Linear / Nonlinear Systems Of Hybrid Dynamic Filtering Theory And Applications

In this thesis,we present the concept of mixed dynamic filtering,which is to use nonlinear and linear filtering methods to estimate nonlinear and linear states respectively,for models where the states have both linear and nonlinear parts.And also several mixed filtering dynamic algorithms are propose,which are composed of Gaussian mixed dynamic filtering algorithm and non-Gaussian mixed dynamic filtering algorithm,which includes extended Kalman filtering-Kalman filtering (EKF-KF),unscented Kalman filtering-Kalman filtering(UKF-KF),central difference filtering-Kalman filtering(CDF-KF),Gaussian Hermite filtering-Kalman filtering (GHF-KF) and marginal Rao-Blackwellized particle filtering(MRBPF),polynomial predictive filtering-Kalman filtering(PPF-KF),Gaussian sum filtering-Kalman filtering(GSF-KF) respectively,where we use EKE UKF,CDF,GHF,marginal particle filter(MPF),PPF,GSF to estimate the nonlinear states of the models respectively,while the linear states are all estimated by the KF.Moreover we analyze the performance of the proposed Gaussian mixed dynamic filtering algorithms and the application environments.The analysis results show that the order of the Gaussian mixed filtering algorithm in errors(sort ascending) is: GHF-KF,UKF-KF(CDF-KF),EKF-KF.Meanwhile we prove of the convergence results of the MPF and also give the qualitative analysis of the performance of the MRBPF and the other non-Gaussian mixed dynamic filtering algorithms,together with their application environments.Further more the proposed algorithms are simulated in the terrain aided navigation(TAN) and the maneuvering target tracking(MTT) domains.The results of the TAN show that the MRBPF outperforms the RBPF in root mean square errors (RMSE) of the state estimate,stability,unique particle count,convergence properties and the particle weight variance.And the results of the MTT show that the proposed algorithm only consume less than 10%the computing time required by the RBPF with just a little filtering performance decline.The performances sequence in descending in MTT simulation is:GHF-KF,CDF-KF(UKF-KF),GSF-KF(EKF-KF),PPF-KF, which coincides with the analysis results.