This paper describes an IIR/FIR fusion filter for a nonlinear system, and analyzes the stability of the fusion filter. The fusion filter is applied to INS/GPS integrated system, and the performance is verified by simulation and experiment. In the fusion filter, an IIR-type filter (SPKF) and FIR-type filter (MRHKF filter) are processed independently, then the two filters are merged using the mixing probability calculated using the residuals and residual covariance information of the two filters. The merits of the SPKF and the MRHKF filter are embossed and the demerits of the filters are diminished via the filter fusion. Consequently, the proposed fusion filter has robustness against to model uncertainty, temporary disturbing noise, large initial estimation error, etc. The stability of the fusion filter is verified by showing the closeness of the states of the two sub filters in the mixing/redistribution process and the upper bound of the error covariance matrices. This fusion filter is applied into INS/GPS integrated system, and important factors for filter processing are presented. The performance of the INS/GPS integrated system designed using the fusion filter is verified by simulation under various error environments and is confirmed by experiment.