On-line state estimation for nonlinear models.

摘要

This work is on recursive state estimators for general classes of nonlinear stochastic models. First, a brief coverage of linear and nonlinear state estimation is given. Then a couple of numerical modifications are being introduced for extending the applicability of the extended Kalman filter to more general nonlinear stochastic models.; Then, in a neural network approach, a nonlinear filter is assigned a given structure in which the values of a certain number of parameters are determined via nonlinear programming so as to minimize the estimation error. The filter structure is implemented by means of multi-layer feed-forward neural networks in which the unknown parameters are given by the synaptic weights. Due to the nonlinear relationship between the inputs and the targets, the back-propagation technique is adopted to train the weights at every step of the recursive neural estimation scheme.; Next, the design of finite-time recursive state estimator is considered for a general class of nonlinear stochastic discrete-time models. By deriving equations for a bound on the estimation error covariance based on a fixed-structure estimator, "bound-optimal" minimum variance estimator parameters are found. Based on this result, the existence conditions for the statistical steady state are also derived and applied to the design of constant gain estimators. Robustness of such schemes is also discussed in quantitative terms.; Finally, a state dependent Riccati equation design methodology is presented. Throughout this dissertation, the newly developed estimators are tested on a signal model that commonly arises in electric power system applications and the simulation results are presented to illustrate the use of such methods.