Studies of optimal memory for discrete-time fir filters in state-space

We address two efficient estimators of optimal memory for FIR filters in discrete-time state-space via the conditional mean square error and real measurement. In the latter case, the algorithm does not involve neither a reference nor the noise covariances, but requires a learning circle. Although a justification has been provided for the Kalman-like unbiased FIR filter, the estimators can be used universally. Testing by the two-state polynomial model has shown a very good correspondence with the predicted values.