Recursive least squares filter

About: Recursive least squares filter is a research topic. Over the lifetime, 8907 publications have been published within this topic receiving 191933 citations.

Low-rank Matrix Recovery via Iteratively Reweighted Least Squares Minimization

Abstract: We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a minimal nuclear norm and an approximately low-rank solution. Under the assumption that the linear measurements fulfill a suitable generalization of the null space property known in the context of compressed sensing, the algorithm is guaranteed to recover iteratively any matrix with an error of the order of the best $k$-rank approximation. In certain relevant cases, for instance, for the matrix completion problem, our version of this algorithm can take advantage of the Woodbury matrix identity, which allows us to expedite the solution of the least squares problems required at each iteration. We present numerical experiments which confirm the robustness of the algorithm for the solution of matrix completion problems, and we demonstrate its competitiveness with respect to other techniques proposed recently in the literature.

Modified least squares algorithm incorporating exponential resetting and forgetting

Abstract: In this paper we present the general analysis of a class of least squares algorithms with emphasis on their dynamic performance particularly in the presence of poor excitation. The analysis is carried out in a deterministic framework and stresses geometrical interpretations. The core of this paper is the proposal and analysis of a new algorithm which incorporates exponential forgetting and resetting to an unprejudiced treatment of data when excitation is poor. The algorithm is particularly suitable for tracking time-varying parameters and is similar in computational complexity to the standard recursive least squares algorithm. The superior performance of the algorithm is verified via simulation studies.

Limited-precision effects in adaptive filtering

Abstract: The effects of limited-precision errors in several popular adaptive-filtering algorithms are analyzed. Performance degradations caused by limited-precision quantization of internal algorithmic quantities are often found to be much larger than what might be otherwise expected. Furthermore, in many cases, limited-precision errors are found to accumulate in time without bound, leading to an eventual overflow. This overflow is an unacceptable phenomenon in practice. Where possible, we list modifications to the infinite-precision design criteria which prevent the overflow at the expense of a small degradation from the performance that is achievable in infinite precision. We also delineate unacceptable numerical problems in some of the adaptive filtering algorithms for which no solution is yet ubiquitously accepted or useful. Stochastic gradient (LMS), recursive least squares (RLS), and frequencydomain methods are all discussed. As such, this paper contains a mixture of tutorial and novel material in an effort to assist the reader in the limited-precision implementation of an adaptive-filtering algorithm.