Lidingöbanan LC ...25
Figure 8 Estimated precision for Lidingöbanan TC ...25
Figure 9 Difference in estimated elevation between LC and TC computations of Lidingöbanan during week seconds 259350-259450 ...26
Figure 10 Difference in estimated longitude and latitude between LC and TC computations of Lidingöbanan during week seconds 259350-259450 ...26
Figure 11 Difference in estimated elevation between LC and TC computations of Lidingöbanan during week seconds 261250-261350 ...27
Figure 12 Difference in estimated longitude and latitude between LC and TC computations of Lidingöbanan during week seconds 261250-261350 ...27
Figure 13 Difference in estimated elevation between LC and TC computations of Lidingöbanan during week seconds 260450-260550 ...28
Figure 14 Difference in estimated longitude and latitude between LC and TC computations of Lidingöbanan during week seconds 260450-260550 ...28
Figure 15 Estimated precision for Lidingöbanan TC without GCPs and with simulated GNSS- free area ...29
Figure 16 Estimated precision for Lidingöbanan TC with 40 seconds between simulated GCPs and with simulated GNSS-free area ...29
Figure 17 Estimated precision for Lidingöbanan TC with 20 seconds between simulated GCPs and with simulated GNSS-free area ...29
Figure 18 Estimated precision for Lidingöbanan TC with 10 seconds between simulated GCPs and with simulated GNSS-free area ...30
Figure 19 Estimated precision for Lidingöbanan TC with 5 seconds between simulated GCPs and with simulated GNSS-free area ...30
Figure 20 Estimated precision for Lidingöbanan TC with 2 seconds between simulated GCPs and with simulated GNSS-free area ...30
Figure 21 Estimated precision for Nockebybanan LC ...31
Figure 22 Estimated precision for Nockebybanan TC ...31
Figure 23 Estimated precision for Nockebybanan TC without GCPs and with simulated GNSS-free area ...32
Figure 24 Estimated precision for Nockebybanan TC with 40 seconds between simulated GCPs and with simulated GNSS-free area ...32
Figure 25 Estimated precision for Nockebybanan TC with 20 seconds between simulated GCPs and with simulated GNSS-free area ...33
Figure 26 Estimated precision for Nockebybanan TC with 10 seconds between simulated GCPs and with simulated GNSS-free area ...33
Figure 27 Estimated precision for Nockebybanan TC with 5 seconds between simulated
GCPs and with simulated GNSS-free area ...34
Figure 28 Estimated precision for Nockebybanan TC with 2 seconds between simulated
Figure 29 Estimated precision for Roslagsbanan LC ...35
Figure 30 Estimated precision for Roslagsbanan TC ...35
Figure 31 Estimated precision for Roslagsbanan TC without GCPs and with simulated GNSS-free area ...36
Figure 32 Estimated precision for Roslagsbanan TC with 40 seconds between simulated GCPs and with simulated GNSS-free area ...36
Figure 33 Estimated precision for Roslagsbanan TC with 20 seconds between simulated GCPs and with simulated GNSS-free area ...37
Figure 34 Estimated precision for Roslagsbanan TC with 10 seconds between simulated GCPs and with simulated GNSS-free area ...37
Figure 35 Estimated precision for Roslagsbanan TC with 5 seconds between simulated GCPs and with simulated GNSS-free area ...38
Figure 36 Estimated precision for Roslagsbanan TC with 2 seconds between simulated GCPs and with simulated GNSS-free area ...38
Figure 37 Estimated precision for Roslagsbanan TC in interval 276960-277240 WS without GCPs ...39
Figure 38 Estimated precision for Roslagsbanan TC with GCPs at 600 m interval ...39
Figure 39 Estimated precision for Roslagsbanan TC with GCPs at 500 m interval ...39
Figure 40 Estimated precision for Roslagsbanan TC with GCPs at 300 m interval ...40
Figure 41 Estimated precision for Roslagsbanan TC with GCPs at 200 m interval ...40
Figure 42 Estimated precision for Roslagsbanan TC with GCPs at 100 m interval ...40
Figure 43 Estimated precision for Roslagsbanan TC with GCPs at 50 m interval ...41
Figure 44 Estimated precision for Saltsjöbanan LC ...41
Figure 45 Estimated precision for Saltsjöbanan TC ...41
Figure 46 Estimated precision for Saltsjöbanan TC without GCPs and with simulated GNSS- free area ...42
Figure 47 Estimated precision for Saltsjöbanan TC with 40 seconds between simulated GCPs and with simulated GNSS-free area ...42
Figure 48 Estimated precision for Saltsjöbanan TC with 20 seconds between simulated GCPs and with simulated GNSS-free area ...43
Figure 49 Estimated precision for Saltsjöbanan TC with 10 seconds between simulated GCPs and with simulated GNSS-free area ...43
Figure 50 Estimated precision for Saltsjöbanan TC with 5 seconds between simulated GCPs and with simulated GNSS-free area ...44
Figure 51 Estimated precision for Saltsjöbanan TC with 2 seconds between simulated GCPs and with simulated GNSS-free area ...44
Figure 52 Positional averaged worst case errors from all tracks with GCPs placed at certain
distances. ...49
Table of Tables
Table 1 Error specification for the OxTS Inertial+. ...18 Table 2 Positional precision and applications when utilizing GCPs in set intervals. ...48
Table of Equations
Equation 1 Conversion from the camera reference frame to the common reference frame.
(Chu and Chiang 2016) ...15
1 Introduction
1.1 Background
Railways are a transportation method that is used frequently for both freight transports and transportation of people. For example, just in the EU the rail freight transport was estimated to almost 400 billion tonne-kilometers (EU 2020). Trains for human transportation is also an ever increasingly discussed topic with high-speed trains in many countries, among others in Sweden where there are plans to build high-speed rails between Stockholm-Gothenburg and Stockholm-Malmö. It is however not only the effectiveness of the trains that make them relevant, but also their environmentally friendly nature, especially when compared to other modes of transport which fill many of the same functions such as cars and planes. Trains do however require much infrastructure to function and this infrastructure is expensive to build, especially if it is the more advanced tracks that are required for high-speed trains (Trafikverket 2020).
