(A) study on suboptimal nonlinear filtering methods

Abstract

Three new suboptimal nonlinear filtering methods are proposed. The damped modified iterated Kalman filter for nonlinear discrete time systems is presented. The modified iterated Kalman filter, which will be called MIKF for brevity, is derived from the modified Newton method to approximate a maximum likelihood estimate. The MIKF is also obtained by an iteration scheme for the extended Kalman filter equations. A convergence analysis of the MIKF is given. By the damping method, we can reduce the total CPU time needed to estimate the state variables or may even obtain a convergent scheme when the MIKF diverges. The modified quasilinear filtering method for estimation of processes in multidimensional nonlinear stochastic systems has been proposed. This method produces more accurate filter coefficients than the standard quasilinear filtering method. To compute these coefficients, it suffices to know the distribution of the state vector of stochastic system. It can be determined by using the software for statistical analysis of multidimensional nonlinear stochastic systems. All computations connected with the determination of coefficients of the modified quasilinear filters do not use the results of observations. Therefore they can be computed in advance in the process of designing the filter. The lower-order suboptimal filtering method for estimating the state vector for a special class of discrete nonlinear systems is proposed. The dimension of state in this filter is less than that in the extended Kalman filter. The comparative less computation time required for calculation of the filter gains and implementation of the estimation process make it possible to apply this method to multidimensional dynamic systems in real time. Numerical examples show the effective convergence behavior of the proposed filters. Depending on several factors, which are required to the particular problem, such as convergence and computational efficiency, one can choose an appropriate method.