A Probabilistic Least-Mean-Squares Filter
This work addresses adaptive filtering in signal processing by offering an incremental improvement with Bayesian techniques.
The authors tackled the problem of improving the Least-Mean-Squares (LMS) filter by introducing a probabilistic approach that provides an adaptable step-size and uncertainty estimation while maintaining linear complexity, resulting in improved performance compared to standard LMS and state-of-the-art algorithms with similar complexity.
We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the proposed approximation preserves the linear complexity of the standard LMS. Numerical results show the improved performance of the algorithm with respect to standard LMS and state-of-the-art algorithms with similar complexity. The goal of this work, therefore, is to open the door to bring some more Bayesian machine learning techniques to adaptive filtering.