On extended state based Kalman filter for nonlinear time-varying uncertain systems with measurement bias

This paper addresses the state estimation for a class of nonlinear time-varying stochastic systems with both uncertain dynamics and unknown measurement bias. A novel extended state based Kalman filter (ESKF) algorithm is developed to estimate the original state, the uncertain dynamics and the measurement bias. It is shown that the estimation error of the proposed algorithm is bounded in the mean square sense. Also, the estimation of the measurement bias asymptotically converges to its true value, such that the influence of measurement bias is eliminated. Furthermore, the asymptotic optimality of the estimation result is proved while the uncertain dynamics approaches to a constant vector. Finally, a simulation study for harmonic oscillator system model is provided to illustrate the effectiveness of proposed method.