非線形系の状態変数の推定に対する-近似法

抄録

This paper is concerned with the problem of estimating the state variables of a discrete-time nonlinear system. For the linear systems with additive white gaussian noises, the procedure for obtaining minimum variance estimates of state variables has been well known as the Kalman filter. The results for the linear systems are frequently applied with considerable success to nonlinear systems by introducing the linearization technique. Applying this approach, the estimation problem is seen to become a problem of approximating the a posteriori probability density function for the state variables conditioned upon noisy observations to be gaussian.
In this paper, it is assumed that the posterior probability density function is appeared in the Taylor series expansion and the estimates which maximize it are determined by the Newton-Raphson method numerically. Digital simulation results indicate that the inclusion of higher order terms of the Taylor series expansion can improve the accuracy of estimates comparing with the linearization technique.