### Estimation of AR Parameters

We estimate the AR parameters with the sinusoidal parameters fixed. The derivatives for the AR parameters may be found in Section 9.2.7 (assume ). But, we do not need to use iterative methods to find the ML parameters that maximize (8.13) since we can obtain them in one step using Levinson algorithm. Treating the residual error as AR noise, we compute the auto-correlation function using the frequency-domain method by taking the inverse FFT of the magnitude-squared of the FFT of . The Levinson algorithm is then used to find the AR coefficients and .

The Fisher's information matrix for AR modeling was given in Section 5.2.8 in terms of the CR bound matrix which is the inverse of the FIM. We have

 (8.16)

where is the auto-correlation matrix. The CR bound for is independent of and given by

 (8.17)

Baggenstoss 2017-05-19