This paper presents the development and performance evaluation of a methodology for distinguishing between mainlobe and sidelobe detections that arise in adaptive radar systems operating in adverse environments. Various adaptive detection test statistics such as the adaptive matched filter (AMF), the generalized likelihood ratio test (GLRT) and adaptive coherence estimate (ACE), and combinations of these, have been previously analyzed with respect to their sidelobe rejection capabilities. In contrast to these methods, which are based on detecting a single target with known direction and Doppler, the present method uses model order determination techniques applied to the AMF or GLRT data observed over the range of unknown angle and Doppler parameters. The determination of model order, i.e., the number of signals present in the data, is made by using least-squares model fit error residuals and applying the Akaike information criterion. Comprehensive computer simulation results are presented which demonstrate substantial improvement in sidelobe rejection performance compared to previous methods.

A design of 2-D complex FIR filters is proposed by minimizing the p/sup th/ power norm used to measure the deviation of the FIR filter response from a desired filter response. The solution of this problem cannot be obtained in closed form except for p=2; for arbitrary p>2 the authors present an approach which treats the problem from a complex variable point of view. An iterative scheme is described based on the complex Newton method to find the solution. It has the feature that, starting with p=2, the value of p is increased after each iteration. Because the objective function is convex any local extremum is the global minimum. Convergence can be attained after a moderate number of iterations. A characterization theorem for factorization of 2-D FIR filters in terms of 1D filters is derived. This has strong implications for large order 2-D filter design. Two filter design examples are included.

This paper presents the design of 2-D complex FIR filters using the weighted integral least-squares error criterion (WLS). Both the cases of arbitrary magnitude with linear and arbitrary phase specifications are addressed. The solution of the linear phase case is obtained using the complex Lagrange multiplier formulation to incorporate the necessary constraints for linear phase response. This results in a computationally efficient filter design technique requiring the solution of a Hermitian Toeplitz-block-Toeplitz system of linear equations for which fast algorithms are available. Two illustrative filter design examples are also presented.

A novel nonlinear estimation technique for the problem of low-angle direction finding of a single source in the presence of fully correlated specular multipath is presented. The formulation used is that of maximum likelihood. The solution is general in that the array geometry, element types, and number of snapshots (which may be as little as one) are arbitrary, and the complex reflection coefficient of the reflecting surface is unknown. Both the symmetric and nonsymmetric scenarios are addressed. For the case where only a single snapshot of data is available, the estimation scheme is shown to reduce to the ML solution for the less-than-fully correlated scenario. Computer simulation verifies the utility of the proposed estimation technique.>

A novel method is presented for maximum-likelihood direction-finding of stochastic sources which may be correlated. It is shown that the maximum-likelihood estimates of the angle parameters and unknown source covariance matrix may be obtained in a separable form, i.e. the angle parameters are obtained by maximizing a function of only the angle parameters. The source covariance matrix estimate is then obtained by an explicit formula. This results in a significant reduction of the dimensionality of the optimization problem to be solved compared to previous approaches based on direct maximization over all parameters. Computer simulation results are presented to demonstrate the performance of the proposed method.>

A recursive Bayesian technique is developed which computes the a posteriori probability density of the location of a dynamic signal in successive sets of low signal-to-noise ratio data. This serves to enhance the detection and tracking of signals which may be undetectable in an individual data frame and, because of unknown target motion between data frames, it may not generally be possible by conventional techniques to integrate the successive data for signal-to-noise enhancement. Computer simulation examples are presented to demonstrate the performance of the Bayesian-Markov technique on simulated low SNR range-doppler amplitude data obtained in a pulse-doppler radar system and on simulated cross-ambiguity surface data obtained by cross correlating the data received at two spatially separated sonar arrays.

This correspondence generalizes some recent results on relations between minimum-variance estimates of random signals in Gaussian noise and likelihood ratios.

This paper considers the joint detection and estimation of Gauss-Markov processes in white Gaussian noise, where the operations of detection and estimation are strongly coupled. Explicit Bayes' optimal recursive estimation and detection rules are derived, and it is shown that the resulting optimal receiver is amenable to a causal estimator-correlator-type interpretation.

Two different problems of estimating a discrete stochastic process, in the face of Markov dependent uncertainty regarding the presence of the process at each stage of the observation sequence, are considered. Recursive Bayes optimal estimator algorithms are derived for the two cases considered, and the differences between them brought out explicitly.