The tracks which are the focus of this work all experience damage in many ways including effects from cold, heat, the sun, vegetation as well as from wear and tear. These are all affecting the tracks differently and they are also managed in different ways which range from preemptive to reactive methods (Trafikverket 2021a). Essentially all tracks that are used require regular maintenance and just in Sweden there are 14 000 kilometers of track that is being maintained to a cost of 6 billion Swedish crowns every year by Trafikverket, the responsible organization (Trafikverket 2021b). With this said, it is evident that the rail tracks have to be kept working at all times, but also that the cost has to be as low as possible.
This is done by performing maintenance only when it is required and one way to find when maintenance is required is to measure the tracks. This measuring can be performed in many ways where some of the examples are track gauge measurement tools, total stations and laser scanning. The collected data is then compared to the original data and a decision is made whether the tracks have to be repaired or not.
In this thesis, the track data is collected using laser scanners mounted on trains or modified vehicles.
The data itself has a very good relative accuracy, which means that the points in the point cloud are very accurate relative to other points in the point cloud. The absolute accuracy of the points is however where the problem lies as this is what is required to analyze whether the tracks are damaged or not.
The need for an increased digitization of track maintenance is also something that has been specified by Trafikverket in Sweden (Trafikverket 2021c). In the pre-study issued by Trafikverket, many different aspects of digitization are mentioned. One of these is a comparison between manual, analog work and automatized, digitized work. In this comparison, there are two aspects that stand out. Firstly, the track time (the time that the track is occupied) is greatly reduced when the work is automated. This leads to reduced delays and increased capacity, both which is beneficial to the passengers and the operating company. Secondly, the automated analysis of the tracks was capable of detecting more urgent errors compared to the manual analysis. This in turn leads to fewer track malfunctions since the urgent errors can be prioritized and this is positive from both an economical and a train safety point of view.
Trafikverket has involved many companies and universities in their attempt to increase digitization, and among these are WSP and KTH. These two are also the organizations behind this thesis which will hopefully further the knowledge of the digitization of track maintenance.
To find the absolute position of the measured points, the absolute position of the laser scanning equipment has to be known and this is calculated using support such as ground control points (GCP) along the tracks, odometers, Inertial Navigation Systems (INS) and Global Navigation Satellite Systems (GNSS). Since the data is not required in real time, the data provided by these sensors can be processed in a filter to improve the accuracy and precision of the result. These filters can be designed in many different ways and are usually divided into either centralized or decentralized filters that can include many algorithms and corrections.
1.2 Objectives
The objective in this thesis is to find ways to improve the positional precision of the laser scanning equipment on trains which will result in a more accurate rail track analysis to find whether maintenance is required or not. The sought-after precision is around the mm-cm level. Some of the options that will be analyzed are Tight Coupling (TC) versus Loose Coupling (LC) as well as positioning and spacing of GCPs.
1.3 Limitations
The data in this report is restricted to data collected by WSP on the Nockebybanan, Lidingöbanan, Saltsjöbanan and Roslagsbanan, all are tracks situated in the Stockholm, Sweden area. Measured GCPs are also only available for Roslagsbanan, which means that simulated GCP will be used for the other railway networks. Lastly, the data that will be used to examine the positional precision are restricted to GNSS, INS, odometer data and GCPs that will be implemented into a Kalman filter using the software Inertial Explorer.
Another limitation is that the true data measured for the tracks, which are then used to compare the collected data with, are measured in a local control network while the data collected afterwards are measured in a global or national control network. Thus, there may be errors in one control network that is not present in another and vice versa. Such errors can be lacking accuracy of points used to establish the control network, which is more likely for local control networks in areas that are not used as often since the starting control network there may have been measured and positioned many years ago without corrections. The local control network should however be more suited to the local area compared to a larger scale system, which may result in positional errors when translating the data from one control network to another.
Since there is no possibility to take these errors in consideration, they will be omitted in this report, but it is still important to know that they may exist if the subject of this thesis is to be replicated somewhere and it will be taken up in more detail in section 2.4 Train Positioning.
2 Literature Study
2.1 Inertial Navigation
The main parts of an INS are accelerometers, gyroscopes and navigation computers. The accelerometer measures inertial acceleration, which means that it does not measure gravitational acceleration, while the gyroscope measures rotations and the navigation computer calculates the gravitational acceleration as well as processes outputs from the accelerometer and gyroscope. Thus, in the most basic explanation, an INS is a tool that estimates the position of a point within the INS and orientation of its sensors. It has the capability to be useful anywhere on the globe, however its positional error will increase with time and thus its position has to be updated every so often using other navigational sources such as GNSS (Andrew, Grewal and Weill 2007).
The reason that positions can be acquired by INS anywhere lies in its simple nature, that is that the position is derived from the acceleration of the body containing the INS. Thus, as long as the initial position and velocity is known the current position can be derived if errors are disregarded. When analyzing INS, a few advantages as well as disadvantages become apparent. Some of the advantages are as earlier mentioned that it can be used anywhere, but also that it can not be jammed. On the flip side, some disadvantages are that its navigational errors increase with time and that it has a significant cost (Andrew, Grewal and Weill 2007).
Before inertial navigation is possible, the INS has to be initialized. Initialization is the process at the beginning of the measurements where the initial state variables such as position, velocity and attitude are determined. Errors in the INS are also estimated during the initialization. There are a few different ways to initialize an INS and usually it involves GNSS or manual positions/data (Andrew, Grewal and Weill 2007). The methods differ from a static to a kinematic initialization, but the data used in this report has been acquired using a kinematic initialization. Depending on what data is required from the INS the initialization will take more or less time, where the most amount of initialization time is required when the attitude and azimuth of the INS is of importance.
