Maximum-Likelihood Estimation of Time-Varying Delay-Part I

This Paper Presents, for the First Time, the Exact Theoretical Solution to the Problem of Maximum-Likelihood (ML) Estimation of Time-Varying Delay d(t) between a Random Signal s(t) Received at One Point in the Presence of Uncorrelated Noise, and the Time-Delayed, Scaled Version as(t - d(t)) of that Signal Received at Another Point in the Presence of Uncorrelated Noise. the Signal is Modeled as a Sample Function of a Nonstationary Gaussian Random Process and the Observation Interval is Arbitrary. the Analysis of This Paper Represents a Generalization of that of Knapp and Carter [1], Who Derived the ML Estimator for the Case that the Delay is Constant, d(t) = do, the Signal Process is Stationary, and the Received Processes Are Observed over the Infinite Interval ([Formula Omitted]). We Show that the ML Estimator of d(t) Can Be Implemented in Any of Four Canonical Forms Which, in General, Are Time-Varying Systems. We Also Show that Our Results Reduce to a Generalized Cross Correlator for the Special Case Treated in [1]. Copyright © 1987 by the Institute of Electrical and Electronics Engineers, Inc

Maximum-Likelihood Time Delay Estimation: A New Perspective

This Paper Introduces a New Realization for Maximum Likelihood Time-Delay Estimation. the New Realization Illuminatesthe Relationships between Maximum Likelihood Time Delay Estimation and Other Methods. We Obtain the Result by Deriving the Likelihood Function using a Fundamental Method that, Surprisingly, Appears to Be New to The field of Array Processing. This Method is a Natural Complement to the Karhunen-Loeve Transform Having Vector Eigenfunctions and Scalar Eigenvalues, and It Generalizes to M Measurements, M 2 2. Moreover, It Can Be Applied to Other Multichannel estimation problems

Time delay estimation in stationary and non-stationary environments

We develop computationally efficient iterative algorithms for finding the Maximum Likelihood estimates of the delay and spectral parameters of a noise-like Gaussian signal radiated from a common point source and observed by two or more spatially separated receivers. We first consider the stationary case in which the source is stationary (not moving) and the observed signals are modeled as wide sense stationary processes. We then extend the scope by considering a non-stationary (moving) source radiating a possible non-stationary stochastic signal. In that context, we address the practical problem of estimation given discrete-time observations. We also present efficient methods for calculating the Jog-likelihood gradient (score), the Hessian, and the Fisher's information matrix under stationary and non-stationary conditions.Funding was provided by the Naval Air Systems Command through contract Number N00014-85-K-0272