10  Recursive Least-Squares Techniques

The powerful technique of fitting a linear system model to the input–output response data with a least-squared error can be made even more useful by developing a recursive form with limited signal data memory to adapt with nonstationary systems and signals. One could successfully implement the block least-squares in Section 9.1 on a sliding record of N input–output signal samples. However, even with today’s inexpensive, speedy, and nimble computing resources, a sliding-block approach is ill-advised. It can be seen that the previous N – 1input–output samples and their correlations are simply being recomputed over and over again with each new sample as time marches on. By writing a recursive matrix equation ...

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