Research On Filtering And Smoothing Methods For Complex Nonlinear Dynamic Systems

Dynamic systems describe the temporal evolution of state variables in the form of ordinary differential equations or discrete mappings.Since most of the physical phenomena describable in terms of classical equations of motion are nonlinear,it seems clear that the study of the nonlinear dynamic systems is of great interest.The filtering and smoothing of a nonlinear dynamic system arise in a wide variety of applications in science and engineering,such as navigational and guidance systems,radar tracking,sonar ranging,and satellite and airplane orbit determination.According to the different problems faced by the complex nonlinear dynamic systems,it has always been a hot and difficult point to propose the corresponding nonlinear filtering and smoothing methods in this field.In order to further expand the research depth and breadth of the complex nonlinear dynamic system,the five problems in state estimation of complex nonlinear dynamic systems are studied in this thesis.The main work and innovations are as follows:1.Aiming at the problem of large initial error and random disturbance in the state estimation of a specific discrete complex nonlinear dynamic system–radar passive tracking system,a switched and iterated square-root Gauss-Hermite filter(SISGHF)algorithm is proposed.The introduction of the switching control enables the algorithm to switch between the normal operation mode and the iterated update mode.On the one hand,it can deal with the random disturbance problem,on the other hand,it can make the algorithm achieve a balance between computational cost and estimation accuracy.2.Two kinds of novel iterated posterior linearization methods are proposed to tackle the problem of the state estimation in discrete complex nonlinear dynamic systems with correlated noises.The proposed algorithms are derived via performing statistical linear regression(SLR)of the functions of the nonlinear dynamic systems with respect to the current posterior approximation in an iterated way.Different iterated posterior linearization estimation algorithms can be obtained through utilizing different numerical methods for computing the Gaussian integrals involved in the SLRs of the nonlinear systems,which is beneficial for the different complex nonlinear dynamic systems to choose the corresponding estimation methods according to their own demands.The proposed methods enjoy not only the accuracy and robustness of the Gauss approximation estimation but also the feasible computational complexity.3.In order to deal with the Bayesian optimal smoothing problem of continuousdiscrete complex nonlinear dynamic systems,two algorithms,the accurate continuousdiscrete extended-cubature Kalman smoother(ACD-ECKS)and the continuous-discrete cubature Kalman smoother(CD-CKS)are proposed.The latter smoothing method solves the problem of time dependent multiplicative term in dynamic systems which can not be dealt with by the previous continuous-discrete cubature Kalman filter(CD-CKF),but also extends the corresponding filtering algorithm to the smoothing domain as the former smoothing method.In the case of Gaussian noise,the new smoothing algorithms can obtain accurate state estimation,and the computational cost and robustness of the algorithms can satisfy the most practical applications.4.In order to deal with the non-Gaussian noise encountered in continuous-discrete complex nonlinear dynamic systems,the accurate Gaussian sum filtering and smoothing methods are proposed theoretically.The Gaussian sum-filter/smoother applies a bank of parallel accurate continuous-discrete extended-cubature Kalman filters/smoothers(ACDECKFs/ACD-ECKSs)to approximate the predicted and posterior densities as a finite number of weighted sums of Gaussian densities.The numerical simulation shows that the proposed algorithms have the capability to estimate the state accurately and robustly,and their computational cost can satisfy various practical applications with weak realtime requirements.5.A novel consensus on measurements and information cubature Kalman filtering/smoothing(CMICKF/S)method is proposed to address the distributed state estimation(DSE)for a class of continuous-discrete complex nonlinear dynamic systems.The new consensus-based filtering and smoothing algorithms enjoy not only the accuracy and robustness of CKF but also the flexibility of the information filter for multiple sensor estimation.