Sensitivity-Analysis Based Robust Estimation And Its Application In GPS Positioning

This dissertation mainly focus on the theory of sensitivity-analysis based robust estimation(SARE) and its application in navigation and positioning in GPS, aiming at solving practical problems in GPS data processing. The main works and contributions are summarized as follows:1. A stochastic modeling procedure for double-differencing (DD) GPS observation model is introduced. Based on the so-called partial continuation model with exact finite measurements, the temporal correlation coefficient of every satellite pair is estimated. Then a data transform matrix is constructed to remove the time correlations of DD measurements. The windowing method is employed to obtain a more realistic VCV matrix at last. Experimental results show that this method can mitigate effectively the impact of residual systematic errors on DD GPS measurement.2. Introduce basic principles of M-estimation and give several different weight functions used in current robust estimation, then a contrast between three main equivalent weight functions (Huber methods, Danish method and IGGâ…¢method) is given in an example. Because all the existing down-weighting strategies are based on LS residuals or standardized LS residuals, in which either the local reliability measure is ignored, or the computational load is heavy. To circumvent these drawbacks, the theory of sensitivity-analysis based robust M-estimation is introduced, and three kinds of modified equivalent weight functions are given.3. Experimental results obtained from traditional methods and improved methods with different equivalent weight functions indicate that the computing efficiency using the improved methods and the precision of position are better than using traditional methods. Then a contrast between three improved methods (Huber method, Danish method and IGGâ…¢) is given through the aspects of times of iterative, equivalent weight factor, computing time and results. The experimental results show that, IGGâ…¢method is more effective than the other two methods.4. Critical values of the equivalent weight functions are often fixed in constants by experience in robust estimation. Sometimes, IGG equivalent weight function can not work, when a rank-defect arises in the iteratives. To make the robust estimation success and more advisable, a scheme based on SARE theory with two steps called variable factor iterative method is put forward. The result of experiment shows that the variable factor iterative method can solve the problem and effectively cope with the corrupt influence of the outliers.5. Based on SARE theory, three baseline examples, including a long baseline, a middle-distance baseline and a short baseline are given in the paper and some helpful conclusions are obtained.6. In order to get the accurate integer ambiguity estimation, an accurate float ambiguity solution should get first. A scheme which using the SARE theory in float ambiguity solution is given. And two experiments of this scheme toward a long baseline and a middle-distance baseline are given. Experimental results show that this scheme can improve the accuracy of float ambiguity and the RATIO value in LAMBDA method. Compared with the former scheme which operates SARE theory after the fix of integer ambiguity, this new scheme can obtain more precise results.7. In the long baseline, the residual system error of double-differencing observation can not be neglected. Just operating robust estimation in this long-baseline can not get the precise estimation of parameter. Accordingly, a scheme is proposed to overcome this situation,in which the DD observation data is transformed before robust estimation. Experimental result obtained from a long baseline indicates that this scheme can get more accurate results than the scheme only include robust estimation.8. At last, application of SARE theory on sequential adjustment is discussed.