An improved inverse filtering method for parametric spectral estimation

For a wide-sense stationary process x(k), it is well known that its power spectrum P_xx(f) can be estimated by whitening the data with the inverse filter, V (z)=1/H(z), of the assumed minimum-phase rational model H(z) associated with x(k ). However, the initial conditions for computing the output e (k) of the recursive filter V(z) are unknown and must be preassigned. An improved inverse filtering method which simultaneously estimates the coefficients of V(z) as well as the initial conditions is proposed. The resultant power spectral estimator, with the initial conditions being estimated, outperforms that with the initial conditions wrongly set to zero as the time constant of V(z) is comparable to the number of data. Some simulation results which support the superior performance of the former are presented