2.2 Supported INS
INS and GNSS can be used together to further improve the achieved position as briefly mentioned earlier, but it is also good to mention that this is not possible in all applications. Submarines for example have to rely on INS alone since they can not be reached by GNSS signals (Andrew, Grewal and Weill 2007). This will however not affect this work since we are working with rail-bound vehicles, but it makes it clear that INS also has to be developed to keep up with the current and future trends since there always will be areas that GNSS can not reach.
When INS and GNSS is then integrated, it improves the measured position of both parts. To improve the outputs from the INS, GNSS positions can be used to reset positions that have large errors in it due to longer measurements. This also enable the use of cheaper INS since it only has to maintain acceptable accuracy for shorter times in many applications. GNSS on the other hand can use INS to find positions quickly after it has lost its signal. The integrated models are very useful when it comes to autonomous vehicles since it has a global reach and minimal positional or velocity errors (Andrew, Grewal and Weill 2007), and some of these factors are also useful for trains even though they do not have the same navigational issues as autonomous vehicles.
One of the methods, and also the method used in this thesis, that can be used for the integration is Kalman filtering. It is a procedure that can combine noisy sensors such as INS and GNSS into a more accurate system state to, for example, finding highly accurate positions or velocities. A usual application is a Kalman filter where GNSS and INS data are combined, but it can also include many sensors apart from these (Andrew, Grewal and Weill 2007). Examples of other support and sensors are GCPs, odometers and track geometry.
The Kalman filter has two primary parts: An estimate of the state vector including all state variables and an estimate of the estimation uncertainty. The estimated state vector contains the state that is of interest, for example position or velocity, as well as variables that may affect other state variables, e.g. GNSS atmospheric errors. The estimation uncertainty estimate is based on the difference between the predicted state vector and the measured state vector. With the differences between the predicted and measured state vectors known, it is possible to combine the sensor data in an optimal way so as to minimize the uncertainty by applying a weighted average between the predicted state vector and the measured state vector to achieve an estimated state vector (Andrew, Grewal and Weill 2007).
Apart from the variables that are used, the Kalman filter also contains two steps: the a posteriori step and the a priori step. In the a posteriori step, the estimate of state variables and the estimate uncertainty are updated based on information from the sensors. In the a priori step, the estimate and estimate uncertainty are updated based on uncertain system dynamics. After the updates are done, a Kalman gain matrix is used as a weighting matrix for combining sensor data with the previous estimate to reach the new estimate (Andrew, Grewal and Weill 2007).
Within a Kalman filter, a method that can be used is a zero-velocity update (ZUPT). The purpose of the ZUPT is to reduce the drift in the INS by utilizing the knowledge that the INS is not moving at certain times and thus there should be no change in measured position. The errors can thus be both measured and reset using ZUPT (Markovska and Svensson 2019). Usually, this is used in areas with subpar GNSS availability to reset the temporal based INS errors, which indicates that a ZUPT has to be performed before the INS drift has become too large to avoid lacking precision in the computed data. The distance between every ZUPT is thereby dependent on the GNSS availability in areas and the grade of the INS.
A necessity when using supported INS with GNSS or GCP is to have information about the distances between the INS and the corresponding sensor/receiver. This is generally called a lever arm and the reason that it is needed is that the origin of the INS and the GNSS receiver can not be at the same physical location. The same goes for the odometer and the cameras or other sensors used to recognize the GCP.
Whether the lever arm between the INS and the supporting sensors is long or short, the distance will still have to be accounted for. Thus, the effect that the lever arm has on the data will have to be compensated. Depending on which sensor is compensated, it will all have different methods since all data is captured independently and according to the sensor's characteristics (Jaewon et al. 2006).
There are generally two methods used when integrating INS with supporting data, and that is loose coupling as well as tight coupling. The difference between LC and TC lies in what data is shared between the different sensors and diagram examples from Gianluca, Marco and Gianluca (2017) can be seen in Figure 1 and Figure 2. In LC, the computed states from the INS and the GNSS are used together after they have been independently calculated, while TC uses the raw data from the different sensors together from the beginning. Theoretically, this should lead to TC being more accurate in areas with either subpar GNSS availability or non-optimal INS conditions since the data that is accurate can improve the data that is not accurate. It is also possible to implement further constraints and algorithms that will reduce errors in a TC model since it has more data to work with in every step compared to the LC (Gianluca, Marco and Gianluca 2017). Another positive part about TC is that it functions even when there are not enough GNSS satellites since the GNSS part of the data is first computed alongside the INS data. There are however some advantages with using LC as well. These are mostly that it is easier to recognize sensor failures since the computed position exists separately for the different sensors as well as it being less computationally heavy (Horemuz 2020).
Figure 1 Example of a LC supported INS (Gianluca, Marco and Gianluca 2017)
Figure 2 Example of a TC supported INS (Gianluca, Marco and Gianluca 2017)
Finally, since both GNSS and INS have position as their primary output, they are relevant to each other for sensor integration, that is a combination of outputs from different sensors to attain a better estimate (Andrew, Grewal and Weill 2007). Based on the objectives in this work, it is important to use this since the worst positional accuracies for trains occur when there is a lack of GNSS such as in non-favorable terrain or in tunnels. Thus, the INS has to be good enough to handle the length of the tunnel without help from GNSS. One way to improve this is by replicating the role that GNSS signal fulfill but within the tunnel, for example by having measured GCPs that are also used in the Kalman filtering as well as being used to restore the INS to the correct position from the time-based errors that has occurred since GNSS signals were lost.
2.3 Acquisition of GCPs
If and when GCPs are available for a mobile laser scanning system (MLSS) or mobile mapping system (MMS) they are commonly registered on the mobile unit through the work of two or more cameras that can capture images that contain the same objects from different angles which allows for full 3D mapping possibilities (Tao and Li 2007).
