A Close to Optimal Adaptive Filter for Sudden System Changes

• Published in: IEEE signal processing letters Vol. 24; no. 11; pp. 1734 - 1738
• Main Authors: Lopes, Paulo A. C., Gerald, Jose A. B.
• Format: Journal Article
• Language: English
• Published: IEEE 01.11.2017
• Subjects: Adaptation models; Algorithm design and analysis; Approximation algorithms; Gaussian sum; impulsive noise; Kalman filter (KF); least mean squares (LMS); Mathematical model; Noise measurement; optimal filtering; Probability density function; Signal processing algorithms; sudden changes; variable step size
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2017.2757147

Most adaptive filtering algorithms are designed with smooth changes in mind. For instance, the Kalman filter (KF) usually assumes a random walk model for the state, where the state noise is simply a multivalue Gaussian random variable. However, in practice changes can be abrupt. In this letter, we consider the case where the state noise of the KF is impulsive, corresponding to a probability density function (PDF) given by the sum of two Gaussians. This will result in a PDF for the state that is given by a sum of Gaussians, corresponding to an implementation of a Gaussian sum filter, with multiple KFs contributing to the resulting output. Simulation and theoretical considerations show that in steady state only one filter is operating, while several filters are important at transitions. The operation of the algorithm is then similar to optimally detecting sudden changes, and restarting the KF at those moments, resulting in an close optimal step size varying algorithm. Simulations show improved performance of the proposed algorithm when compared to state of the art algorithms.