Research On Kinematic GPS Positioning Relative To A Moving Reference

On-the-fly GPS positioning relative to a moving reference, referred to as KINRTK in, this thesis, has many applications, such as fleet management, battlefield command, formation flying, vehicles positioning, satellite-to-satellite orbit determination, aerocraft safety approach, and others, where a static reference is difficult to establish. In this application, the absolute positions of the objects are not important but rather their relative positions, so that the configuration of the reference station with precisely known coordinates is not mandatory. High relative positioning accuracy and reliability are required. Most of the existing methods of relative positioning assume that the precise position of a reference station is given a priori. Thus, the accuracy of the relative positioning only depends on the measurement errors. However, in this research, such a precondition is not given. Therefore, those previous approaches cannot be directly used for this research. Modifications are required to process the kinematic data simultaneously. The impact of these modifications on the effectiveness of relative positioning is to be investigated in this thesis.To achieve high positioning accuracy, the double-differenced GPS carrier phase method is usually adopted. When the inter-platform distances are short, e.g., less than 10 km, double differencing can largely reduce spatially correlated errors in the carrier phase measurements. Satellite and receiver clock errors are cancelled, regardless of the inter-platform distance. When the remaining errors are small, centimeter-level accuracy relative positions can be obtained with fixed integer ambiguities. High accuracy relative positioning depends mostly on successful integer ambiguity resolution of the double-differenced carrier phase measurements. Before the carrier phase observable can be utilized as a precise range information its inherent integer cycle ambiguity must be resolved and carrier phase positioning rely on the ambiguities being constant. Unfortunately, high user dynamics, the receiver's oscillator, shadowing and multipath can cause cycle slips, i.e. jumps of the carrier phase observable by an integer multiple of wavelengths. Every cycle slip would deteriorate the high accuracy of the affected carrier phase range and also that of the position derived from such carrier phase observables. Therefore, integer ambiguity resolution and cycle slips detection and repairing are two of the crucial problems to resolve for high accuracy relative positioning.Observations are made to derive certain parameters. However, observations often contain biases and errors. To reduce the effect of the errors and assess the accuracy of the solution, redundancy is required. That is, more than the minimum number of observations is required to determine the estimated parameters. These observations must be adjusted so that the solution will be consistent with these adjusted observations. To adjust observations and to obtain the desired parameters, the method of least-squares estimation is often used. In least-squares estimation, parameters and corrected observations are derived by minimizing the weighted sum of the squared residuals. As well known, least-squares estimation can only process a linear system, while the desired parameters, rover station coordinates, are contained in the geometric range between the satellite and the receiverantenna. Therefore, linearization is the basic work in GPS data processing. Two modes of linearization can be found in the GPS literature. In the first approach, observation equation is linearized by rover station coordinates, whose estimated parameters are the correction to the approximated station coordinates. The other one linearizes the equations with baseline vector between rover station and the reference, whose estimated parameters are the correction to the approximated baseline vector. There are three presupposition assumptions in the former approach, i.e., known precise reference station coordinates, the coordinates and observables are in the same coordinate system, and the approximated rover station coordinates are also in the system. Obviously, these assumptions do not exist in KINRTK, and the equation must be linearized by the latter. A simple and efficient linearization method is presented, and the differences between KINRTK and other GPS positioning modes are analyzed.Most receivers attempt to keep their internal clocks synchronized to GPS Time. This is done by periodically adjusting the clock by inserting time jumps. Two typical examples of receiver clock jumps exist in different manufacturer's receivers. The first example is a millisecond jump which occurs when the clock offset becomes larger than ± 1 millisecond, the receiver corrects the clock by ± 1 millisecond. The second example is a very small clock jump which occurs every second and the jumps are often small. At the moment of the clock correction, two main effects are transferred into the code and phase observables. The effects of the geometric range corresponding to the clock jump are common to all measurements at the moment of the clock jump at one receiver. By single-differencing (SD) the measurements between satellites or double-differencing (DD) the measurements (that is, differencing between receivers followed by differencing between satellites or vice versa), the common effects can be removed. However, the effects of the geometric range rate corresponding to the jump are different for each observation. They cannot be removed by the SD or DD operation. However, like cycle slips, their effects on the code and phase observables are more or less known to users and hence it is possible to detect and remove their effects almost completely in both the measurement and parameter domains.The quality of GPS positioning is dependent on a number of factors. For attaining high-precision positioning results, we need to identify the main error sources impacting on the quality of the observations. In terms of data processing, cycle slips, receiver clock jumps and quasi-random errors are the main sources which can deteriorate the quality of the observations and subsequently, the quality of positioning results. Cycle slips are discontinuities of an integer number of cycles in the measured (integrated) carrier phase resulting from a temporary loss-of-lock in the carrier tracking loop of a GPS receiver. In this event, the integer counter is reinitialized which causes a jump in the instantaneous accumulated phase by an integer number of cycles. The detection and correction of cycle slips is needed if accurate positioning is to be carried out. Cycle slip detection and correction requires the location of the jump and the determination of its size. It can be completely removed once it is correctly detected and identified. Slip detection and repair still represents a challenge to carrier phase data processing even after years of research. For completeness, a short description of the development of strategies for detecting and determining cycle slips over the past two decades or so is presented. For the most part, techniques used in the detection and determination of cycle slips have not changed drastically since the first methods were devised in the early 1980s. The focus has alwaysbeen on attempting to develop