Research On Nonlinear Filteringalgorithm Based On Convex Optimization

With the rapid development of science and technology, the system is becoming more and more complicated. Due to the nonlinear effects, uncertainty and the higher requirements for the system performance, a more advanced method for system analysis and synthesis is needed. Among all the methods, a special non-linear filtering method is being widely studied at home and abroad.In convex optimization problems, any local extreme point is a global extreme point. Moreover, when the convex optimization problem is a strict convex optimization, the global minimum point is unique. If the problem can be expressed as a convex optimization problem. The global optimal solution of the problem can be acquired without worrying about the algorithm initialization, the step length selection and trap of local minima problems. The convexity can be applied into the nonlinear filtering problem to simplify it due to this great feature. The problem of linear/nonlinear turns into one of convex/non-convex through the view of filter integration and non-linear regression filtering. Therefore, there is great practical significance to study on the convex optimization based filtering method.The optimization algorithms, statistical learning theory and multi-model systems are combined to solve the problem in nonlinear filtering algorithm and its application in inertial systems. The study is conducted in the following aspects.Firstly, to solve the state filtering problem for nonlinear systems, the Lagrange Duality and optimality conditions have been studied under the basic theory of convex optimization. Based on this, nonlinear filtering problem is transferred into convex quadratic optimization problem. The application of convex linear combination in dynamic filtering systems is also derived. The conclusion is drawn that combined filtering is better than single filtering method. The conclusion lays foundation for the following research.Secondly, nonlinear filtering method using support vector machine is studied, which is actually a convex quadratic optimization problem. In order to improve the real-time performance and reduce complexity, a least squares support vector machine is proposed. It solves linear equations instead of convex quadratic optimization problems in the standard support vector machine.Thirdly, to solve problems in the initial alignment of inertial navigation system, the application of convex combination method in nonlinear filtering is discussed. A new method is proposed. The SVM of two layers in convex linear combination can be acquired by using a convex linear combination of support vector machine to filter and then calculating the combination coefficients by the second layers of SVM through linear regression method.In order to improve the real-time performance and stability of nonlinear filtering, a new adaptive federated filter algorithm based on convex optimization is proposed. It solves the problem of precision reduction or even divergence, which results from the change in system environment and the uncertainty of the noise distribution. Real-time filtering of the dynamic system is realized through the adaptive fusion processing of SINS/CNS/GNSS integrated navigation system. Simulations verify the feasibility and effectiveness of the algorithm.Finally, the hybrid filter of H2/H combined navigation is studied. Due to the system uncertainty and non-Gaussian noise, the adaptive H2/H filtering algorithm based on convex optimization is proposed. Based on convex optimization, the algorithm adjusts the filter gain matrix, takes advantages of the H2and H filers, and has better robustness. It is a special case of multi-model filter algorithm and a new adaptive filtering method.