ON THE GENERALISED BURG TECHNIQUE.

A new maximum-likelihood algorithm for Toeplitz covariance matrix estimation is introduced. The new algorithm requires less computational cost than the generalized procedure proposed by Burg et al. It solves for the reflection coefficients rather than the covariance lags, and it calculates these coefficients successively starting from filter length one: the kth reflection coefficient a//k//k is computed by maximizing the associated likelihood function and assuming that the reflection coefficients a//n//n, n equals 1,. . , k minus 1, have been previously calculated. The algorithm does not assume that the noise data are expressed by an autoregressive (AR) filter. This assumption is incorrect since noise is always present in real signals and usually has serious consequences at low snr where the approximation due to the assumption is significant and the true spectrum is required for reliable detection. The optimization associated with the kth-order recursion specifying the kth reflection coefficient a//k//k, produces a cubic equation whose root with absolute value less than one is taken equal to a//k//k; if more than one root satisfies this condition, the one with the higher likelihood is chosen.