A Practical Approach to the Estimation of Amplitude and Time-Delay Parameters of a Composite Signal

Abstract

Abstruct-A method for estimating the amplitude and timedelay parameters for signals that can be represented as a sum of a number of scaled and delayed replicas of a known signal in the presence of nonwhite Gaussian noise is presented. The method is based npon the principles of maximum likelihood (ML) estimation, but at certain key points simplifying assumptions are made that result in a computationally Practical estimation scheme. The results are compared with other related results in the literature. Simulation results are presented which support the methods derived.

A Signal Synthesis Procedure Designed for Discreet Ocean Acoustic Tomography

“…Our objective does not consist in contributing towards a novel optimal estimator of an underwater channel IR, already widely studied, but to use a simple usual method well known in the estimation domain and to develop an original effective procedure around the concept of DAT. Classical parameter estimation is performed using method based on the principles of maximum likelihood estimation [7] because the maximum likelihood estimator has the relevant useful property to be asymptotically ef cient (for large data records) [8]. The Cramer Rao Bound (CRB) represents the lower bound on the variance of any unbiased estimator and, in this manner, aids to evaluate estimation performances.…”

Time-delay estimation via optimizing highly oscillatory cost functions

“…The above data model applies to some multipath propagation environments [3], [4], [16]. In practice, many problems can be described by this model.…”

“…In practice, many problems can be described by this model. As pointed out in [4], this model applies to any problems where a known probe signal excites a linear time-invariant filter whose output is observed in the presence of noise and where the impulse response of the filter is a finite sum of the scaled and timeshifted Dirac delta functions.…”

“…Provided that aliasing is negligible, then can be written as (3) where (4) Note that the time-delay estimation problem is similar to the sinusoidal parameter estimation problem except that the exponential signals are weighted by the known signal spectrum. If we divided both sides of (3) by , the problem would become identical to the sinusoidal parameter estimation problem.…”

“…For active sonar systems, the most commonly used signal waveforms are bandpass signals. For some propagation environments [3], [4], [16], the received signal can be modeled as the sum of amplitude-scaled and time-shifted replicas of the known transmitted bandpass signal. Since the transmitted signal is bandpass, the correlation function between the received and the known transmitted signal will oscillate near the carrier frequency of the transmitted signal.…”