This is done by placing the cameras on the MMS-unit with as much distance as possible between them to create a wider angle between the objects in the images and the cameras. These camera positions are then connected to the body frame by applying a rotation matrix on the lever arm which converts the camera frames to the body frame. The body frame is then connected to the common reference frame
through another rotation matrix and a vector that connects the two. The equation for this conversion from an object seen on cameras to the common reference frame can be found below in Figure 3 and Equation 1 (Chu and Chiang 2016).
Figure 3 Visual representation of camera GCP acquisition. (Chu and Chiang 2016)
Equation 1 Conversion from the camera reference frame to the common reference frame. (Chu and Chiang 2016)
𝑟
𝑜𝐴𝑀= 𝑟
𝑜𝑏𝑀(𝑡) + 𝑅
𝑏𝑀(𝑡) × ( 𝑟
𝑏𝑐𝑏+ 𝑠𝑅
𝑐𝑏𝑟
𝑐𝐴𝑐)
𝑟𝑜𝐴𝑀 is the vector from the common reference frame to an object shared by two or more cameras.
𝑟𝑏𝑀(𝑡) is the vector from the common reference frame to the location of the body frame that is given by the INS/GNSS at the timestamp t.
𝑅𝑏𝑀(𝑡) is the 3D rotation matrix that rotates the body frame into the common reference frame at the timestamp t.
𝑟𝑏𝑐𝑏 is the lever arm vectors from the body frame to each camera
𝑠 is a scale factor that is interpolated from INS/GNSS at the specific timestamp t.
𝑅𝑐𝑏 is the rotation matrix which rotates the camera frame to the common reference frame.
𝑟𝑐𝐴𝑐 is the vector given by each camera frame.
Once this conversion is done these GCPs can be used as control points to reset the errors generated by an IMU or other supporting setups in a MMS.
2.4 Train Positioning
To achieve highly accurate train positioning in areas that lack GNSS, GCPs along the tracks are required but they are also relevant in areas with GNSS since they can be used in Kalman filtering to correct noisy measurements. The GCPs that are measured around railways that are used to position the trains are often measured in the control network local to the railway, which is established in a truss format to be more reliable perpendicular to the measured length. The control network is erected based on points established so as not to become displaced as time passes, that means that the points are established for example in hard grounds or on the facade of buildings (Lantmäteriet 2020).
When working with control networks, there are a few aspects that have to be considered to know what accuracy the network has. Since the data used in this thesis is from Sweden, the process begins with an analysis of how well the local control network has been adapted to SWEREF 99, the Swedish national coordinate system, since most local control networks existed before SWEREF 99 was established. If there were large differences between the true and the measured positions, the control network had to be corrected, however these are all parts that have been performed beforehand. The corrections are not without flaws and they vary from place to place depending on how well the local control networks were implemented into SWEREF 99 positions, which may lead to error propagations in the results.
A similar process has also been performed for the height system where local control networks have been connected and assimilated into RH2000, the Swedish national height system. As it follows the same general process, it also has the same issues with varying accuracy of the data from place to place (Lantmäteriet 2020). If the measurements are to be performed in another country, it is still important to consider how the local and the national/world-wide control network are related and what errors can be expected between them.
Thus, with all this knowledge, it is up to every project whether the local control network should be based on a pre-existing control network or if a new control network should be established using GNSS. Usually, the project is connected in one way or another to national control networks to make general work and cooperation easier. With that said, since the objective is to reach mm-cm level on the absolute precision of the measured data, every improvement is beneficial and the realization of the control network should be thought upon carefully in each project since the circumstances vary between every project that is performed.
2.4.1 GNSS-free environments
When trains operate in GNSS-free environments such as tunnels or difficult terrain, the utilized method will rely heavily on GCPs along the tracks as well as a highly accurate IMU. Another method that can be used is to replace the GCPs and GNSS with track-alignment. By using this method, the environment is no longer an issue since the positioning is based purely on the INS and the track-alignment. When pure inertial navigation is compared to inertial navigation coupled with track-alignment using a consumer- grade IMU, the pure inertial navigation quickly diverged from the actual position while the coupled version more or less managed to keep the errors on a constant level (Hung, King and Chen 2016).
The coupled version was however not without flaws as it experienced greater errors in certain directions as well as in different orientations. A few of these errors came from limitations with the initialization and the model of the train and could thus be reduced when used in an improved environment. Overall, it proved to be a good method to use in GNSS-free environments to reduce the positional errors, but in order to reach accuracies close to millimeters it has to be complemented or replaced with other methods (Hung, King and Chen 2016).
Another way to navigate in a GNSS-free environment using control points was investigated in the subway systems of Wuhan, China in an article by Wang et al. (2020). In the case of scanning the Wuhan, China subway GNSS-free lines number 1 and 6, dead reckoning (DR) sensors were used such as a gyroscope, accelerometer and an odometer where the gyroscope and accelerometer are a part of the IMU. One issue that usually occurs when using an IMU and DR is that the accuracy drops over time as the MLSS moves through the tunnel. To compensate for this the report investigates the possibility of using GCPs inside of the tunnels in order to reset the error of the IMU and DR. GCPs were placed along the track at 60-meter intervals which could be used to test for several different interval distances 60, 120, 240 and 480 meters respectively. After correcting the IMU and DR it was possible to reach a horizontal error RMS of 0.004m and elevation error RMS of 0.002 at 60 meter intervals, giving a 0.004m 3D RMS. At 480 meter intervals 0.004m was acquired for horizontal RMS and 0.007m for elevation, giving a 3D RMS of 0.008m. The results are above the required level for accuracy in the subways of Wuhan and can be done rather quickly. The processing of a 5-6 km tunnel takes less than 4 hours assuming that the GCPs already exists.
2.4.2 Environments with GNSS
When in environments with GNSS, trains have certain characteristics such as being bound to a track and travelling at quite high velocities that can be utilized and considered when acquiring the position of the train. One positive part is that the train can only be on the track, which eliminates a lot of errors.
