A Unified Bayesian Perspective for Conventional and Robust Adaptive Filters

• URL: http://arxiv.org/abs/2502.18325v1
• Date: Tue, 25 Feb 2025 16:20:10 GMT
• Title: A Unified Bayesian Perspective for Conventional and Robust Adaptive Filters
• Authors: Leszek Szczecinski, Jacob Benesty, Eduardo Vinicius Kuhn,
• Abstract summary: We present a new perspective on the origin and interpretation of adaptive filters.<n>We can present, in a unified framework, derivations of many adaptive filters which depend on the probabilistic model of the observational noise.<n> Numerical examples are shown to illustrate the properties and provide a better insight into the performance of the derived adaptive filters.
• Score: 15.640261000544077
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work, we present a new perspective on the origin and interpretation of adaptive filters. By applying Bayesian principles of recursive inference from the state-space model and using a series of simplifications regarding the structure of the solution, we can present, in a unified framework, derivations of many adaptive filters which depend on the probabilistic model of the observational noise. In particular, under a Gaussian model, we obtain solutions well-known in the literature (such as LMS, NLMS, or Kalman filter), while using non-Gaussian noise, we obtain new families of adaptive filter. Notably, under assumption of Laplacian noise, we obtain a family of robust filters of which the signed-error algorithm is a well-known member, while other algorithms, derived effortlessly in the proposed framework, are entirely new. Numerical examples are shown to illustrate the properties and provide a better insight into the performance of the derived adaptive filters.

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