Study of robust \(H_{\infty}\) filtering application in loosely coupled INS/GPS system (Q1719344)

Summary: Since a celebrate linear minimum mean square (MMS) Kalman filter in integration GPS/INS system cannot guarantee the robustness performance, a \(H_{\infty}\) filtering with respect to polytopic uncertainty is designed. The purpose of this paper is to give an illustration of this application and a contrast with traditional Kalman filter. A game theory \(H_{\infty}\) filter is first reviewed; next we utilize linear matrix inequalities (LMI) approach to design the robust \(H_{\infty}\) filter. For the special INS/GPS model, unstable model case is considered. We give an explanation for Kalman filter divergence under uncertain dynamic system and simultaneously investigate the relationship between \(H_{\infty}\) filter and Kalman filter. A loosely coupled INS/GPS simulation system is given here to verify this application. Result shows that the robust \(H_{\infty}\) filter has a better performance when system suffers uncertainty; also it is more robust compared to the conventional Kalman filter.