Nonrecursive and recursive methods for parameter estimation in filtering problems
Michael A. Kouritzin, Hongwei Long, Xinjian Ma, Wei Sun · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2003
Nonlinear filtering is an important and effective tool for handling estimation of signals when observations are incomplete, distorted, and corrupted. Quite often in real world applications, the signals to be estimated contain unknown parameters which need to be determined. Herein, we develop and analyze non-recursive and recursive methods, which can deal with combined state and parameter estimation for nonlinear partially-observed stochastic systems. For the non-recursive method, we obtain the unknown parameters through solving a system of non-singular finite order linear equations. For the recursive method, we generalize the least squares method and develop a particle prediction error identification algorithm so that it can be applied to general nonlinear stochastic systems. We use the branching particle filter to do the signal state estimation and implement simulations for both methods.