However, it does not ensure that the acquired position is perfect. Another positive aspect regarding INS is that trains can not handle sharp turns. Since gyroscopes that are used in INS also have difficulties recording sharp turns, this will result in a more reliable reading from the INS. On the other hand, being on a rail and the lack of sharp turns also enables trains to travel faster, which may result in larger errors in both velocity, acceleration and position readings (Guoliang Zhu 2014). It is however important to mention that slow or static movement will result in greater errors since the GNSS and INS work together, so the optimal speeds will have to be found through analysis of the data.
In this report, the focus lies on establishing positions of trains that are not traveling at very high speeds, but the accuracy has to be a lot higher. Some aspects do however remain the same between finding the position of trains with high and low velocities. One such aspect is the tools that are used: In both cases, INS, GNSS and odometers are used. Apart from these tools, other sensors such as radar for tracking the track geometry can also be used.
In his thesis, Guoliang Zhu (2014) takes up 4 issues that are of utmost importance regarding train positioning, namely Accuracy, Integrity, Continuity and Availability. Accuracy in this context means how close the estimated position and velocity is to the true value. In this work, the focus is on the position part of the accuracy since the velocities in the available data are quite low. However, since most GCPs used in the positional computations are simulated, a positional accuracy will not be acquired. Instead, a positional precision will be used. The integrity is another factor that is very important in this thesis and it represents how reliable the navigation system is. It may thus be the most important factor since even a lower precision with high reliability is more useful than high precision with low reliability. Continuity is directly related to accuracy and integrity and defines how well the system is capable of maintaining the required accuracy and integrity during the whole procedure. This is another important factor in the work as there is no problem maintaining a good accuracy in good conditions, but it must also function in more difficult locations such as in tunnels. Lastly, availability is the time where the system is available.
Since we require it to be available at all times we must consider this as well, and to ensure that it always is available the system has to be composed of complementary parts such as GCPs and GNSS (Guoliang Zhu 2014).
2.5 Track Monitoring
Just measuring tracks are not relevant unless there is some basis to examine the measured tracks with.
This is usually based on how the tracks were when they were first laid out and with this information a comparison between the measured track and the original track can be made, resulting in a track irregularity. Apart from having something to measure against, it is also important to know what on the track is examined. Five of these measurement areas are Cant (difference in elevation between rails), Gauge (distance between rails), Twist (difference between two cross levels at certain distance), vertical alignment (difference in vertical direction) and horizontal alignment (difference in horizontal direction) (Chen, Cheng and Zhang 2014).
The measured values will be compared to the original value of the position that the measured value believes it is at, and this requires a very high accuracy from the sensor equipment. The reason for this is that the allowed difference between measured and original values can be on a millimeter level, and if the measured data is a few centimeters wrong the result may be faulty. This is a main reason that this thesis aims to achieve a positional precision on the mm-cm level with the post-processed data, to be able to find areas affected by changes with a high confidence.
3 Study Areas and Data Description
3.1 INS Specifications
In this thesis, the INS Inertial+ manufactured by Oxford Technical Solutions Ltd (OxTS) has been used.
To use the OxTS Inertial+ effectively, its errors will have to be modeled and its optimal initialization process has to be known. The specifications are displayed in Table 1 and are taken from data provided by WSP. The initialization process is not something that can be accounted for in the available data since all the data is already collected, but the initialization process specific for the OxTS Inertial+ will be described regardless.
There are four important factors when initializing the OxTS Inertial+, but all of the factors are also relevant for other GNSS/INS coupled systems, even though their specifics might differ. The first factor is that there should be at least 15 minutes of measurements before the measuring missions are performed so that all or most of the errors can be accurately estimated.
Secondly, the GNSS receiver connected to the INS must have good conditions regarding the sky environment, which includes satellite geometry and the absence of obstacles.
The third factor is that the lever arm between the GNSS receiver and the INS has to be accurately determined so that it is known with a margin of 5 mm.
The last factor is that the initialization (apart from the breaks) and the measurements have to be performed under dynamic conditions (OxTS 2018).
Table 1 Error specification for the OxTS Inertial+.
X-axis Y-axis Z-axis
Accelerometer Bias Initial Std Dev (Initial offset of output value compared to input value)
0.03 m/s^2 0.03 m/s^2 0.03 m/s^2
Gyro Drift Initial Std Dev (Initial offset of output value compared to input value)
0.138889 deg/s 0.138889 deg/s 0.138889 deg/s
ARW (Angle Random
Walk) 0.4356 deg/sqrt(s) 0.4356 deg/sqrt(s) 0.4356 deg/sqrt(s) Accelerometer Bias
(Constant offset of output value compared to input value)
8.1*10^-9
m/s^2/sqrt(s) 8.1*10^-9
m/s^2/sqrt(s) 8.1*10^-9 m/s^2/sqrt(s)
Gyro Drift (Constant offset of output value compared to input value)
3.05665*10^-5
deg/s/sqrt(s) 3.05665*10^-5
deg/s/sqrt(s) 3.05665*10^-5 deg/s/sqrt(s)
VRW (Velocity
Random Walk) 4.68722*10^-6
m/s/sqrt(s) 4.68722*10^-6
m/s/sqrt(s) 4.68722*10^-6
m/s/sqrt(s)
3.2 GCP Specifications
The GCPs are measured using a total station in the year 2020 and are located on the ground along the tracks, as can be seen in Figure 4. The GCPs are marked using targets which are recognized and applied to the Kalman filter using cameras mounted on the MMS. The cameras are oriented towards the tracks so that they can register the targets, but other possible camera placements and orientations are mentioned in section 6.6 Increased efficiency in the use of GCP.
Figure 4 GCP target established along Roslagsbanan (WSP 2020) 3.3 File formats
3.3.1 .GTT
GTT (GeoTracker Trajectory) is a specialized text based format designed for the software GeoTracker Trajectory which is produced by SwedVision. The software uses the GTT-files for post processing of point clouds and RAW images as well as position calculations (Geotracker 2021).
