Researches Of Nongaussian/Nonlinear Filtering Algorithms And Its Applications In GPS Kinematic Positioning

This dissertation mainly focuses on the theories and algorithms of Non-Gaussian/Nonlinearfilter, combining closely with GPS dynamic positioning, especially under the condition ofNon-Gaussian colored measurement noises. The main works and contributions are summarizedas follows:1. In this paper, the present research situation of Nonlinear/Non-Gaussian filter issystematically studied and the advantages and disadvantages of each method is compared.2. The statistical characteristics of GPS measure noises are analysesed by choosing kurtosisand Q-Q plot for measure methods of non-gaussian distribution, Meanwhile, choosingautocorrelation coefficient methods for judgment standard of the colored noises. The researchshows that GPS measure noises is weak non-gaussian colored noises on best observationcondition, Conversely, if the observation condition deteriorate, GPS measure noises turn intonon-stationary non-gaussian colored noise.3. EKF,UKF,CKF and PF are compared and analyzed each other. Accuracy, Consistency,Confidence has been adapted to evaluating the performance of filter. with the emphasis on thefilter consistency. Research shows that the linearization error of the GPS measurement equationmay be overlooked if the initial error is little. Instead, non-gaussian noises exert moreremarkable influence on filter.which reduce filter consistency. Particle filtering is a quiteeffective algorithm to improve the consistency of filter, but, enormous computation and particledegeneracy phenomenon influenced the application of particle filter in engineering practice field.4. It is a effective way of compensating model error caused by non-gaussian colored noisebased on time series parameter model. AR (1) model is frequently used, but, It was found thatinaccurate model parameters of AR (1) cannot ensure the consistency of filter. Therefore, aadaptive algorithm based on real-time estimation of AR(1) model parameters is presented, whichimproves the accuracy and consistency of filter.5. A adaptive two-stage filter based on MA model is presented, Experiments show that thealgorithm has good performance aiming at actual instance that complex colored noise andconsidering the time-varying model parameter.6. A adaptive filter based on polynomial AR model was presented, AR model parameteronly related with the degree of polynomials can be previously determined. The computationalefficiency of filter is greatly improved.7. By analyzing semi-parametric model and its estimation method, the surveying meaningsof regularization matrix used in Penalized Least Squares estimation for semi-parametric modelswere presented. In order to solve the over-fitting problems existing in the kernel functions estimation for semi-parametric model. a regularization kernel estimation for semi-parametricmodel is presented, which improves the generation ability of the model.8. The filtering-compensation method based on regularization kernel estimation waspresented. The algorithms operate based on data completely, without using transcendentalinformation about the complicated colored noise. Which particularly suits for the situation thatcolored noise can not be separated with system noise.9. The approximation capability of gaussian mixture model for Non-Gaussian distributionis analyzed.A adaptive gaussian mixture EKF and a gaussian mixture AR EKF based gaussianmixture ARMA model were presented. Through the theoretical analysis and the results ofcalculation examples, it is shown that filter is suitable for universal non-gaussian colored noise.the method not only improves the accuracy and consistency of filter estimation, but also thecomputations is very small compared with particle filter.