Abstract
A Kalman filter is applicable to a state estimation problem in a linear stochastic system. In this case, the filter must take into account information concerning system model structure, initial condition, and probabilistic characteristics of noises. In this paper, the robustness of a Kalman filter against uncertainties of noise covariances is discussed. When covariance matrices of process noise and observation noise change from nominal level multiplied by random variables, a Kalman filter designed for nominal noise condition is shown to be more robust than observers designed by pole placement technique in terms of the amount of deviation of the estimation accuracy from a nominal value. Considering the above feature, it becomes possible to design a kind of robust state estimator by adding the amount of variation of estimation accuracy to a nominal performance index. This idea is then demonstrated using a simple example.
