Iterative Frequency-Weighted Filtering and Smoothing Procedures

Minimum-variance filters and smoothers exhibit performance degradations when they are designed with inexact models and noise statistics. Filter and smoother estimation errors are assumed herein to be generated by a first-order moving-average system. This assumed system is identified and used to design a frequency weighting function to improve mean square error performance. It is shown under prescribed conditions that the sequence of frequency-weighted estimation error variances are nonincreasing. An example is presented which demonstrates the efficacy of repeated frequency weighting iterations.