Joint parameter and time-delay estimation for a class of Wiener models based on a new orthogonal least squares algorithm

This paper focuses on the identification of piecewise-linear Wiener systems alone with multiple inputs, unknown time-delays and system orders in input channels. The parameters and time-delays are jointly estimated by the proposed Householder transformation-based greedy orthogonal least squares (H-GOLS) algorithm. With the help of greedy selection, this algorithm derives the sparse solution. The Householder QR decomposition is employed to reduce the ill-conditioning of the least squares problem, which frequently appears in nonlinear systems. Then we use the Bayesian information criterion to choose the optimal sparsity level for order estimation. Numerical experiments show that the H-GOLS algorithm is more accurate and easier to implement than the LASSO algorithm, which makes it an attractive alternative to identifying sparse Wiener systems within limited data.