3.3.2 .PVA
PVA stands for position, velocity and acceleration and is a file format used to support the usage of inertial processing engines created by NovAtel such as Inertial Explorer that is used frequently throughout this thesis. This is done by storing external coordinate updates that can then be applied to IMUs to reset errors that are generated over time since the last known position of the MMS (Novatel 2020).
3.4 Lidingöbanan
Lidingöbanan is located in the Stockholm area and runs from Ropsten to Gåshaga brygga. This is also the range of the data available for analysis.
The data is collected in 2019 using the INS OxTS Inertial+, an odometer and a GNSS-receiver. It has access to GPS and GLONASS, but the initialization on the Ropsten side has somewhat subpar GNSS availability, which may lead to subpar error estimation of the INS errors.
To reference the measured points, two virtual reference stations have been used and are respectively placed close to the beginning and the end of the measured track. There are also no GCPs available for this track and thus simulated GCPs will be used.
3.5 Nockebybanan
Nockebybanan is located in the Stockholm area and runs from Alvik to Nockeby. It has been in use since 1910 and its current stretch was established in 1929 (SL 2021). This is also the range of the data available for analysis.
The data is collected in 2019 using the INS OxTS Inertial+, an odometer and a GNSS-receiver. It has access to GPS and GLONASS and a somewhat lacking initialization on the Nockeby side regarding GNSS availability. It does however have better GNSS availability than the Lidingöbana and the errors should be minimal.
To reference the measured points, two virtual reference stations have been used and are respectively placed close to the beginning and the end of the measured track. There are also no GCPs available for this track and thus simulated GCPs will be used.
3.6 Roslagsbanan
Roslagsbanan is located in the Stockholm area and runs from Stockholm Östra to either Kårsta, Österskär or Näsbypark depending on the stretch (Region Stockholm 2021a). The data in this work ranges from Roslags-Näsby to Kårsta. The data is collected in 2020 using the INS OxTS Inertial+, an odometer and a GNSS-receiver. It has access to GPS, GLONASS and Galileo.
To reference the measured points, three virtual reference stations have been used and are respectively placed close to the beginning, the middle and the end of the measured track. Along the tracks there is a section towards the end of the measurement with established GCPs that were used, but simulated GCPs were also used to be able to compare the acquired results with the other tracks.
3.7 Saltsjöbanan
Saltsjöbanan is located in the Stockholm area and runs from Slussen to Saltsjöbaden. It was opened in 1893 and the longest part of it stretches 15,3 km (Region Stockholm 2021b). However, due to construction works, the data available in this work only ranges from the Henriksdal station to the Saltsjö-Duvnäs station.
The data is collected in 2020 using the INS OxTS Inertial+, an odometer and a GNSS-receiver. It has access to GPS, Galileo, GLONASS and Beidou data, however the Beidou data is non-existent in the study area.
To reference the measured points, two virtual reference stations have been used and are respectively placed at the beginning and the end of the measured track. There are also no GCPs available for this track and thus simulated GCPs will be used.
4 Methodology
4.1 Inertial Explorer
The main software that was used for processing and analysis is Inertial Explorer. The software focuses on post processing of GNSS and INS to generate an accurate position of MMS at each recorded position in time and space. The software is generally used to automate the processing which saves a lot of time since all that needs to be done in order to process any data collection is to import the measurement from the data collection and enter all the specifications for the GNSS, INS and more.
4.2 Mobile Mapping Toolbox
Mobile Mapping Toolbox is a software developed by Martin Brandin at WSP and is used exclusively by WSP. It has several tools that are used for production but focuses mainly on the following tools.
• Transformation, corrections of the geoid and division of laser data
• Tunnel position calculations
• Point density and overlap analysis for laser data
• Section analysis and report tool for roads and railroads
• Track wear analysis
4.3 Data Collection
The data that is used in this thesis was already collected by WSP beforehand. It was collected using a laser scanner mounted to a rail-bound vehicle that utilized GNSS, INS and odometer. These MLSS can have varying appearances, but two versions used by WSP are visible in Figure 5 and Figure 6. The data collection started by initializing the INS and it ended by once again initializing the INS to allow forward and reverse computations. The initialization of the INS is best done by moving in different directions at different speeds, and the reason for this is so that the Kalman filter can determine errors in the sensors used in the INS (OxTS 2018). However, since this data was collected on a railway the initialization was instead performed by going forward and backwards at different speeds. Apart from the movements used in the initialization, it is also important to perform the initialization during an extended period of time.
Figure 6 MLSS mounted on a train used by WSP to scan tracks (WSP 2020)
4.4 Preparations
Initially, the data that is required to perform the computations in Inertial Explorer has to be acquired.
The required data consists of virtual reference stations which are located so that no measured position will be too far from a reference station. This usually results in the reference stations being placed at the start and end of the measured track, but if it is a long track additional reference stations can be utilized.
Apart from the reference stations, the measurements from the odometer, GNSS receiver and the INS are also required, together with data regarding the positioning of the GNSS receiver and the INS relative to each other. If there are GCPs available, they will also be imported before running and if simulated GCPs are to be used in the case where there are no GCPs they will have to be extracted and inserted after the data has been computed once.
4.5 Computations
All of the computations are made using Inertial Explorer and Mobile Mapping Toolbox. The LC and TC computations are also made with the same settings which is described in more detail below.
4.5.1 Loosely Coupled 4.5.1.1 Overview
Loosely coupled computations compute the different inputs separately and then combine them in a filter, in this case a Kalman filter. In this thesis, the GNSS data is computed first and results in a trajectory based purely on GNSS data. This data will thus have gaps where there is no GNSS data, but these gaps will be filled in when the INS and odometer data is processed in the next step. After both GNSS and INS/odometer data have been processed forward and in reverse, the data is combined in a Kalman filter and is smoothed into a combined product (Andrew, Grewal and Weill 2007).
