Research On Volterra-Kalman Filter Algorithm Based On Maximum Versoria Criterion

This thesis mainly studies the problems of Kalman filter algorithm based on Volterra function expansion in the face of practical engineering application.It is mainly improved from two aspects: Firstly,it is aimed at the non-Gaussian mixture noise problem that may occur in practical applications.Secondly,the computational complexity of Volterra function expansion is relatively high.In this thesis,various algorithms are deduced respectively.At the same time,the performance analysis and computational complexity analysis of these algorithms are carried out,and the conclusion of the algorithm is verified by the system identification simulation experiment.In addition,a variety of short-term traffic flow prediction models are established based on the proposed algorithms.The specific work includes the following points:(1)The Kalman filter algorithm based on second order Volterra architecture(SOVKalman)is derived under the minimum mean square error criterion(MMSE).It only uses the second moment of the error signal and cannot handle non-Gaussian noise.However,the actual system does not always satisfy the Gaussian assumption.In order to effectively deal with nonGaussian noise,especially impulse noise,with the help of the maximum Versoria criterion,the second-order Volterra maximum Versoria Kalman filter(SOV-MVKF)algorithm is proposed.(2)Aiming at the high computational complexity of SOV-Kalman algorithm,a pipelined architecture is used based on the algorithm.The joint process pipelined feedforward second order Volterra Kalman filter algorithm(JPPSOV-Kalman)is proposed,which combines the better convergence characteristics of the Kalman filter and the low complexity of the pipelined architecture.The algorithm has better nonlinear prediction performance compared with JPPSOV-NLMS algorithm,and the computational complexity is lower than that of SOVKalman algorithm.In addition,in view of the problem that SOV-Kalman algorithm cannot deal with impulse noise and high complexity,combined with the maximum Versoria criterion of SOV-MVKF and the pipeline structure of JPPSOV-Kalman,the joint process pipelined feedforward second order Volterra maximum Versoria Kalman filter(JPPSOV-MVKF)algorithm is proposed.(3)The architecture of the above adaptive filter is only feedforward.In order to further overcome the problem of high computational complexity of the feedforward SOV filter,the modules in the pipeline feedforward SOV filter are improved here,using RSOV and Bilinear filter is used as the architecture of each module,and each module also feeds back the output as input,joint process pipelined feedback recursion second order Volterra Kalman filter(JPPRSOV-Kalman)algorithm and joint process pipelined feedback bilinear perception Kalman filter(JPBP-Kalman)algorithm are proposed.In addition,joint process pipelined feedback recursion second order Volterra maximum Versoria Kalman filter(JPPRSOVMVKF)algorithm and joint process pipelined feedback bilinear perception maximum Versoria Kalman filter(JPBP-MVKF)algorithm are proposed.