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Undifferenced GPS for Deformation Monitoring PDF

118 Pages·2006·2.72 MB·English
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Undifferenced GPS for Deformation Monitoring Johan Vium Andersson Licentiate thesis in Geodesy Royal Institute of Technology (KTH) Department of Transport and Economics Division of Geodesy 100 44 Stockholm June 2006 Abstract This thesis contains the development of a deformation monitoring software based on undifferenced GPS observations. Software like this can be used in alarm systems placed in areas where the earth is unstable. Systems like this can be used in areas where people are in risk of getting hurt, like in earthquake zones or in land slide areas, but they can also be useful when monitoring the movements in buildings, bridges and other artefacts. The main hypotheses that are tested are whether it is possible to detect deformations with undifferenced observations and if it is possible to reach the same accuracy in this mode as when working in a traditional mode where the observations are differenced. The development of a deformation monitoring software based on undifferenced GPS observations is presented. A complete mathematical model is given as well as implementation details. The software is developed in Matlab together with a GPS observation simulator. The simulator is mainly used for debugging purposes. The developed software is tested with both simulated and real observations. Results from tests with simulated observations show that it is possible to detect deformations in the order of a few millimetres with the software. Calculations with real observations give the same results. Further, the result from calculations in static mode indicates that the commercial software and the undifferenced software diverge a few millimetres, which probably depends on different implementations of the tropospheric corrections. In kinematic mode the standard deviation is about 1 millimetre larger in the undifferenced mode than in the double differenced mode. An initial test with different observation weighting procedures indicates that there is a lot of potential to improve the result by applying correct weights to the observations. This is one of the aims in the future work within this project. This thesis are sponsored by the Swedish Research Council for Enviroment, Agricultural Sciences and Spatial Planning, FORMAS within the framework “Monitoring of construction and detection of movements by GPS ref no. 2002-1257” Keywords: deformation monitoring, GPS, modified NGS-parameters, undifferenced GPS-observations, Kalman filter 1 Acknowledgements First and foremost, I want to express my gratitude to my supervisors Professor Lars E Sjöberg and Ph.D. Milan Horemuz, how have helped, supported and encouraged me through my entire thesis work. Their knowledge and experience have been a true help for me during these three years. I also want to thank all my former and present colleagues and the Ph.D.-students at the division of Geodesy for all the support and for the interesting discussions we had during lunches and coffee breaks. I am thankful to the Swedish Research Council for Enviroment, Agricultural Sciences and Spatial Planning, FORMAS, for sponsoring this research. I further wish to thank Michael Skoglund at the Swedish National Road Administration and Bo Jonsson at the National land survey for letting me access the ftp-archive with GPS-observations from the permanent reference stations in Gothenburg. It saved me a lot of headache and several hours of work. I am also indebted to my former and future colleagues at WSP Sweden AB for the encouragement to continue my study as well as for the economical support provided for participation in the meetings of the Nordic Geodetic Commission and all the internal events and meetings at WSP. Finally I want to express my gratitude to my family and friends that have been patient with me being hard to reach and difficult to meet. But without you being there, this work would have been difficult to finish. 2 Contents 1 Introduction 6 1.1 Author’s contribution 8 2 Observation Equations 9 2.1 Pseudorange observations 9 2.2 Phase observations 10 2.3 Phase differences 13 2.3.1 Single differences 13 2.3.2 Double differences 15 2.3.3 Correlations 16 2.3.3.1 Single differences 17 2.3.3.1.1 Single differences in a multipoint solution 18 2.3.3.2 Double differences 19 2.3.3.2.1 Double differences in a multipoint solution 19 2.3.3.3 Correlation in time 20 2.4 Undifferenced solution 21 2.5 Double differences vs. undifferenced data 22 3 The Model 24 3.1 The Kalman filter 24 3.1.1 The prediction step 25 3.1.2 The filtering step 27 3.1.3 Summarising of the Kalman filter 28 3.2 Parameter modelling 28 3.2.1 Position and velocity 29 3.2.2 Receiver clock 31 3.2.3 The Atmospheric delays 33 3.2.3.1 Ionospheric delay 34 3.2.3.1.1 Deterministic mode 36 3.2.3.1.2 Parameter modelling 37 3.2.3.2 Tropospheric refraction 38 3.2.3.2.1 A priori models 41 3.2.3.2.2 Mapping function 42 3 3.2.3.2.3 Parameter modelling 43 3.2.4 Receiver antenna models and multipath 44 3.2.4.1 NGS antenna parameters 45 3.2.4.2 Modification of the NGS antenna parameters 46 3.2.4.3 Multipath 49 3.2.5 Common errors 50 3.3 Updated observation equations and observation weighting 50 3.3.1 Updated observation equations at the reference stations 51 3.3.2 Updated observation equations at the rover stations 52 3.3.3 Observation weighting 53 3.3.3.1 Weighting methods 54 3.4 Complete model 56 4 Details of Implementation 58 4.1 Read data files and generate ephemerides polynomial coefficients 59 4.1.1 Observation and orbit parameters in RINEX format 60 4.1.2 Precise ephemerides 60 4.1.3 NGS antenna files 61 4.1.4 Generate standard ephemerides polynomial coefficients 61 4.2 Start values of unknown parameters 64 4.3 Fill in matrices L, H, R and Add/Remove