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Algorithms 2018, 11(12), 211; https://doi.org/10.3390/a11120211

A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms

1
Department of Telecommunications, University Politehnica of Bucharest, 1-3, Iuliu Maniu Blvd., 061071 Bucharest, Romania
2
Energy Materials Telecommunications Research Centre, National Institute of Scientific Research (INRS-EMT), University of Quebec, Montreal, QC H5A 1K6, Canada
*
Author to whom correspondence should be addressed.
Received: 1 December 2018 / Revised: 13 December 2018 / Accepted: 14 December 2018 / Published: 17 December 2018
(This article belongs to the Special Issue Adaptive Filtering Algorithms)
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Abstract

The system identification problem becomes more challenging when the parameter space increases. Recently, several works have focused on the identification of bilinear forms, which are related to the impulse responses of a spatiotemporal model, in the context of a multiple-input/single-output system. In this framework, the problem was addressed in terms of the Wiener filter and different basic adaptive algorithms. This paper studies two types of algorithms tailored for the identification of such bilinear forms, i.e., the Kalman filter (along with its simplified version) and an optimized least-mean-square (LMS) algorithm. Also, a comparison between them is performed, which shows interesting similarities. In addition to the mathematical derivation of the algorithms, we also provide extensive experimental results, which support the theoretical findings and indicate the good performance of the proposed solutions. View Full-Text
Keywords: adaptive filter; Kalman filter; optimized LMS algorithm; bilinear forms; system identification adaptive filter; Kalman filter; optimized LMS algorithm; bilinear forms; system identification
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Dogariu, L.-M.; Ciochină, S.; Paleologu, C.; Benesty, J. A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms. Algorithms 2018, 11, 211.

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