MAXIMUM-LIKELIHOOD-ESTIMATION OF SIGNALS IN AUTOREGRESSIVE NOISE

Time series modeling as the sum of a deterministic signal and an autor egressive (AR) process is studied. Maximum likelihood estimation of th e signal amplitudes and AR parameters is seen to result in a nonlinear estimation problem. However, it is shown that for a given class of si gnals, the use of a parameter transformation can reduce the problem to a linear least squares one. For unknown signal parameters, in additio n to the signal amplitudes, the maximization can be reduced to one ove r the additional signal parameters. The general class of signals for w hich such parameter transformations are applicable, thereby reducing e stimator complexity drastically, is derived. This class includes sinus oids as well as polynomials and polynomial-times-exponential signals. The ideas are based on the theory of invariant subspaces for linear op erators. The results form a powerful modeling tool in signal plus nois e problems and therefore find application in a large variety of statis tical signal processing problems. We briefly discuss some applications such as spectral analysis, broadband/transient detection using line a rray data, and fundamental frequency estimation for periodic signals.