A new algorithm which provides adaptive model selection and estimation on-line is derived based on the polynomial nonlinear ARMAX model (NARMAX). The algorithm uses rectangular windowing regression procedures where the forgetting factor is unity within a sliding data window. Variations in the model structure, or which terms are in the model, and the parameter estimates are tracked by using a sliding rectangular window based on Givens rotations. The algorithm which minimizes the loss function at every step by selecting significant regression variables and computing the corresponding parameter estimates provides an efficient adaptive procedure which can be applied in nonlinear signal processing applications. Simulated examples are included to demonstrate the performance of the new algorithm.
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