Donald D. Weiner

Non-Gaussian random vector identification using spherically invariant random processes

With the modeling of non-Gaussian radar clutter in mind, elegant and tractable techniques are presented for characterizing the probability density function (PDF) of a correlated non-Gaussian radar vector. The need for a library of multivariable correlated non-Gaussian PDFs in order to characterize various clutter scenarios is discussed. Specifically,. the theory of spherically invariant random processes (SIRPs) is examined in detail. Approaches based on the marginal envelope PDF and the marginal characteristic function have been used to obtain several multivariate non-Gaussian PDFs. An important result providing the PDF of the quadratic form of a spherically invariant random vector (SIRV) is presented. This result enables the problem of distributed identification of a SIRV to be addressed. >

An L-shaped array for estimating 2-D directions of wave arrival

A simple structured 2-D array, the L-shaped array, is presented. The L-shaped array consists of two uniform linear arrays (ULA) connected orthogonally at one end of each ULA. It is shown that the Cramer-Rao bounds (CRB) of the estimated wave directions based on the L-shaped array are about 37% smaller than those for the cross array. The CRB indicates the accuracy potential because it is the (reachable) lower bound on the variance of any unbiased estimate. An efficient maximum likelihood algorithm is developed utilizing the ULA structure inherent in the L-shaped array. >

Ambiguity function for a bistatic radar

A new framework for the ambiguity function for a bistatic radar is presented. Modeling of radar measurements of a slowly fluctuating point target involving delay and Doppler shift is considered. Effects of bistatic geometry on these measurements are discussed in detail. It is shown by means of two examples that geometry factors play an important role in the shape of the ambiguity function for a bistatic radar as the system configuration is varied.

Computer generation of correlated non-Gaussian radar clutter

We develop computer simulation procedures which enable us to generate any correlated non-Gaussian radar clutter that can be modeled as a spherically invariant random process (SIRP). In most cases, when the clutter is a correlated non-Gaussian random process, performance of the optimal radar signal processor cannot be evaluated analytically. Therefore, in order to evaluate such processors, there is a need for efficient computer simulation of the clutter. We present two canonical simulation procedures for the generation of correlated non-Gaussian clutter. A new approach for the goodness-of-fit test is proposed in order to assess the performance of the simulation procedure. >

Some mathematical considerations in dealing with the inverse problem

Many problems of mathematical physics can be formulated in terms of the operator equation Ax = y , where A is an integro-differential operator. Given A and x , the solution for y is usually straightforward. However, the inverse problem which consists of the solution for x when given A and y is much more difficult. The following questions relative to the inverse problem are explored. 1) Does specification of the operator A determine the set \{y\} for which a solution x is possible? 2) Does the inverse problem always have a unique solution? 3) Do small perturbations of the forcing function y always result in small perturbations of the solution? 4) What are some of the considerations that enter into the choice of a solution technique for a specific problem? The concept of an ill-posed problem versus that of a well-posed problem is discussed. Specifically, the manner by which an ill-posed problem may be regularized to a well-posed problem is presented. The concepts are illustrated by several examples.

Multistatic radar systems signal processing

In this paper, a multistatic radar system with multiple receivers and one transmitter is analyzed. We address the rules for selecting the weights for fusing multiple receivers in order to meet pre-specified performance goals. A multistatic radar ambiguity function is used to relate different radar performance measures to system parameters such as radar geometry and radar waveforms. Simulations are used to demonstrate that different performance criteria can lead to different rules for combining the signals from multiple receivers.

Non-Gaussian clutter modeling with generalized spherically invariant random vectors

This paper describes the modeling of non-Gaussian clutter with a set of generalized spherically invariant random vectors (SIRVs). The generalization extends the traditional model to account for dependence between successive SIRV realizations. Significant properties of generalized SIRVs are derived, as well as a closed-form expression for a family of generalized SIRV density functions. The density underlying recorded sonar reverberation is approximated with this function through appropriate choice of a shape parameter. Given this reverberation model, the optimum detector is derived from the generalized SIRV density likelihood ratio. This paper concludes by showing how applying this optimum detector to non-Gaussian data leads to a reduction in the false alarm rate when compared to processing with a matched filter alone.

Implementing digital terrain data in knowledge-aided space-time adaptive processing

Many practical problems arise when implementing digital terrain data in airborne knowledge-aided (KA) space-time adaptive processing (STAP). This paper addresses these issues and presents solutions with numerical implementations. In particular, using digital land classification data and digital elevation data, techniques are developed for registering these data with radar return signals, correcting for Doppler and spatial misalignments, adjusting for antenna gain, characterizing clutter patches for secondary data selection, and ensuring independent secondary data samples. These techniques are applied to select secondary data for a single-bin post-Doppler STAP algorithm using multi-channel airborne radar measurement (MCARM) program data. Results with the KA approach are compared with those obtained using the standard sliding window method for choosing secondary data. These results illustrate the benefits of using terrain information, a priori data about the radar, and the importance of statistical independence when selecting secondary data for improving STAP performance

L-shaped array for estimating 2-D directions of wave arrival

An L-shaped array of sensors to improve the estimation accuracy of two-dimensional directions of plane wave arrival is proposed. The Cramer-Rao bounds for several two-dimensional array configuration are shown. An efficient least-squares algorithm based on the L-shaped array is presented to achieve its theoretical limit. >

A generalized approach to direction finding

Assuming d sources and m sensors, a generalized formulation is proposed for the direction of arrival estimation problem. It is shown that several different techniques are special cases of the generalized approach. The techniques differ depending upon the manner in which either 1) the measured data is processed or 2) the angular information is extracted from the resulting equations. In the generalized formulation a matrix pencil M - ¿N is constructed. In general, the rank of the matrix pencil is d. However, for particular values of ¿, the rank is decreased by 1. The values of ¿ for which this happens contain the information needed to estimate the angles of arrival. The pencil theorem establishes the relationship between these values of ¿ and some functional form f(¿i) generated by the operators applied to the measurements.