Extended State based Kalman Filter for Uncertain Systems with Bias

Abstract

This paper addresses the state estimation for a class of stochastic systems with both uncertain dynamics and measurement bias. By using the idea of uncertainty/disturbance estimation, an extended state based Kalman filter algorithm is developed to estimate the original state, the uncertain dynamics and the measurement bias. Furthermore, a necessary and sufficient condition for the observability of augmented system is presented. Also, the stability of the proposed algorithm is analyzed. It is shown that the proposed filter can achieve unbiased estimation of measurement bias, such that the influence of measurement bias is eliminated. Finally, a simulation study is provided to illustrate the effectiveness of proposed method.