states 65 4.4 Cycle slip detection 69 4.4.1 Single frequency phase / code combinations 70 4.4.2 Dual frequency phase combinations 70 4.4.3 Geometry free solution 71 4.4.4 Implementation of cycle slip detection 72 4.5 Phase ambiguity fixing 72 4.6 Output parameters, standard errors 73 5 The simulator 75 5.1 Stochastic processes 75 5.2 The flow in the simulator 77 5.2.1 Initialisation of the simulator 77 5.2.2 Simulator loop and output 79 4 6 Tests 81 6.1 Tests on simulated observations 81 6.1.1 Deformation detection 81 6.1.2 Influence of the NGS-antenna parameters 84 6.2 Tests on real observations 89 6.2.1 The observations 89 6.3 Calculations with real observations 91 6.3.1 Static calculations 91 6.3.2 Kinematic calculations 94 6.3.2.1 Kinematic results calculated with Trimble Total Control 95 6.3.2.2 Undifferenced GPS in kinematic mode 97 6.3.3 Different weighting procedures 102 6.3.4 Deformation detection with real observations 104 7 Summary, Conclusions and Further Research 107 7.1 Summary and Conclusions 107 7.2 Further developments and research 110 8 References 112 9 Appendix A 117 5 1 Introduction Everything on earth is in motion. The main part of these motions is very slow and we can not sense them with our human senses. Other motions are larger and more hazardous, as earth quakes and land slides, and if we are unlucky be killed by them. Most of these dangerous motions are preceded by slow motions of the type that we cannot sense. By the use of special sensors, it is possible to detect these small motions and predict when a catastrophe is to come. This is what this thesis is about the developing of a system which can detect small motions and alarm if something unpredicted is about to happen. There are several different types of sensors that can be used to detect slow and small motions. They either work in relative or in absolute mode. In relative mode all sensors are placed on the object that is moving and the sensors sense relative changes among each other. Absolute sensors, on the other hand, are placed both on the moving object and on some non moving objects away from the moving object. The benefit of the absolute method is that the absolute change is sensed but a problem is that there is often a long distance between the moving and the fix objects. During a long time motion monitoring has been a subject for surveying engineers. Several different techniques have been used to measure movements as triangulation with total stations, precise levelling, close range photogrammetry, laser scanning and with satellite methods as GPS, DORIS and SLR. Common within all these methods are that they are measured in repeated campaigns and the result is presented determined after the campaign is finished. If an alarm function is wanted or if the motions must be monitored all of the time, the mentioned systems will not fulfil the needs, since they do not operate in real-time. A type of sensors that have become very popular during the last 15 years for motion and deformation monitoring are the GPS-receivers. The GPS-technology has some good properties; one is that it possible to measure baselines with a high accuracy over long distances without any demand of a line-of-sight between the receivers. This makes it possible to perform absolute motion and deformation monitoring where the distance between the moving area and the fix points are long. There are several different movement and deformation monitoring systems available on the market today like • GRAZIA, developed at Graz University of Technology, Gassner et al. (2002) • GOCA, (GPS based online control and alarm system) developed at Gachhochschule Kalsruhe, Jäger and Kälber (2004) 6 • RT-MODS2- Real-Time Monitoring Of Dynamic Systems, developed at Istambul Technical University, Ince and Sahin (2000) • GNPOM, Geodetic Navstar - Permanent Object Monitoring, Geo++®, (www.geopp.de) • Motion Tracker, by Trimble (www.trimble.com) The deformation monitoring systems can be separated into three categories according to their way of using the observations. The first category is the post processing category, where Motion tracker from Trimble belongs. The observations from the GPS- receivers in this category are stored in observation files that are placed in a file library. The baselines are calculated with a given time interval and the result is stored in a database from which one can perform the deformation analyses. This is not a true real- time system but still a system that perform deformation analyses automatically, however with a little time delay. The second category uses the result calculated in the receivers in RTK-mode (Real Time Kinematic) for deformation monitoring. RT-MODS2 and GOCA are typical softwares of this category. In RT-MODS2 the coordinates from the RTK solution are directly used in the deformation monitoring. GOCA uses the same information but instead of taking the coordinates directly, it first performs an adjustment of all the observations from the same epoch in a traditional network adjustment. The benefit of this approach is that outliers can be detected as well as movements in the static receivers. A problem with this approach is that the correlations among the baselines are not treated correctly. The third category is the one that uses raw data; all observations are sent into the central computer, where the calculations are performed. GRAZIA and GNPOM are softwares that follow this approach. The differences between these softwares are that GARZIA is based on double differenced observations while GNPOM is based on undifferenced observations. More about the mathematical principles of the differenced and the undifferenced approaches follows in the next chapter of the thesis. The goal with the project, which this thesis is a part of, is to build a system for real- time movement detection at mm level, based on GPS observations. The system will consist of two or more GPS receivers, data-links between them and a central computer with software developed to detect deformation and an alarm system. As one part of the research a software based on undifferenced GPS observations is developed. The reason for developing a new software is to fully understand each step in this type of software and to have a platform for further research within the area. For the evaluation, the software is developed in object oriented Matlab code, which in the 7 future will be converted into a programming language that is more adapted for real- time applications. 