a reliable, somewhat automatic detection and repair procedure. All methods have the common premise that to detect a slip at least one smooth (i.e., low noise) quantity derived from the observations must be tested in some manner for discontinuities that may represent cycle slips. The derived quantities usually consist of linear combinations of the undifferenced or double-differenced L1 and L2 carrier-phase and possibly pseudorange observations. Examples of combinations useful for kinematic data are. the geometry-free phase (a scaled version of which is called the ionospheric phase delay), and widelane phase minus narrowlane pseudorange. Once the time series for the derived quantities have been produced, the cycle-slip detection process (that is, the detection of discontinuities in the time series) can be initiated. Of the various methods available, a novel approach, called Non-integer Linear Combination (NLC), is proposed.Time-relative positioning is a recently developed method for processing GPS observations. Observe first carrier phases at a station of known coordinates (a geodetic point, for example) for a short period of time (1-2 min). Preferably, the observation rate must be high—e.g., 1 s. The user then moves the receiver and the antenna quickly (e.g., 30 s) toward the station of unknown coordinates located about a hundred meters (depending on the type of transportation) away from the first one, while continuously observing carrier phases. At the second station, phase observations are recorded again for a short period of time (1-2 min). Relative positioning is then obtained by processing carrier phase observations taken at different epochs (and different stations)with a single GPS receiver. The main distinction between time-relative positioning and conventional relative positioning is that in the former there is a combination of observations taken at two different epochs and two different stations with the same receiver to detennine the position of the unknown station with respect to the known station. In other words, simultaneous observations using a second GPS receiver at a reference station are not required, unlike conventional relative positioning. The disadvantage of time-relative positioning compared to conventional relative positioning is that, since observations at both stations are not obtained simultaneously, it is also affected by the temporal "decorrelation" of errors (time variation of errors) in addition to the spatial "decorrelation" of errors also present in conventional relative positioning. In most GPS applications, regardless of surveying modes (static and kinematic) and baseline lengths (short, medium and long), the effects of the epoch-differenced biases and noise (i.e., atmospheric delay, satellite orbit bias, multipath, and receiver system noise) are more or less below a few centimetres as long as observation sampling interval is relatively short (e.g., sampling interval less than 1 minute). Based on high sampling interval assumption, time-relative positioning observation equation is further analyzed, the concept of virtual measurement is applied, which results in a robust linearization scheme. A new cycle slip detection approach based on time-relative positioning theory is studied for the first time, and valuable unrecognized knowledge of relation between satellites geometry and cycle slip detection is obtained.GPS carrier phase positioning has a higher accuracy than code positioning, assuming the integer ambiguity is correctly fixed. OTF ambiguity resolution refers to the case when the ambiguities are resolved when at least one receiver is moving, i.e., when the receiver is in kinematic mode. It differs from the static ambiguity resolution in two ways: In kinematic applications, errors of measurement cannot be reduced by time averaging because the movement of platforms can significantly change the testing environment; In kinematicapplications, the position and velocity of the object is required for every epoch, so the batch processing cannot be adopted if real-time processing is required. Since less information is available and larger errors occur, OTF ambiguity resolution is more difficult in kinematic than in static mode. Here are some major factors affecting the OTF ambiguity resolution: Selection of observables; Inter-receiver distance; Number and geometry of satellites; Magnitude of GPS errors; Ambiguity search method; Performance required, etc. The major challenges of OTF ambiguity resolution are relative error modeling, and the efficiency and reliability of the ambiguity search technique. There are many methods that have been developed for solving On-The-Fly (OTF) ambiguity since the 1980's. Basically, they have the same strategies to fix ambiguities, namely, float ambiguity resolution, integer ambiguity searching, and the use of a distinguishing test. The float ambiguity and its variance are used to define the initial search point, and the search range of the integer candidates. Therefore, float solution is more important than anything else in ambiguity resolution. In static mode, float solution can be obtained by only processing carrier phase observables, while in the KINRTK application, although redundancy number exists with epochs increasing, no robust float solution can be achieved, and pseudo-range measurements must be added to the adjustment system.In the GPS literature there are two of the many different approaches proposed for integer ambiguity estimation, which have drawn much interest. The two approaches differ in the model used for integer ambiguity estimation. In the first approach, which is the common mode of operation for most surveying applications, an explicit use is made of the available relative receiver-satellite'geometry, named the "geometry-based" model. Integer ambiguity estimation is also possible however, when one opts for dispensing with the relative receiver-satellite geometry, and is named the "geometry-free" model. In fact from the conceptual point of view, this is the simplest approach to integer ambiguity estimation. The pseudo-range data are directly used to determine the unknown integer ambiguities of the observed phase data. Of particular interest here is the shape and orientation of the ellipsoid of standard deviation for the ambiguities. The orientation for the geometry-free model does not change as the number of epoch increases. The orientation of LI and L2 for the same satellite is exactly 37.93°, i.e., the slope is k = XLXI A.12, and the semi-minor axes for the geometry-based are equal to those of the geometry-free model, while the semi-major axes for the geometry-free model are longer than those of the geometry-based model, which means that the ellipse for the geometry-free model always contains the ellipse for the geometry-based model. The geometry is the same for every epoch solution, as long as the stochastic model remains unchanged. The orientation for the geometry-free model does not change for every epoch, while the orientation of two different satellites for the geometry-based model is closer to the axes as the number of epoch increases, which means that these two ellipses overlap each other partly. Combining these two models' advantages, a new concept for ambiguity resolution, called Dual-space Ambiguity Resolution Approach (DARA), involving a search in both spaces at the same time, is proposed.