Robust mixture filtering block based on logarithmic Student’s t-based criterion

Abstract

Determining an appropriate cost function is crucial to develop adaptive filters. However, current robust algorithms may not be capable of satisfying the requirements of various non-Gaussian environments due to their limited performance surfaces and gradient relationships. To this end, a novel and robust cost function called logarithmic Student’s $t$-based (logST) criterion using Student’s $t$ distribution is first proposed in this paper. Owing to its excellent properties in the algorithm generalization, robust gradient relationship, and efficient performance surface, the proposed logST algorithm achieves filtering accuracy improvement in both Gaussian and non-Gaussian environments. To further enhance the convergence performance and tracking capability in nonlinear system identification, a novel nonlinear block-oriented framework is constructed using the mixture of original space and random Fourier features space. Then, a recursive method is applied to achieve optimization solution in this nonlinear block-oriented framework, generating the mixture random Fourier features recursive logST (MRFFRlogST) algorithm. Finally, simulations on linear and nonlinear system identifications, as well as Chua’s time-series prediction under various noise environments validate the superiorities of logST and MRFFRlogST.