A Huber recursive least squares adaptive lattice filter for impulse noise suppression

This paper proposes a new adaptive filtering algorithm called the Huber Prior Error-Feedback Least Squares Lattice (H-PEF-LSL) algorithm for robust adaptive filtering in an impulse noise environment. It minimizes a modified Huber M-estimator-based cost function, instead of the least squares cost function. In addition, the simple modified Huber M-estimate cost function also allows us to perform the time and order recursive updates in the conventional PEF-LSL algorithm so that the complexity can be significantly reduced to O(M), where M is the length of the adaptive filter. The new algorithm can also be viewed as an efficient implementation of the recursive least M-estimate (RLM) algorithm (Zou et al., 2000), which has a complexity of O(M²). Simulation results show that the proposed H-PEF-LSL algorithm is more robust than the conventional PEFLSL algorithm in suppressing the adverse influence of the impulses at the input and desired signals with small additional computational cost