The Exact Cramer-Rao Bound for Gaussian Autoregressive Processes

An explicit expression is derived for the Cramer-Rao bound(CRB)on unbiased estimates of the parameters of autoregressiveprocesses, given a finite number of measurements. The expressionconverges to the well-known asymptotic form of the CRB when thenumber of measurements tends to infinity. The behavior of thebound is illustrated by some numerical examples.     

A Parametric Technique for Time Delay Estimation

The problem of estimating the time difference of arrival of a signal with unknown spectrum to two receivers is treated. A signal model containing both spectral and delay parameters is derived. The model parameters are computed by a two-step procedure: (1) the modified Yule-Walker equations are used to estimate the autoregressive spectrum of the source signal, and (2) a frequency domain squared error criterion is minimized to provide the delay estimate. The performance of the proposed technique is illustrated by simulation results.     

Accuracy of source localization using multipath delays

The depth and range of underwater source can be estimated from measurements of propagation delay differences along multiple propagation paths. The accuracy of depth and range estimation using the Cramer-Rao lower bound is studied. The formulas derived can be used in conjunction with a propagation medium (nonconstant velocity profile). Explicit formulas for the bounds are derived for the case of homogeneous medium (constant velocity profile). Numerical examples are presented to illustrate the behavior of these bounds     

A Generalized Clutter Computation Procedure for Airborne Pulse Doppler Radars

A general procedure for analyzing ground clutter effects in airborne pulse Doppler radars is described. The quantity computed is the expected clutter power at the output of any specified range gate/ Doppler filter processing cell. The procedure has been computerized and is quite general with respect to antenna gain pattern, clutter cross section variation, PRF, pulse and range gate shapes, and the various receiver processing functions. It is applicable only to distributed ground clutter and linear processing, and excludes the dynamic effects of continuous antenna scanning. To exemplify the use of the procedure, two studies conducted for a postulated high PRF radar are described, and the results are presented.     

The exact Cramer-Rao bound for Gaussian autoregressive processes

An explicit expression is derived for the Cramer-Rao bound (CRB) on unbiased estimates of the parameters of autoregressive (AR) processes, given a finite number of measurements. The expression converges to the well-known asymptotic form of the CRB when the number of measurements tends to infinity. The behavior of the bound is illustrated by some numerical examples     

Performance of diversely polarized antenna arrays for correlatedsignals

The performance of direction finding systems in a correlated signal environment utilizing diversely polarized antenna arrays is investigated. The Cramer-Rao bound (CRB) is used to evaluate the accuracy of the estimated directions of arrival (DOAs). Compact closed form formulas are presented for the CRB corresponding to the joint estimation of the DOAs, signal covariance matrix, signal polarization parameters, and noise variance. The CRB is evaluated numerically for selected examples, to provide insights into the potential improvement in direction-finding accuracy due to polarization diversity     

Sensitivity analysis of the maximum likelihood direction-findingalgorithm

A first-order analysis is performed of the sensitivity of the maximum likelihood (ML) direction-finding algorithm to system errors which cause differences between the array manifold used by the algorithm and the true array manifold. The effect of such errors on the directions-of-arrival (DOA) estimates is investigated. The ability of the ML algorithm to resolve two closely spaced sources in the presence of phase and gain errors in the array elements or in the receivers, or errors in the element locations, is analyzed. A formula for computing the failure threshold of the algorithm as a function of source separation and other system parameters is derived and tested by simulation. The analysis assumes that the exact covariance matrix of array element outputs is known     

Efficient dynamic programming in presence of nuisance parameters

The dynamic programming approach for maximum a posteriori (MAP) estimation of Markov sequences is frequently proposed for problems in control theory, communications, and signal processing. It is usually assumed that the observation sequence is a perfectly known function of the Markov sequence of interest, except for some additive noise with known statistics. However, often the observation is not only a function of the Markov sequence but also of a vector of unknown nuisance parameters. It is shown how the dynamic programming methodology can be extended to estimate both the nuisance parameters and the Markov sequence, using a combined maximum-likelihood and MAP framework. The technique is efficient relative to other possible solutions. The problem of detecting and tracking moving targets observed by imaging sensors is used to demonstrate the efficiency of the procedure     

VSAR: a high resolution radar system for ocean imaging

The velocity synthetic aperture radar (VSAR) is a conceptual synthetic aperture radar (SAR)-based sensor system for high resolution ocean imaging. The VSAR utilizes data collected by a multielement SAR system, to extract information not only about the radar reflectivity of the observed area, but also about the radial velocity of the scatterers in each pixel. This is accomplished by making use of the phase information contained in multiple SAR images, and not just the magnitude information as in conventional SAR. Using this velocity information, the VSAR attempts to compensate for the velocity distortion inherent in conventional SAR and to reconstruct the ocean reflectivity. We present the basic theory of the VSAR system and its performance. We also provide an analysis of the VSAR imaging mechanism for a statistical model of the radar returns, designed to capture the effects of speckle and of resolution degradation due to the decorrelation of the radar returns     

Eigenstructure-based algorithms for direction finding withtime-varying arrays

This paper considers the problem of finding the directions of narrowband signals using a time-varying array whose elements move during the observation interval in an arbitrary but known way. We derive two eigenstructure-based algorithms for this problem, which are modifications of techniques developed originally for time-invariant arrays. The first uses array interpolation, and the second uses focusing matrices. Like other eigenstructure-based methods, these algorithms require a modest amount of computations in comparison with the maximum likelihood (ML) estimator. The performance of the algorithms is evaluated by Monte-Carlo simulations, and is compared with the Cramer Rao Bound (CRB). Although both techniques were successful for wideband array processing with time-invariant arrays, we found that only the interpolated array algorithm is useful for direction finding (DF) with time-varying arrays