Neural approximators for nonlinear finite-memory state estimation

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