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