Abstract
The recursive least squares (RLS) algorithm is one of the most popular adaptive algorithms that can be found in the literature, due to the fact that it is easily and exactly derived from the normal equations. In this paper, we give another interpretation of the RLS algorithm and show the importance of linear interpolation error energies in the RLS structure. We also give a very efficient way to recursively estimate the condition number of the input signal covariance matrix thanks to fast versions of the RLS algorithm. Finally, we quantify the misalignment of the RLS algorithm with respect to the condition number.
Highlights
Adaptive algorithms play a very important role in many diverse applications such as communications, acoustics, speech, radar, sonar, seismology, and biomedical engineering [1, 2, 3, 4]
We show exactly how the misalignment of the recursive least squares (RLS) algorithm is affected by the condition number, output signal-to-noise ratio (SNR), and parameter choice
The RLS algorithm plays a major role in adaptive signal processing
Summary
Adaptive algorithms play a very important role in many diverse applications such as communications, acoustics, speech, radar, sonar, seismology, and biomedical engineering [1, 2, 3, 4]. Among the most well-known adaptive filters are the recursive least squares (RLS) and fast RLS (FRLS) algorithms. The latter is a computationally fast version of the former. The convergence rate, the misalignment, and the numerical stability of adaptive algorithms depend on the condition number of the input signal covariance matrix. For ill-conditioned input signals (like speech), the LMS converges very slowly and the stability and the misalignment of the FRLS are more affected. The objective of this paper is threefold We first give another interpretation of the RLS algorithm and show the importance of linear interpolation error energies in the RLS structure. We show exactly how the misalignment of the RLS algorithm is affected by the condition number, output signal-to-noise ratio (SNR), and parameter choice
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