Soutenance mémoire
GPS segments
Navstar Global Positioning System known as GPS, owned by the United States Government (USG) and operated by the United States Air Force (USAF), is the earliest and the most accurate space-based radio-navigation system of the world. This project, which has been started in 1973 and completed in 1994, provides accurate Positioning, Navigation, and Timing (PNT) 24 hours a day, in all weather and all over the world. GPS consists of three main segments: Space, Control and User segments.
The Space Segment: The Space Segment (SS) consists of six orbital planes at an altitude of about 20,200 km above the earth’s surface at an inclination angle of 55° with respect to the equatorial plane.
Each orbit has four equally-spaced slots for satellites, which is covered by at least one operational satellite all the time. For global coverage, USAF ensures availability of at least 24 satellites for 95% of the time. With this arrangement we always have at least 4 visible satellites, which is the minimum required number of satellites to calculate 3D position and time. GPS satellites carry atomic clocks with nanosecond accuracy and broadcast continues radio frequency signals on the two carrier frequencies of L1 (1575.42 MHz) and L2 (1227.6 MHz).
The Control Segment: The Control Segment (CS) is a ground-based global network to track and monitor GPS satellites consisting two master control stations, 16 monitoring stations including six from the Air Force and 10 from the National Geospatial-Intelligence Agency (NGA), 4 ground antennas and 8 Air Force Satellite Control Network (AFSCN).The monitoring stations collect data from each visible satellite and send them to the master control stations. The master control stations are responsible for computing extremely precise satellite orbits and send them, as an updated navigation massages, to the ground antennas.
Then the ground antennas send updated navigation massage to each visible satellite. Finally in order to increase tracking robustness, the control segment is tracked by eight AFSCN remote tracking stations.
The User Segment: User Segment (US) consists of all GPS receivers which receive and process GPS signals in order to calculate position and time.
Navigation data structure
Navigation data with 50 bps rate is a 1500 bit-long frame which is consists of 5 subframes and each 300 bits long. Each subframe contains 10 words and each of them has 30 bits length. By 50 bps rate, a transmitted subframe lasts 6 s, one frame lasts 30 s and one entire navigation massage lasts for 12.5 minutes, Each subframe contains 10 words which always starts with two words, the telemetry and handover word followed by 5 subframes as follows:
telemetry (TML) is the first word that is repeated every 6 s. TML contains 8-bit preamble and 16 reserved bit and parity which are used for frame synchronization;
handover (HOW) contains of 17-bit of time of week and antispoofing flag followed by the subframe ID;
satellite clock and health is used to calculate navigation message transmission time and satellite information is used to inform whether the data can be trusted or not; satellite ephemeris data subframe is used for satellite position calculation;
support data subframe is contained almanac, ionospheric model, UTC parameters, etc. The almanac data is the ephemeris data with reduced precision. Each satellite send almanac data for all GPS satellites while each satellite only transmits ephemeris data for itself.
GPS measurement and associated errors
Most of the GPS receivers provide three types of measurements: Pseudorange, Carrier phase, and Doppler. These measurements can be used either directly or using differential techniques to calculate Position, Navigation and Timing (PNT) parameters, (Scaccia, 2011).
Code measurement and associated errors
The earliest and the easiest GPS positioning method is based on the code measurement. Receiver counts the amount of chips of the received C/A code and the one which is generated by its oscillator. Then it can calculate time difference of the corresponding GPS satellite and itself. By multiplying the radio signal’s speed in vacuum, the distance between the receiver and the GPS satellite (pseudorange) can be computed. Each satellite transmits its Keplerian elements in the World Geodetic System established in 1984 (WGS-84) reference system to calculate its position in the orbit. So we have a sphere with the center of satellite and the radius of pseudorange. Therefore by using a least-squares method or Kalman filter, with at least four satellites a 3D position and the receiver clock error can be computed, (Delaporte, 2009; Lu, 1995; Scaccia, 2011).