1.1 Author’s contribution This thesis describes the fundamental process in developing a deformation monitoring software. The author has contributed with a software, based on undifferenced GPS observations, that are able to calculate coordinates and detect deformations. In the beginning of the second chapter, the observation equations for GPS observations are introduced. Thereafter follows a comparison of the undifferenced and double differenced algorithms to compare their advantages and disadvantages. The theory of each of these technologies is mainly known information summarised to motivate the undifferenced solution. The undifferenced model we use is described in Chapter 3 together with deterministic models of all unknown parameters that are estimated in the software. The Kalman filter described in this chapter is a known general mathematical approach for solving the state parameters of a dynamic system. The author has to find a suitable dynamic model for each parameter and derive corresponding transmission and process noise covariance matrix. This part of the thesis is performed in collaboration with supervisor Milan Horemuz. In Chapter 4, follows a description of the implementation details. Two new algorithms are presented in this chapter: first an algorithm that unifies the calculation methods for the satellite coordinates, presented by Horemuz et al. (2006), and then an algorithm that makes it possible to use GPS-antenna calibrations from NGS (U.S. National Geodetic Survey) in an arbitrary direction. The author has contributed in the paper where he implemented the algorithm in Matlab and did the numerical calculations. The new antenna orientation algorithm is developed by the author. To study the performance and simplify the debugging procedure, a simulator is generated, which is described in Chapter 5. The contribution of the author in this chapter was to implement the same type of stochastic and deterministic models in the simulator. A series of calculations are done with the developed software, the result from these are presented in Chapter 6. The author has here compared the result from the developed software with the result from commercial softwares. Initial tests with different weighting models are also done here. Finally in Chapter 7, summary and conclusions and some proposals for further research are presented. 8 2 Observation Equations Three types of observations can be done with a geodetic GPS-receiver: pseudorange, phase and Doppler observations. These observations are done with the receivers in epochs with a fix time interval i.e. each second. The pseudorange observations are based on the PRN-code message that is modulated on the carrier wave, the phase observations are based on the fractional part of the carrier phase and an integer number representing full wavelengths from a reference timet and the Doppler count 0 observations, represent the difference between nominal and the received frequencies between two observation epochs. The purpose of this chapter is to derive the observation equations for both pseudoranges and phase observations and to introduce the error sources that influence them along their travel path from the satellite to the receiver. The Doppler observations are not used in this thesis and are therefore not described further within the report. The derivation of the observation equations follows the derivation given by Leick (2004) and Hoffmann-Wellenhof et al.(2001). When this is done two different approaches of positioning with GPS-observations are introduced: differential and undifferenced positioning. At the end of this chapter the advantages and disadvantages of each approach are discussed to motivate why the use of the undifferenced approach in this thesis. 2.1 Pseudorange observations Pseudorange observations are based on the PRN-code message that is sent out from each satellite modulated on the carrier phase signal. The main idea with the pseudorange observations is to determine the true travelling time from the satellite to the receiver and then to multiply it with the speed of light, to determine the distance between the satellite and the receiver. The travelling time is determined in the receivers by generating a replica of the PRN-code message in the receiver and then maximising the correlation between the incoming signal and the generated signal by time shifting the latter in the instrument. The total time shift will then correspond to the travelling time from satellite to receiver. The pseudorangePSbetween a satellite antenna S and a A receiver antenna A can be expressed as: PS(t )=(t −tS)c (1) A A A wheret and tS are nominal times of reception in the receiver and emission of the A signal from the satellite, respectively c is a constant which represents the speed of light in vacuum. From now on we use subscripts for the receivers and superscript to for the satellites. Nominal times in the receivert and satellitetSare related to true GPS-times A t and tS respective as A,GPS GPS 9

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Undifferenced GPS for Deformation Monitoring Johan Vium Andersson Licentiate thesis in Geodesy Royal Institute of Technology (KTH) Department of Transport and Economics
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