Performance Analysis of Linear-Equality-Constrained Least-Squares Estimation

TL;DR

This paper evaluates the performance of linear-equality-constrained least-squares algorithms, introducing a relaxed version (rCLS) that simplifies analysis and examining the limiting behavior of the original CLS algorithm.

Contribution

It presents a novel performance analysis approach for the rCLS algorithm and investigates the limiting performance of CLS as the relaxation parameter increases.

Findings

rCLS algorithm's convergence and estimation accuracy are characterized in mean and mean-square senses.

The limiting performance of CLS is derived as the relaxation parameter approaches infinity.

Numerical examples confirm the theoretical analysis accuracy.

Abstract

We analyze the performance of a linear-equality-constrained least-squares (CLS) algorithm and its relaxed version, called rCLS, that is obtained via the method of weighting. The rCLS algorithm solves an unconstrained least-squares problem that is augmented by incorporating a weighted form of the linear constraints. As a result, unlike the CLS algorithm, the rCLS algorithm is amenable to our approach to performance analysis presented here, which is akin to the energy-conservation-based methodology. Therefore, we initially inspect the convergence properties and evaluate the precision of estimation as well as satisfaction of the constraints for the rCLS algorithm in both mean and mean-square senses. Afterwards, we examine the performance of the CLS algorithm by evaluating the limiting performance of the rCLS algorithm as the relaxation parameter (weight) approaches infinity. Numerical examples verify the accuracy of the theoretical findings.