Research On Bayes Filtering Algorithm In Kinematic Positioning With Prior Information

In kinematic positioning, navigation and satellite orbit-determination moving of target is often constrained by external factors which are often known functional formulas or theoretical relationships. These factors which may are anticipatory knowledge are known as prior constraint information, such as non-negative parameter, integral parameter, the upper and lower bound of the state, the form of noise interfere, the size of noise interfere, the range of noise interfere and their statistical distribution properties. According to the actual situation of kinematic positioning, it is obvious that making rational use of constraints information which is based on objective conditions can simplify models, improve the accuracy of parameter estimation and well control the filtering. Because the existence of the state constraint condition changes the probability structure of kinematic positioning and brings a certain degree of difficulty of problem analyzing and filtering solving. In practice, the commonly used method is to eliminate some state parameters through the state constraint equations, and then deal with it as an average filtering. For some nonlinear, such treatment often makes the calculation complex, and changes the original filtering equation, therefore it is inconvenient to use in practice. Due to the development of science and technology, in kinematic positioning, there are more means of observing and more observation data accumulated, so that we get increasingly understanding of any observation objects'physical and mechanical properties, and the possibility of establishing constraints according to priori information. It is relatively reliable to describe all kinds of priori information by using constraints. So if you can resolve the calculation and accuracy analysis of the dynamic filtering with priori restraint information, it will be widely applied to data processing in kinematic positioning, and meanwhile can promote the filtering theory to the case with a priori restraint information, so that it can make kinematic filtering data processing theories fully developing and perfecting.In this paper, the status and the existing problems of kinematic positioning filtering algorithm with a priori information have been studied, Main contributions are as follows1. The study about the effects of kinematic positioning that caused by abnormal noise, and temporal series which know how to use the observations and the predicted value, can eliminate its influence. In kinematic positioning, when the observations were contaminated, we can give a robust Bayes filtering algorithm which can resist the abnormal influence well, gross errors belong to the case that the observations are contaminated, so the method which was referred can resist the effects that caused by gross errors. We don't know either the existence of gross errors or the size of the contaminated rates, consequently, it is very important to on-line estimation. The paper provides us the kinematic positioning method and the way of contamination rates.2. This paper studied the filtering algorithm of the state variable which exist equality restriction, and advanced the solution according to sequential adjustment and the adaptive algorithm. This paper also studied the method which introduced to reserve the state parameter, added the restricted conditional equation of the mathematics model in Kalman filtering, and deduced Kalman filtering recurrence equation under the restricted condition, its style was similar to normal Kalman filtering recurrence equation, This paper could add a restricted conditional correction in the predicted value and its covariance matrix, so it is extraordinary convenience in the application.3. This paper studied the filtering algorithm of the state variable which existed inequality restriction, and supplied two different filtering methods to deal with inequality restriction, first, solved the nonrestrictive filtering solution, and then continued to optimize it. Second, This paper could get gain matrix in allusion to its inequality restriction, and gained the filtering state estimation. Theoretical analysis and simulating calculation show that we can improve the filtering precision through making the best of restricted priori information, consequently, improve the precision of kinematic positioning.4. This paper drew on the idea that we sought the optimum solution in real number, at first, sought the local optimum solution during the searching process for the integer solution, and then sought the next optimum solution along the direction of the fastest decline in, at last, given a filtering algorithm for kinematic positioning of an effective measurement equation, which contained unknown integer parameter. Main contributions are as follows1) Given the integer parameter recursive estimation of the float solution.2) Achieved to estimate the various interval of integer parameter 9 dynamically.3) Given a fast algorithm on estimation of integer parameterθ. The experiment showed that the newly algorithm greatly improved the efficiency of the traditional branch-bound algorithm and existing relevant algorithm. It could be applied to the kinematic positioning solution of GPS as the ambiguity was unknown, and the determination of the integer ambiguity.5. For Vehicle Kinematic Positioning under road condition, H∞Filtering algorithm with road constraint is proposed. Using the characteristics of ground targets, the algorithm sets up a system model with road constraints and the corresponding H∞Filtering algorithm is derived. The simulation results show that the proposed H∞Filtering algorithm with constraint condition has a better state estimation performance and higher filtering accuracy than the standard H∞Filtering algorithm and Kalman Filter algorithm. It has practical significance for Vehicle Kinematic Positioning in a complex environment.6. In order to reduce the system errors arising from linearization, we studied the application of nonlinear Bayes Filtering and Particle Filtering in Kinematic positioning, focused on the research of the solution that dynamic equation is linear but the observation equation is non-linear, and given the corresponding Bayes Recursive Filtering and Particle Filtering algorithm.In this paper, the study of the Kinematic Positioning Filtering theory with a priori constraint information is comprehensively and systematically for the first time. This paper carry out a more detailed research in getting information with the priori constraint, model building, resolving methods of the filtering, and giving some new resolving methods of the filtering. In the non-linear Kalman filtering. The papers studied of some new algorithms for the non-linear characteristics in measurement equation of the kinematic positioning and navigation. The paper compared the given algorithm and the existing algorithm, made data simulation and took some solution example, and consequently verified the validity of the algorithm and made the algorithm well be applied to engineering calculations and military navigation.