RCLCFilter

RCLCFilter is a family of adaptive digital filters designed to operate under linear inequality constraints while updating coefficients recursively to minimize prediction error. The acronym is used variably, but it is commonly interpreted as Recursive Constrained Linear-Combination Filter. The approach combines adaptive filtering with constraint enforcement to ensure that the filter’s behavior adheres to predefined limits or design criteria.

In operation, the filter forms a regressor vector from recent input samples and computes the output as a weighted sum of this regressor. The coefficient update aims to minimize a squared-error objective, typically with a constraint set that the weight vector must satisfy (for example, energy bounds, passband ripples, or stability requirements). Implementation methods include projection-based updates, which enforce constraints after each adaptation step, or penalty and Lagrange multiplier schemes, which incorporate constraints into the optimization objective. These methods seek a balance between fast adaptation and adherence to the constraints.

RCLCFilter supports several variants, including sparse, robust, and multi-channel forms, and can be extended to time-varying or data-dependent constraint sets. It often uses a recursion similar to recursive least squares to achieve quick tracking while maintaining constraint feasibility.

Applications for RCLCFilter span audio processing, communications channel equalization, echo cancellation, and sensor fusion in robotics, where constrained behavior helps maintain stability and physical plausibility. Limitations include higher computational cost relative to unconstrained filters and the need to select appropriate constraints to avoid biasing estimates or slowing convergence. See also adaptive filtering, constrained optimization, projection methods, and recursive least squares.