Second-Order Extended $H_{\infty}$ Filter for Nonlinear Discrete-Time Systems Using Quadratic Error Matrix Approximation

In this paper, the second-order extended (SOE) H
_∞
filter for nonlinear discrete-time systems is derived based on an approximation to the quadratic error matrix. The solution is obtained by the game theory approach. It is shown that the result bears a strong resemblance to the SOE Kalman filter when the performance bound goes to infinity. An example of vehicle state tracking is simulated to compare the performances of the SOE Kalman filter, the first order extended and the SOE H
_∞
filter. Noises with unknown bias are injected into both process dynamics and measurements. The results show that the SOE H
_∞
filter has the smallest state tracking error.