A tutorial - game theory-based extended H infinity filtering approach to nonlinear problems in signal processing

In this paper, we provide a tutorial for the applications of “game-theory-based extended H infinity filtering (EHIF)” approach to various problems in disciplines of signal processing. The algorithm of this filtering approach is similar to that of the extended Kalman filtering (EKF). Since its invention, the Kalman filtering approach has been successfully and widely employed for many problems in scientific and engineering fields, e.g. target tracking, satellite systems, control, communications, etc. Therefore, the H infinity filtering approach also can be applied to all these problems. One big difference of EHIF from the EKF approach is that we apply it with unknown noise statistics of the state and measurement. In this tutorial, we introduce this non-well-known approach in spite of its practical usefulness, by providing the step by step algorithm with example problems of a number of signal processing disciplines. We also show that EHIF can outperform other approaches including the EKF that need to know the noise statistics in their applications, in some scenarios. By the contribution of this tutorial, we look forward to easy, and disseminative applications of EHIF to problems where, particularly, the EKF or particle filter could have been applied if noise statistics were known.