Discrete Stochastic Processes and Optimal Filtering

6.8. Estimation of gradient and LMS algorithm

We can consider the estimate and of p and R in the calculation of the gradient. We have changed to the notation and and not and as the criterion is no longer the traditional criterion “min L²” but an approximation of this latter.

We had:

Thus, we are going to consider its estimate:

The estimated values will be the observed data.

Let:

and

thus

and

This recursive expression on λ_K returns to suppress the calculation of the expectation, in effect ...