4.5.1.2 Inertial Explorer
In Inertial Explorer the step-by-step process for loosely coupled computations are done as follows. First the computation of the GNSS is done with both forward and reverse processing at the same time. During this step the available satellites are shown and if certain satellites are not desirable they can be omitted during the processing.
Once the GNSS has been processed the loosely coupled calculations can be prepared by setting up an error model for the IMU. In this work, the OxTS Inertial+ was used and the standard deviation values for the IMU and the spectral densities such as gyro drift and acceleration needs to be assigned. Inertial Explorer can then properly run the loosely coupled computations.
4.5.2 Tightly Coupled 4.5.2.1 Overview
Tightly coupled computations compute the different inputs together and combine them in a Kalman filter. This allows errors in both the INS and the GNSS measurements to be reduced by taking other observations into consideration. These observations can be most observations that are related to one or more state variables, but in this thesis it is, apart from INS and GNSS, odometer data and GCP. The tightly coupled computations also process the data forward and in reverse ending with a Kalman filter just like the loose coupling. Due to the possibility to correct input data using other input data early on in the processing, tightly coupled results are usually more reliable compared to loosely coupled results (Andrew, Grewal and Weill 2007).
4.5.2.2 Inertial Explorer
In Inertial Explorer the step-by-step process for tightly coupled computations are done as follows. Just like with the loosely coupled computation the settings for GNSS and the IMU needs to be done. The difference this time is that they can both be made at the same time and does not require any preprocessing of GNSS. The settings are set up the same way as the loosely coupled computation on both forward and reverse processing.
4.5.3 Applying GCP
This thesis applies two different approaches to applying GCP to the tracks. One method is to simulate GCP which is explained in the next section, and then apply them to the area while removing the GNSS signals for that specific location and run the tightly coupled calculations again but with the GCP and no GNSS support in order to simulate a dense forest or a tunnel. The other method is by using GCPs that were measured on Roslagsbanan in the year 2020 and then perform the tightly coupled computations with them.
4.5.3.1 Simulated GCP
The first step is to run a normal tightly coupled calculation for the original tracks since it is generally known that tightly coupled calculations have a higher accuracy and in order to generate GCPs there is a need for high precision locations along the track. By analyzing the resulting plots, a time span of 800 seconds with high positional precision can be extracted. The threshold that was set for these simulations was that the positional error has a requirement of 0.1 meters or less for the entire duration. The entire tightly coupled measured tracks is then sent to the software Mobile Mapping Toolbox to generate PVA files which Inertial Explorer uses to import GCPs. In this tool the time span that was located can be inserted and a distance or time setting can be set to generate GCPs along the inserted time span. A PVA file is created for 2, 5, 10, 20 and 40 seconds respectively for each track that was exported which roughly translates to 6, 15, 30, 60 and 120 meters since the MLSS travels on average 3 meters per second along these specific tracks.
The next step is to generate a simulated version of a tunnel or dense forest by turning off the GNSS in Inertial Explorer. Since the GCPs were extracted previously with high precision these GCPs can then be used to simulate how the different distances can be used to reduce errors over longer distances where GNSS might not be available. This is done by running the IMU with the PVA files as updates for GCPs usage. IE will then be able to generate user specified plots to visualize the results that can be found in section 5 Results.
4.5.3.2 Measured GCP
The data for the measured GCPs are available in a .PVA format produced by WSP for Roslagsbanan so there is not any preprocessing needed. The preprocessing that WSP had done was to take the measured GCPs at 50 meter intervals along 600 meters of tracks and then convert them into 50, 100, 200, 500 and 600 meters PVA files respectively by omitting certain GCPs. The next step was to process a TC computation without any GCPs for the area where the measured GCPs are located to create an unmodified view of the area to have as a reference. Once the reference graphs are done, the IMU runs with the PVA files to insert the known points at different intervals and generate the relevant plots.
5 Results
The primary results will be based on the estimated position precision of the different measurements.
This has to be used since there are no actual GCPs along most of the measured tracks and thus an estimate will be used. There is also other data such as carrier and code residuals, satellite availability and separation between forward and reverse solutions from the Kalman filtering that will be used to achieve conclusions in section 6.3 Problematic areas regarding GNSS/INS integration. Lastly, the horizontal axis is based on time since that is the major cause of INS errors. On average, the MLSS travelled at a speed of 3 m/s except when stationary.
5.1 Lidingöbanan
For Lidingöbanan, one LC and one TC computation were performed with the original data, which is GNSS, INS and odometer data, see Figure 7 andFigure 8. After this, GNSS was removed in the interval 260100-260900 week seconds (WS) and simulated GCPs were placed at certain time intervals in the GNSS free interval see Figure 15-Figure 20. It is noteworthy that the initial spikes in Figure 16Figure 20 that uses simulated GCPs is due to a lack of a known precision just before the vehicle enters the GNSS- free area.
Figure 7 Estimated precision for Lidingöbanan LC
Figure 8 Estimated precision for Lidingöbanan TC
5.1.1 Comparison Between LC and TC
Figure 9Figure 14 display the differences in the position estimate between LC and TC computations from Figure 7 and Figure 8. Figure 9Figure 12 are from areas with lacking positional precision and represent the time span 259350-259450 and 261250-261350 WS respectively, while Figure 13Figure 14 is from an area with high positional precision in the interval 260450-260550 WS. The longitude and latitude differences are displayed in decimal degrees where 1 degree longitude in Stockholm is approximately 57 km and 1 degree latitude is approximately 111 km (NHC/NOAA 2021). Based on this, the differences between LC and TC computations ranges from 0.00114-0.057 m in longitude and 0.0111-0.0888 m in latitude.
