Least squares and recursive least-squares signal processing
The Wiener and adaptive filters belong to the statistical framework since the signal statistics are being invoked and it is required that a priori knowledge exists of the second-order moments. On the other hand, the method of least squares belongs to the deterministic frame. There are several important cases that such restrictions of signal measurements can be applied, such as modeling applications, linear predictive coding, and communications, where the desired signal is taken to be the training set. In the method of least squares the filter coefficients are optimized by using all the observations from the time the filter begins until the present time and minimizing the sum of the squared values of the error samples that are equal to the measured desired signal and the output signal of the filter. The least-squares technique is a mathematical procedure that enables us to achieve a best fit of a model to experimental data.