Nearest Kronecker Product Decomposition Based Linear-in-The-Parameters Nonlinear Filters

A linear-in-the-parameters nonlinear filter consists of a functional expansion block, which expands the input signal to a higher dimensional space nonlinearly, followed by an adaptive weight network. The number of weights to be updated depends on the type and order of the functional expansion used. When applied to a nonlinear system identification task, as the degree of the nonlinearity of the system is usually not known a priori, linear-in-the-parameters nonlinear filters are required to update a large number of coefficients to effectively model the nonlinear system. However, all the weights of the nonlinear filter may not contribute significantly to the identified model. We show via simulation experiments that, the weight vector of a linear-in-the-parameters nonlinear filter usually exhibits a low-rank nature. To take advantage of this observation, this paper proposes a class of linear-in-the-parameters nonlinear filters based on the nearest Kronecker product decomposition. The performance of the proposed filters is superior in terms of convergence behaviour as well as tracking ability in comparison to their traditional linear-in-the-parameters nonlinear filter counterparts, when tested for nonlinear system identification. Furthermore, the proposed nearest Kronecker product decomposition-based linear-in-the-parameters nonlinear filters has been shown to provide improved noise mitigation capabilities in a nonlinear active noise control scenario.