Recursive orthogonal least squares method and its application in non-linear adaptive filtering

An OLS (orthogonal least squares) algorithm which efficiently combines structure and parameter estimation has been studied and applied to system identification for general NARMAX (nonlinear autoregressive moving average with exogenous input) stochastic systems by Chen et al. (1989). Based on QR decomposition, we present here how the OLS algorithm can be implemented recursively for general nonlinear stochastic systems. In such a way, the computation procedure can be performed in real time theoretically and save huge amounts of memory usage. Also because of the numerical stability of QR decomposition, we can expect to achieve good numerical performance. Volterra adaptive filtering is implemented to verify the algorithm. The results of computer simulation for two cases are shown. This algorithm may also be applied to other nonlinear signal processing problems.