Carrier phase measurement
The GPS satellites have two constant carrier frequencies which are centered at 1575.42 and 1227.60 MHz. In order to track satellite signals, a receiver first establishes a carrier and code phase lock so that it can measure the range difference over time. Then not only the receiver can measure difference between the received phase signal and the generated one, but also it can measure the phase difference over time as long as it does not lose the lock. By this way, the receiver can track the range changing with respect to the satellite, however, it contains environmental errors. As a result, the true range between the receiver and the satellite must be estimated or inferred. Since this method use pure carrier frequency, and all cycles are the same, there is no way for receiver to distinguish one cycle to another and in order to count the number of travelled signal cycles. This ambiguous number is known as integer ambiguity, which is needed to be solved in a quick and reliable method for each epoch.
Important references for GNSS navigation
Earth centred earth fixed reference frame
The Earth Centred Earth Fixed (ECEF) reference frame is a commonly used navigation frame, on which their axis are fixed with respect to the earth and its origin is the mass center of the earth. The z axis is pointing toward true North Pole (not the magnetic pole). The x axis points toward the intersection of the equator and International Earth Rotation and Reference Systems Service (IERS) reference meridian which defines the zero degree longitude. The y axis completes the right handed orthogonal set. This is an important reference frame in navigation because the axis is fixed with respect to the earth.
Local frame
The local frame is a frame that is fixed with respect to a chosen position and its origin is the desired position (i.e. navigation system position or user position or the mass center of anobject). The x axis is always pointing toward the East and it is known as E axis. They axis is the projection of the vector pointing to the North Pole into the orthogonal plane to the earth surface and it is known as North (N) axis. The z axis completes the right handed rule and it is known as Up (U) axis. This frame is an important frame in navigation because it is convenient to know the user’s position with respect to the East, North, and Up.
Methods of GPS ambiguity resolution
Carrier phase measurement is the result of the phase difference of the received signal relative to the replica that is generated by the receiver. Therefore the fractional part of the phase difference can be measured within a millimetre accuracy (Verhagen et Teunissen, 2006), which is the reason why carrier phase measurement is much more accurate than code measurement. However the initial number of wavelengths from satellite to receiver is unknown and needs to be estimated for each satellite in view.
Since calculating the ambiguity of the carrier phase measurement is the key to use in high accuracy applications, we review here the most commonly used methods in literature. Based on the literature, there are two main categories of ambiguity resolution methods consisting of (Crassidis, Lightsey et Markley, 1999; Teunissen, Giorgi et Buist, 2011): dynamic or motion-based; search-based, motionless or instantaneous.
The first category is dynamic or motion-based which uses a collected data set in a certain period in which the ambiguity remains constant and provides a batch solution. These methods are based on the satellite and body frame motion. These methods are not fast and they need high amount of memory to save the collected data and non-coplanar baselines, (Wang et al., 2009b). Despite these disadvantages, this method is highly reliable because of several criteria to accept the solution. Statistical checks of the error and considering the closeness of the floating point solution and the actual integers are among those criteria (Crassidis, Lightsey et Markley, 1999).
