Adaptive Filtering Techniques in Signal Processing

Adaptive filtering encompasses a class of algorithms in which filter parameters adjust dynamically in response to streaming data, with the aim of tracking changing signal or noise characteristics. Early adaptive filters relied on the mean square error criterion, yielding simple yet powerful schemes such as the least mean squares (LMS) and recursive least squares (RLS) algorithms. As real-world environments often exhibit impulsive disturbances and non-Gaussian noise, robust criteria—most notably the maximum correntropy criterion—have been introduced to enhance resilience against outliers. Simultaneously, nonlinear and kernel-based approaches have extended adaptive filters to capture complex signal relationships by mapping inputs into high-dimensional feature spaces. In parallel, distributed adaptive filters exploit cooperation among spatially dispersed sensors or agents, using diffusion or consensus strategies to improve global estimation in networks. Together, these developments have underpinned advances in echo cancellation, wireless channel equalisation, biomedical signal enhancement and large-scale sensor systems, demonstrating the global significance of adaptive filtering in modern communications, control and machine-learning applications.

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Adaptive Filtering Techniques in Signal Processing publication trend

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Technical terms

Adaptive filter: A system whose parameters are updated continuously to minimise a defined error measure between its output and a desired signal.

Least mean squares (LMS): An adaptive algorithm that adjusts filter weights in proportion to the instantaneous error and input, offering simplicity and low computational cost.

Recursive least squares (RLS): An adaptive scheme that minimises a weighted sum of past squared errors, yielding rapid convergence at the expense of higher complexity.

Correntropy: A similarity measure based on kernel functions that captures higher-order statistics and provides robustness against outliers.

Kernel adaptive filter: A nonlinear filter that projects inputs into a reproducing kernel Hilbert space, enabling the modelling of complex relationships via linear operations in feature space.

Diffusion strategy: A distributed approach in which neighbouring agents share intermediate estimates, fostering network-wide adaptation and consensus in parameter estimation.

References

1. Kernel Affine Projection Algorithms. EURASIP Journal on Advances in Signal Processing (2008).
2. Robust Hammerstein Adaptive Filtering under Maximum Correntropy Criterion. Entropy (2015).
3. Robust Geman-McClure Based Nonlinear Spline Adaptive Filter Against Impulsive Noise. IEEE Access (2020).
4. A variable step-size strategy for distributed estimation over adaptive networks. EURASIP Journal on Advances in Signal Processing (2013).