H∞ filtering of uncertain predictive models: Gain computation using LMI and performance evaluation

Increasing the process informativity and the efficiency of control is achieved using state estimators, which need to be robust under harsh conditions. In this paper, we look at the robust state estimation problem of uncertain models using the transfer function approach through the bias correction gain $K$ of a recursive $H_{\infty }$ filter. The filter is designed for processes represented in discrete time using the forward Euler method, which allows for predictive modeling. Since the error covariance of a state estimator is a quadratic function of $K$, a new theorem is proved and a numerical algorithm is developed for computing $K$ using linear matrix inequality (LMI). An LMI-based algorithm for iterative $K$ computation is also given. Numerical investigations are provided using two random models with uncertainties. Using the “Box” benchmark of visual object tracking, an experimental comparison of the $H_{\infty }$, Kalman, and robust unbiased finite impulse response (UFIR) filters is provided in terms of root mean square error, robustness factor, and estimation quality factor. It is shown that $K$ of the $H_{\infty }$ filter is in the range between the Kalman gain and the UFIR filter gain.