Figure 9 Difference in estimated elevation between LC and TC computations of Lidingöbanan during week seconds 259350-259450
Figure 10 Difference in estimated longitude and latitude between LC and TC computations of Lidingöbanan during week seconds 259350-259450
Figure 11 Difference in estimated elevation between LC and TC computations of Lidingöbanan during week seconds 261250-261350
Figure 12 Difference in estimated longitude and latitude between LC and TC computations of Lidingöbanan during week seconds 261250-261350
Figure 13 Difference in estimated elevation between LC and TC computations of Lidingöbanan during week seconds 260450-260550
Figure 14 Difference in estimated longitude and latitude between LC and TC computations of Lidingöbanan during week seconds 260450-260550
5.1.2 Simulated GCPs for Lidingöbanan
Figure 15 Estimated precision for Lidingöbanan TC without GCPs and with simulated GNSS-free area
Figure 16 Estimated precision for Lidingöbanan TC with 40 seconds between simulated GCPs and with simulated GNSS-free area
Figure 17 Estimated precision for Lidingöbanan TC with 20 seconds between simulated GCPs and with simulated GNSS-free area
Figure 18 Estimated precision for Lidingöbanan TC with 10 seconds between simulated GCPs and with simulated GNSS-free area
Figure 19 Estimated precision for Lidingöbanan TC with 5 seconds between simulated GCPs and with simulated GNSS-free area
Figure 20 Estimated precision for Lidingöbanan TC with 2 seconds between simulated GCPs and with simulated GNSS-free area
5.2 Nockebybanan
For Nockebybanan, one LC and one TC computation were performed with the original data, which is GNSS, INS and odometer data. After this, GNSS was removed in the interval 261000-261800 WS and simulated GCPs were placed at certain time intervals in the GNSS free interval. All of the above mentioned results can be seen in Figure 21-Figure 28.
Figure 21 Estimated precision for Nockebybanan LC
Figure 22 Estimated precision for Nockebybanan TC
5.2.1 Simulated GCPs for Nockebybanan
Figure 23 Estimated precision for Nockebybanan TC without GCPs and with simulated GNSS-free area
Figure 24 Estimated precision for Nockebybanan TC with 40 seconds between simulated GCPs and with simulated GNSS-free area
Figure 25 Estimated precision for Nockebybanan TC with 20 seconds between simulated GCPs and with simulated GNSS-free area
Figure 26 Estimated precision for Nockebybanan TC with 10 seconds between simulated GCPs and with simulated GNSS-free area
Figure 27 Estimated precision for Nockebybanan TC with 5 seconds between simulated GCPs and with simulated GNSS-free area
Figure 28 Estimated precision for Nockebybanan TC with 2 seconds between simulated GCPs and with simulated GNSS-free area
5.3 Roslagsbanan
For Roslagsbanan, one LC and one TC computation were performed with the original data, which is GNSS, INS and odometer data, see Figure 29 and Figure 30. GNSS was removed in the interval 268000- 268800 WS and simulated GCPs were placed at certain time intervals in the GNSS free interval which can be seen in Figure 31-Figure 36 . This was followed up by multiple TC computations using real GCPs available in the interval 276960-277300 WS. The above mentioned results can be seen in Figure 37- Figure 43.
Figure 29 Estimated precision for Roslagsbanan LC
Figure 30 Estimated precision for Roslagsbanan TC
5.3.1 Simulated GCPs for Roslagsbanan
Figure 31 Estimated precision for Roslagsbanan TC without GCPs and with simulated GNSS-free area
Figure 32 Estimated precision for Roslagsbanan TC with 40 seconds between simulated GCPs and with simulated GNSS-free area
Figure 33 Estimated precision for Roslagsbanan TC with 20 seconds between simulated GCPs and with simulated GNSS-free area
Figure 34 Estimated precision for Roslagsbanan TC with 10 seconds between simulated GCPs and with simulated GNSS-free area
Figure 35 Estimated precision for Roslagsbanan TC with 5 seconds between simulated GCPs and with simulated GNSS-free area
Figure 36 Estimated precision for Roslagsbanan TC with 2 seconds between simulated GCPs and with simulated GNSS-free area
5.3.2 Measured GCPs for Roslagsbanan
Figure 37 Estimated precision for Roslagsbanan TC in interval 276960-277240 WS without GCPs
Figure 38 Estimated precision for Roslagsbanan TC with GCPs at 600 m interval
Figure 39 Estimated precision for Roslagsbanan TC with GCPs at 500 m interval
Figure 40 Estimated precision for Roslagsbanan TC with GCPs at 300 m interval
Figure 41 Estimated precision for Roslagsbanan TC with GCPs at 200 m interval
Figure 42 Estimated precision for Roslagsbanan TC with GCPs at 100 m interval
Figure 43 Estimated precision for Roslagsbanan TC with GCPs at 50 m interval
5.4 Saltsjöbanan
For Saltsjöbanan, one LC and one TC computation were performed with the original data, which is GNSS, INS and odometer data. After this, GNSS was removed in the interval 258200-259000 WS and simulated GCPs were placed at certain time intervals in the GNSS free interval. All of the above mentioned results can be seen in Figure 44-Figure 51.
Figure 44 Estimated precision for Saltsjöbanan LC
5.4.1 Simulated GCPs for Saltsjöbanan
Figure 46 Estimated precision for Saltsjöbanan TC without GCPs and with simulated GNSS-free area
Figure 47 Estimated precision for Saltsjöbanan TC with 40 seconds between simulated GCPs and with simulated GNSS-free area
Figure 48 Estimated precision for Saltsjöbanan TC with 20 seconds between simulated GCPs and with simulated GNSS-free area
Figure 49 Estimated precision for Saltsjöbanan TC with 10 seconds between simulated GCPs and with simulated GNSS-free area
Figure 50 Estimated precision for Saltsjöbanan TC with 5 seconds between simulated GCPs and with simulated GNSS-free area
Figure 51 Estimated precision for Saltsjöbanan TC with 2 seconds between simulated GCPs and with simulated GNSS-free area
