Non‐linear FIR smoothing filter for systems with a modelling error and its application to the DR/GPS integrated navigation

Infinite impulse response (IIR) filter generally used in estimation, positioning, etc. has problems in that, when there is a modeling error even if the system is completely observable, the estimates may converge to incorrect values or the varying values cannot be estimated quickly. The finite impulse response (FIR) filter, which has been investigated as a method to solve this problem, has faster estimation performance than the IIR filter in the presence of modelling error, but there is a limit to the convergence characteristic of the state variables. In this paper, a non‐linear FIR smoothing (NFS) filter is proposed to overcome the limitation of the state variable convergence characteristic of the FIR filter. The proposed NFS filter adds the smoothing concept to the modified receding horizon Kalman FIR filter. In order to verify the performance of the NFS filter, this filter is applied to a delay‐tolerant integrated navigation system using magnetic compass (MC) of which error is difficult to be modelled accurately. If an un‐modeled jump or ramp error occurs in the MC measurement, it shows that the NFS filter can estimate the measurement error more accurately than the FIR filter as well as the IIR filter through a simulation.