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

Generalized Likelihood Signal Resolution

This Paper Defines an M-Ary Generalized Likelihood Ratio Test (MGLRT) that overcomes Root\u27s Early Objection to the Application of Generalized Likelihood Ratio Testing to the Resolution of Correlated Signals. the Proposed Test Extends the Form of a Conventional Binary Generalized Likelihood Ratio Test (GLRT) in a Manner that Permits a Generalization of the Minimax Properties of the Binary Test to the M-Hypotheses Case. When the Estimated Signals Are Orthogonal, the Test Reduces to a Sequence of Conventional Binary Tests Duplicating the Performance of a Narrow-Band Matched Filter Envelope-Detector Receiver. © 1975, IEEE. All Rights Reserved

On the Relation between Triangular Matrix Decomposition and Linear Interpolation

The December 1983 Letter by C. W. Therrien Concerning the Relation between Triangular Matrix Decomposition and Linear Prediction is Extended to Include Linear Interpolation. © 1984 IEE

A Stochastic One-Dimensional Image Model based on Occluding Object Images

This Paper Provides New Insights into the Formation of One-Dimensional (Line-Scan) Image Autocorrelation Functions. We Model a Line Scan as a Composition of Individual Object-Images that Have Random Positions, Widths and Intensities and that Occlude One Another. We Derive the Autocorrelation Function of This Model as a Function of Object-Image Width and Intensity Distributions. We Show that Any Assumption Regarding the Form of the Autocorrelation Function Places a Constraint on Object-Image Width and Intensity Distributions and We Derive the Object-Image Width Distribution Associated with the Widely Used Symmetric-Exponential Autocovariance Model

Generalized Running Discrete Transforms

This Paper Introduces a Generalized Running Discrete Transform with Respect to Arbitrary Transform Basea, and Relates the Generalized Transform to the Running Discrete Fourier Z and Short-Time Discrete Fourier Transforms. Concepts Associated with the Running and Short-Time Discrete Fourier Transforms Such as 1) Filter Bank Implementation, 2) Synthesis of the Original Sequence by Summation of the Filter Bank Outputs, 3) Frequency Sampling, and 4) Recursive Implementations Are All Extended to the Generalized Transform Case. a Formula is Obtained for Computing the Transform Coefficients of a Segment of Data at Time N Recursively from the Transform Coefficients of the Segment of Data at Time N – 1. the Computational Efficiency of This Formula is Studied, and the Class of Transforms Requiring the Minimum Possible Number of Arithmetic Operations Per Coefficient is Described. © 1982, IEEE. All Rights Reserved

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

Intraframe Sequential Picture Coding

This Paper Generalizes Time-Discrete Autoregressive Source Coding Results of Rate-Distortion Theory to Two Dimensions. a 2-D Discrete Autoregressive Source is Defined and Shown to Produce a 2-D Wide-Sense Markovian Field. the Rate Distortion Function of the Source is Then Obtained under Assumption of Gaussian Field Statistics and a Squared Error Fidelity Criterion. a Procedure for Generating an Ensemble of 2-D Codewords Whose Statistics Satisfy the Variational Equations for R(D) is Given. These 2-D Codewords Are, by Space-Time Mappings, 1-D Tree Codes, and It is Noted that a Tree Coding Theorem of Jelinek, Berger, Davis and Hellman Applies. the Problem of Instrumenting Nearly Optimum 2-D Sequential Encoding is Discussed Briefly. the Paper Stresses Potential Application to Image Coder Design. Copyright © 1977 by the Institute of Electrical and Electronics Engineers, Inc

An Image Model based on Occluding Object Images and Maximum Entropy

This Paper Introduces a Statistical Image Model based on Occlusion and Maximum Entropy. the Statistical Model Combines a Fundamental Property of Image Formation, Occlusion, with Both Object-Image Shape and Nonuniform Object-Image Intensity. the Model is a Composition of Individual Object-Images that Have Random Positions, Shapes, and Intensities, and that Occlude Both Background and One Another. We Derive the Autocorrelation and Second-Order Probability Density Functions of This Model and Give Several Examples. © 1998 IEEE

Least Squares Order-Recursive Lattice Smoothers

Conventional Least Squares Order-Recursive Lattice (LSORL) Filters Use Present and Past Data Values to Estimate the Present Value of a Signal. This Paper Introduces LSORL Smoothers Which Use Past, Present and Future Data for that Purpose. Except for an overall Delay Needed for Physical Realization, LSORL Smoothers Can Substantially Outperform LSORL Filters While Retaining All the Advantages of an Order-Recursive Structure. © 1995 IEE

Linear Interpolation Lattice

The Well-Known Analysis and Synthesis Filters of Linear Prediction Theory Are Extended Here to Include Linear Interpolation. © 1991 IEE