Robust State Estimation with Imperfect Sensors

Robustness properties of extended Kalman-type filters are investigated for time-varying plants when nonlinearities or linear dynamics are present at the plant input and output. Sufficient conditions for the asymptotic stability (of the state estimation error) in the absence of noise are obtained when the nonlinearities or the linear dynamics are perfectly known. When the nonlinearities are known only within bands of uncertainty, the estimation error is shown to be ultimately bounded under certain conditions. The results obtained highlight the robustness properties of such filters, which are similar to, but not exact duals of those of linear quadratic regulators.