A Recursive Algorithm for Least Squares Estimation with a Sliding Window Based on J-Orthogonal QR Factorization

Abstract

When estimating parameters in time-varying systems using data that exhibit sharp changes, it is desirable to place greater emphasis on newer data than on older data. The sliding window method is an effective approach that reduces the influence of older data by discarding it as new data arrive. This allows parameter estimation to be performed using only the most recent data within a fixed-size window. This study considers a recursive algorithm for the least squares estimation with a sliding window. The least squares estimate with the sliding window can be viewed as an estimate with updating and downdating of data. A new, efficient, and numerically stable recursive algorithm is proposed using QR factorization for the updating step and J-orthogonal QR factorization for the downdating step.