Recursive Algorithm for the Best Approximate Solution of Linear Equations with Applications to System Identification and State Estimation

摘要

The sequential solution, in recursive form, of a growing set of linear equations, based upon the least-square-error and a weighted least-square-error criterion, are developed. For comparison these results are applied to the discrete-time solution of several estimation and identification problems. Recursive algorithms for pseudo inversion and the best approximate solution of a set of linear equations are included. Finally, efficient state estimation procedures for time-invariant systems using a sliding-window observer are presented. (Author)