A new FIR filter for state estimation and its application

This paper proposes a new FIR (finite impulse response) filter under aleast squares criterion using a forgetting factor. The proposed FIRfilter does not require information of the noise covariances as well asthe initial state, and has some inherent properties such astime-invariance, unbiasedness and deadbeat. The proposed FIR filter isrepresented in a batch form and then a recursive form as an alternativeform. From discussions about the choice of a forgetting factor and awindow length, it is shown that they can be considered as usefulparameters to make the estimation performance of the proposed FIR filteras good as possible. It is shown that the proposed FIR filter canoutperform the existing FIR filter with incorrect noise covariances viacomputer simulations. Finally, as a useful application, an imagesequence stabilization problem is considered. Through this application,the FIR filtering based approach is shown to be superiorto the Kalman filtering based approach.