Radial basis network approach for nonlinear filtering in discrete time

This paper presents a new method to deal with nonlinear filtering problems in discrete time. Our approach is based on radial basis neural networks and on the principle of particles filters. More precisely, the usual learning phase of the network is replaced by the generation of a lot of particles, i.e. simulated system trajectories. Particles so generated correspond to neural centers. Inspite of its complex structure such a network possesses good properties. First, we show that the network output converges to the optimal filter when the number of particles grows. Second, the implementation is very simple and the computational time is reasonable. And finally, on simulations good performances are observed with respect to that of the extended kalman filter and that of an optimal recurrent neural network.