A Unified Bayesian Perspective for Conventional and Robust Adaptive Filters
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911031054303232 |
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| author | Szczecinski, Leszek Benesty, Jacob Kuhn, Eduardo Vinicius |
| author_facet | Szczecinski, Leszek Benesty, Jacob Kuhn, Eduardo Vinicius |
| contents | 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 that depend on the probabilistic model of the measurement 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 derive new adaptive algorithms. Notably, under the assumption of Laplacian noise, we obtain a family of robust filters of which the sign-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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_18325 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Unified Bayesian Perspective for Conventional and Robust Adaptive Filters Szczecinski, Leszek Benesty, Jacob Kuhn, Eduardo Vinicius Information Retrieval Statistics Theory 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 that depend on the probabilistic model of the measurement 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 derive new adaptive algorithms. Notably, under the assumption of Laplacian noise, we obtain a family of robust filters of which the sign-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. |
| title | A Unified Bayesian Perspective for Conventional and Robust Adaptive Filters |
| topic | Information Retrieval Statistics Theory |
| url | https://arxiv.org/abs/2502.18325 |