This paper presents efficient batch and recursive least squares (BLS and RLS) algorithms for identifying matrix parameters in a linear measurement process. The key insights are:
The traditional vec-permutation approach, which transforms the matrix parameter estimation problem into a standard vector form, introduces extraneous zero terms in the regressor matrix, leading to increased computational and storage requirements.
The authors derive BLS and RLS formulations that, under mild assumptions, minimize the same cost function as the vec-permutation approach, but with significantly lower computational and storage complexity.
Two variants are presented:
It is shown that persistent excitation guarantees convergence of the matrix RLS algorithm to the true matrix parameters, extending established results for vector parameter estimation.
The proposed matrix RLS algorithm is applied to improve the online identification step in an indirect adaptive model predictive control scheme, demonstrating significant reductions in computation time.
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by Brian Lai,De... at arxiv.org 04-18-2024
https://arxiv.org/pdf/2404.10911.pdfDeeper Inquiries