FAST MAXIMUM-LIKELIHOOD-ESTIMATION OF SIGNAL PARAMETERS USING THE SHAPE OF THE COMPRESSED LIKELIHOOD FUNCTION

In this paper, we propose a computationally efficient Fast Maximum Lik elihood (FML) estimation scheme, which makes use of the shape of the s urface of the Compressed Likelihood Function (CLF). This estimation ap proach is demonstrated by applying it to two different problems. The f irst problem involves the estimation of time of arrival and Doppler co mpression of a wide-band Hyperbolic Frequency Modulated (HFM) active s onar signal. An example of the estimation of parameters of a HFM signa l buried in reverberation is presented using data from the Acoustic Re verberation Special Research Program (ARSRP). The second problem deals with the estimation of frequencies of sinusoids. Maximum Likelihood ( ML) estimators are of great interest because their superior statistica l performance. However, ML estimation generally requires a multidimens ional search which can be computationally intensive. Our efficient FML estimation scheme uses only multiple one-dimensional searches oriente d along appropriate ridges on the surface of the CLF. Simulations indi cate that the performances of the proposed estimators match those of t he corresponding Maximum Likelihood estimators with very high probabil ity. Another important contribution of this paper is a threshold analy sis of the proposed scheme to predict the signal-to-noise ratio (SNR) at which large estimation errors begin to occur, i.e., the threshold S NR. The predicted threshold SNR is verified through computer simulatio ns. Finally, the computational complexity of the proposed scheme is di scussed.