The second category which is usually called motionless or instantaneous or search-based methods are based on estimating a set of integers of one epoch and search for the best solution, (Hatch, 1991; Park et Teunissen, 2003). Due to the high convergence speed, this method is a suitable method for real time applications, (Li et al., 2004; Park et Teunissen,2003), but since it can converge to an incorrect solution in the presence of noise especially multipath, all solutions should be checked several times before selecting the final solution, (Teunissen, 1997; Yoon et Lundberg, 2002). The instantaneous category, consists of three steps: float solution, integer ambiguity resolution and integer ambiguity validation. The first step usually is the result of an estimation process consisting of estimation the ambiguity in real numbers. The second step can be done with three types of methods: Simply rounding, integer bootstrapping and Integer Least-Squares (ILS) estimator, (Zheng, 2010). The instantaneous category can be divided into three types of search domains, (Kim et Langley,1999):
The measurement domain: It uses the C/A code or P-code directly to calculate the integer ambiguity of the corresponding carrier phase measurement. In order to achieve this ambiguity with a proper accuracy, usually observation combination of L1 and L2 is needed, (Cocard et Geiger, 1992; Collins, 1999);
The coordinate domain: The coordinate domain is the biggest subcategory in the instantaneous category. Many ambiguity search methods are in this category such as: Least-Squares Ambiguity Search Technique (LSAST), Fast Ambiguity Search Filter (FASF), Ambiguity Function Method (AFM), Fast Ambiguity Resolution Approach (FARA), (Kim et Langley, 2000);
The ambiguity domain: The ambiguity domain is known as an efficient with high success rate method and has recently received lots of attention. This method is based on the original search domain transformation in ambiguity domain which is easier and faster to solve, (Teunissen, Giorgi et Buist, 2011). LAMBDA is the most important and well known method in the ambiguity domain.
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Table des matières
CHAPTER 1 INTRODUCTION
1.1 Research problems
1.2 Research objectives
1.3 Research methodology
1.4 Contributions
CHAPTER 2 GPS OVERVIEW
2.1 GPS segments
2.2 GPS signal and data characteristics
2.2.1 Navigation data structure
2.3 Mathematical modelling of GPS measurements and errors
2.3.1 GPS measurement and associated errors
2.3.1.1 Code measurement and associated errors
2.3.1.2 Carrier phase measurement
2.3.1.3 Doppler
2.3.2 Differential GPS
2.3.2.1 Single difference
2.3.2.2 Double difference
2.3.2.3 Triple difference
2.3.3 Other residual errors
2.3.3.1 Phase center variation
2.3.3.2 Multipath
2.4 Important parameters in satellite geometry
2.4.1 Elevation and azimuth
2.4.2 Quality metrics of GNSS constellation
2.5 Important references for GNSS navigation
2.5.1 Earth centred earth fixed reference frame
2.5.2 Local frame
2.5.3 Body frame and Euler angles
2.6 Rotation Matrix
CHAPTER 3 LITERATURE REVIEW
3.1 Methods of GPS ambiguity resolution
3.1.1 Ambiguity function method
3.1.2 Least-squares ambiguity search technique
3.1.3 Fast ambiguity resolution approach
3.1.4 Fast ambiguity search filter
3.1.5 Least-squares ambiguity decorrelation adjustment
3.1.6 Summary
3.2 Attitude determination methods
3.2.1 Direct method for attitude determination
3.2.2 Baseline method for attitude determination
3.2.2.1 Quaternion method for attitude determination
3.2.2.2 QUEST method for attitude determination
3.2.2.3 SVD method for attitude determination
3.2.2.4 FOAM method for attitude determination
3.2.2.5 ESOQ method for attitude determination
3.2.2.6 ESOQ2 method for attitude determination
3.2.3 Summary of attitude determination algorithms
3.3 GPS and GLONASS integration
3.4 Conclusion
CHAPTER 4 ADS ALGORITHM DESIGN
4.1 Data selection
4.2 Single point positioning algorithm with pseudorange
4.3 Presentation of designed baseline estimation algorithm
4.3.1 General optimization problem
4.3.1.1 RLS mathematical procedure
4.3.2 Ambiguity resolution using LAMBDA method
4.3.3 Check the constraint
4.4 Attitude determination using the SVD method
CHAPTER 5 IMPLEMENTATION AND ANALYSIS OF THE RESULTS
5.1 ADS performance analysis, test case 1
5.2 ADS performance analysis, test case 2
5.3 ADS performance analysis, test case 3
5.4 ADS performance analysis, test case 4
CHAPTER 6 CONCLUSION AND FUTURE WORKS
6.1 Conclusion
6.2 Future works
LIST OF REFERENCES
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