Title :
Exact maximum likelihood time delay estimation for short observation intervals
Author :
Champagne, Benoit ; Eizenman, Moshe ; Pasupathy, Subbarayan
Author_Institution :
INRS-Telecommun., Quebec Univ., Verdun, Que., Canada
fDate :
6/1/1991 12:00:00 AM
Abstract :
An exact solution is presented to the problem of maximum likelihood time delay estimation for a Gaussian source signal observed at two different locations in the presence of additive, spatially uncorrelated Gaussian white noise. The solution is valid for arbitrarily small observation intervals; that is, the assumption T≫τ c, |d| made in the derivation of the conventional asymptotic maximum likelihood (AML) time delay estimator (where τ c is the correlation time of the various random processes involved and d is the differential time delay) is relaxed. The resulting exact maximum likelihood (EML) instrumentation is shown to consist of a finite-time delay-and-sum beamformer, followed by a quadratic postprocessor based on the eigenvalues and eigenfunctions of a one-dimensional integral equation with nonconstant weight. The solution of this integral equation is obtained for the case of stationary signals with rational power spectral densities. Finally, the performance of the EML and AML estimators is compared by means of computer simulations
Keywords :
eigenvalues and eigenfunctions; integral equations; parameter estimation; signal processing; white noise; Gaussian source signal; Gaussian white noise; asymptotic maximum likelihood estimator; computer simulations; eigenfunctions; eigenvalues; exact maximum likelihood estimator; exact solution; finite-time delay-and-sum beamformer; maximum likelihood time delay estimation; one-dimensional integral equation; quadratic postprocessor; short observation intervals; spatially uncorrelated AWGN; Additive white noise; Computer simulation; Delay effects; Delay estimation; Eigenvalues and eigenfunctions; Instruments; Integral equations; Maximum likelihood estimation; Random processes; White noise;
Journal_Title :
Signal Processing, IEEE Transactions on