NEURAL APPROXIMATORS FOR NONLINEAR FINITE-MEMORY STATE ESTIMATION

No general analytical tools are available to estimate the state of a n onlinear stochastic system observed through a nonlinear noisy channel. This problem is addressed in this paper under the assumption that the statistics of the random variables are unknown, hence a statistical a pproach is followed instead of a probabilistic one. The following appr oximations are enforced: (i) the state estimator is a finite-memory on e, (ii) the estimation functions are given fixed structures in which a certain number of parameters have to be optimized (multilayer feedfor ward neural networks are chosen from among various possible nonlinear approximators), (iii) the algorithms for optimizing the parameters (i. e. the network weights) rely on a stochastic approximation. Simulation results are reported to compare the behaviour of the proposed estimat or with the extended Kalman filter and the estimators based on the on- line minimization of the estimation error.