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 Likelihood (FML) estimation scheme, which makes use of the shape of the surface of the Compressed Likelihood Function (CLF). This estimation approach is demonstrated by applying it to two different problems. The first problem involves the estimation of time of arrival and Doppler compression of a wideband Hyperbolic Frequency Modulated (HFM) active sonar signal. An example of the estimation of parameters of a HFM signal buried in reverberation is presented using data from the Acoustic Reverberation 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 statistical performance. However, ML estimation generally requires a multidimensional search which can be computationally intensive. Our efficient FML estimation scheme uses only multiple one-dimensional searches oriented along appropriate ridges on the surface of the CLF. Simulations indicate that the performances of the proposed estimators match those of the corresponding Maximum Likelihood estimators with very high probability. Another important contribution of this paper is a threshold analysis of the proposed scheme to predict the signal-to-noise ratio (SNR) at which large estimation errors begin to occur, i.e., the threshold SNR. The predicted threshold SNR is verified through computer simulations. Finally, the computational complexity of the proposed scheme is discussed.