Adaptive fuzzy hybrid unscented/H-infinity filter for state estimation of nonlinear dynamics problems

Abstract

In this paper, a new hybrid unscented Kalman (UKF) and unscented ${\mathrm{H}}_{\infty }$ (U ${\mathrm{H}}_{\infty }$ F) filter is presented that can adaptively adjust its performance better than that of either UKF and/or U ${\mathrm{H}}_{\infty }\mathrm{F}$ , accordingly. In this way, two Takagi-Sugeno-Kang (TSK) fuzzy logic systems are presented to adjust automatically some weights that combine those UK and U ${\mathrm{H}}_{\infty }$ filters, independent of the dynamics of the problem. Such adaptive fuzzy hybrid unscented Kalman/ ${\mathrm{H}}_{\infty }$ filter (AFUK ${\mathrm{H}}_{\infty }$ ) is based on the combination of gain, a priori state estimation, and a priori measurement estimation. The simulation results of an inverted pendulum and a re-entry vehicle tracking problem clearly demonstrate robust and better performance of this new AFUK ${\mathrm{H}}_{\infty }$ filter in comparison with those of both UKF and U ${\mathrm{H}}_{\infty }$ F, appropriately. It is shown that, therefore, the new presented AFUK ${\mathrm{H}}_{\infty }$ filter can simply eliminate the need for either UKF or U ${\mathrm{H}}_{\infty }$ F effectively in the presence of Gaussian and/or non-Gaussian noises.