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

• Published in: Algorithms Vol. 11; no. 12; p. 211
• Main Authors: Dogariu, Laura-Maria, Ciochină, Silviu, Paleologu, Constantin, Benesty, Jacob
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.12.2018
• Subjects: Adaptive algorithms; adaptive filter; Algorithms; bilinear forms; Identification; Kalman filter; Kalman filters; Noise control; optimized LMS algorithm; Parameter identification; Signal processing; System identification; Wiener filtering
• ISSN: 1999-4893; 1999-4893
• DOI: 10.3390/a11120211

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.