A Novel Fitting H-Infinity Kalman Filter for Nonlinear Uncertain Discrete-Time Systems Based on Fitting Transformation

The classical Kalman-based filtering algorithm, such as extended Kalman filter or unscented Kalman filter, commonly assumes that the accurate system model or precise noise statistics is known for using. Hence, these filters are not robust estimation to practical systems and always with poor stability, low precision or even divergence since uncertain items exist. In order to tackle these issues, a novel scheme referred to as the fitting H-infinity Kalman filter (FHKF) is proposed and used for robust estimation of the nonlinear uncertain systems. The hardcore of FHKF is the fitting transformation, which is a numerical approximation approach to get the estimation values of coefficient matrix based on least weighted squares. Moreover, FHKF is proposed by applying the coefficient matrix to the structure of the extended H-infinity Kalman filter. Based on the stochastic stability lemma, the stability analysis is presented to verify the error boundness of the proposed filtering. Its efficiency is demonstrated by taking Monte Carlo simulation for the uncertain system and practical experiments in the INS/GPS integrated navigation.