Exponential data weighting filter design for a class of nonlinear stochastic systems

The author considers unbiased linear state estimation of a class of nonlinear stochastic systems with noisy nonlinear measurement equations. Exponential data weighting ideas of linear filtering are applied to this class of systems. Results are obtained for both finite- and infinite-time filtering. In the time-invariant case, it is shown that mean square stability of the original system is sufficient for the existence of the unique nonnegative definite solution of the filter Riccati equation and that the filter has an exponential convergence rate