Maximum correntropy recursive three-step filter

Recursive three-step filters are often used for state estimation of systems with unknown input direct feedthrough, that is, systems where the unknown input simultaneously affect the state equation and measurement equation. However, when the system is disturbed by non-Gaussian noise, especially heavy-tailed impulsive noise, the performance of such recursive three-step filters will deteriorate. This paper proposes a maximum correntropy recursive three-step filter that can effectively handle non-Gaussian measurement noise pollution. The derivation of this filter is based on the traditional recursive three-step filter and utilizes a maximum correntropy criterion and a fixed-point iterative algorithm to simultaneously estimate the unknown input and state. It is shown that when the kernel bandwidths approach infinity, the derived maximum correntropy recursive three-step filter will degenerate into the traditional recursive three-step filter. Finally, the effectiveness and reliability of the proposed algorithm are demonstrated through simulation experiments.