Graham V. Weinberg

Removing logarithms from Poisson process error bounds

We present a new approximation theorem for estimating the error in approximating the whole distribution of a finite-point process by a suitable Poisson process. The metric used for this purpose regards the distributions as close if there are couplings of the processes with the expected average distance between points small in the best-possible matching. In many cases, the new bounds remain constant as the mean of the process increases, in contrast to previous results which, at best, increase logarithmically with the mean. Applications are given to Bernoulli-type point processes and to networks of queues. In these applications the bounds are independent of time and space, only depending on parameters of the system under consideration. Such bounds may be important in analysing properties, such as queueing parameters which depend on the whole distribution and not just the distribution of the number of points in a particular set.

Management of interference in Pareto CFAR processes using adaptive test cell analysis

Designing a constant false alarm rate detector to manage successfully interfering targets and clutter transitions has presented researchers with some serious design challenges. One approach has been the application of test cell analysis, using a switching detection mechanism. Such a process has resulted in detector performance improvement in a number of clutter model scenarios. Here a switching based detector is developed for targets embedded within Pareto distributed clutter. It is shown that this new detector can rectify many of the performance issues of detectors introduced recently for target detection in such a clutter environment.

General transformation approach for constant false alarm rate detector development

Abstract A general result is derived, allowing the transformation of incoherent constant false alarm rate detection processes from a given clutter environment to that of any clutter model of interest. This generalises recent work where detection processes for Pareto distributed clutter are developed in a similar way. The approach preserves the original probability of false alarm and threshold multiplier relationship. To illustrate the application of the method, a simple example is considered for target detection in uniformly distributed clutter. An extensive application to target detection in Weibull distributed clutter is presented, with the focus being on producing transformed detectors to run on real X-band maritime surveillance radars.

Validity of whitening-matched filter approximation to the pareto coherent detector

It has been observed that the coherent multilook detector for targets embedded within Pareto intensity clutter can be approximated by the Gaussian optimal detector, or whitening-matched filter, in a number of real data sets. These correspond to clutter returns obtained from the Defence Science and Technology Organisations Ingara radar, operating in X-band, at high grazing angles and in a circular spotlight mode. This study will establish conditions under which this can be explained mathematically. The key to this is to apply Steins method from probability theory to establish rules of thumb to determine the validity of the approximation.

Non-uniform bounds for geometric approximation

Crucial to the Stein-Chen method for distributional approximation is the estimation of differences of the solution to a Stein equation associated with the distributions being compared, and the usual approach has been to obtain uniform bounds on these differences. The purpose of this paper is to demonstrate, in the geometric case, that improvement can be obtained by taking non-uniform bounds. The results are illustrated with an application to Polya distribution convergence.

Poisson representation and monte carlo estimation of generalized marcum Q-function

We derive a new relationship which links the generalized Marcum Q-function to a probabilistic comparison of a pair of independent Poisson random variables. Consequently, a new expression for the detection probability of a series of incoherently integrated pulses, in Gaussian cluster is also derived. These results lead to simple Monte Carlo estimators of the Marcum Q-function. We thus investigate if Monte Carlo techniques are useful in the estimation of the Marcum Q-function

On the Construction of CFAR Decision Rules via Transformations

The Pareto distribution has been validated as a suitable model for X-band maritime surveillance radar clutter returns, and consequently there has been much interest in developing radar detection algorithms under such a clutter model assumption. Recent research has shown that it is possible to apply a transformation approach to adapt the traditional constant false alarm rate (CFAR) detectors, designed to operate in exponentially distributed clutter, to the Pareto setting. However, it was found that this approach resulted in the decision rule requiring a priori knowledge of the Pareto scale parameter. It is shown here that this shortcoming can be rectified by application of a complete sufficient statistic to the transformed detector. Consequently, new decision rules are derived and it is shown that they not only achieve the CFAR property but in some instances can improve the performance of the decision rules from which they are derived.

Analysis of a dual order statistic constant false alarm rate detector

A dual order statistic detector is examined and shown to have the constant false alarm rate property when the clutter is modelled by a certain class of distributions. For the case of Pareto distributed clutter, mathematical analysis establishes some rules of thumb that can be used to select appropriate order statistic indices. The performance of this detector is then examined in such clutter, including an analysis of the effects of interfering targets and clutter transitions.

Optimised binary integration with order statistic CFAR in Pareto distributed clutter

Binary integration developed under a Pareto clutter model assumption.Mathematical analysis of the merits of binary integration.Binary integration coupled with order statistic CFAR investigated.Application to real X-Band maritime surveillance radar clutter provided. This paper examines the application of binary integration to X-band maritime surveillance radar, with a view to enhancing detection performance. The clutter is assumed to follow a Pareto distribution, since this model has been validated for high resolution X-band maritime clutter returns. The binary integration process is based upon an order statistic detection scheme, which has the constant false alarm rate property with respect to the Pareto shape parameter. An optimisation procedure is outlined, which results in ideal choices for the binary integration factor and the order statistic index. Performance of the resultant detection process is analysed, with homogeneous and heterogeneous simulated clutter, whose parameters are matched to those obtained from real clutter data sets. A direct application to real data is also included.

Coherent CFAR detection in compound Gaussian clutter with inverse gamma texture

Recent publications have explored coherent radar detection in a compound Gaussian clutter environment with inverse gamma texture, since the latter clutter model has been validated for X-band high-resolution maritime surveillance radar clutter returns. This paper explores the development of coherent constant false alarm rate (CFAR) detectors for this scenario. In the first instance, a detector is constructed with explicit knowledge of the clutter parameters. It is then shown that the probability of false alarm/threshold relationship does not vary with the clutter power. To achieve a CFAR detector, clutter parameter approximations are then introduced, and the cost associated with this is then analysed.