Keith D. Copsey

Bayesian analysis of generalized frequency-modulated signals

General frequency-modulated (GFM) signals can be used to characterize many vibrations in dynamic environments, with applications to engine monitoring and sonar. Most work into parameter estimation of such signals assumes knowledge of the number of carrier frequencies. In this paper, we make no such assumption and use Bayesian techniques to address jointly the problem of model selection and parameter estimation. Following the work of Andrieu and Doucet (see ibid., vol.47, p.2667-76, 1999), who addressed the problem for nonmodulated sinusoids, a posterior distribution for the parameters and model order is obtained. This distribution is too complicated for analytical extraction of moments and to sample from directly; therefore, we use a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to draw samples from the distribution. Some simulated examples are presented to illustrate the algorithms performance.

A Bayesian approach to simultaneous autofocus and superresolution

This paper presents a numerical Bayesian approach to the autofocus and super-resolution of targets in radar imagery. An ill-posed inverse problem is studied in which the known linear imaging operator is subject to an unknown degree of distortion (defocusing). The goal is simultaneously to reconstruct a high-resolution representation of a target based on noisy lower resolution image measurements and to estimate the degree of defocus. We present a Markov chain Monte Carlo algorithm for parameter estimation, illustrate the approach on an explanatory example and compare our technique with a maximum likelihood approach. Given a model for the sensor measurement process, this technique may be applied to any type of radar image such as those produced by a synthetic aperture radar (SAR), inverse SAR (ISAR) or a real beam imaging radar. The proposed approach fits into a larger set of procedures aiming to exploit targeting information from different radar sensors.

Bayesian Networks for Incorporation of Contextual Information in Target Recognition Systems

In this paper we examine probabilistically the incorporation of contextual information into an automatic target recognition system. In particular, we attempt to recognise multiple military targets, given measurements on the targets, knowledge of the likely groups of targets and measurements on the terrain in which the targets lie. This allows us to take into account such factors as clustering of targets, preference to hiding next to cover at the extremities of fields and ability to traverse different types of terrain. Bayesian networks are used to formulate the uncertain causal relationships underlying such a scheme. Results for a simulated example, when compared to the use of independent Bayesian classifiers, show improved performance in recognising both groups of targets and individual targets.

Bayesian Approach to Mixture Models for Discrimination

This paper develops a Bayesian mixture model approach to discrimination. The specific problem considered is the classification of mobile targets, from Inverse Synthetic Aperture Radar images. However, the algorithm developed is relevant to the generic classification problem. We model the data measurements from each target as a mixture distribution. A Bayesian formalism is adopted, and we obtain posterior distributions for the parameters of our mixture models. The distributions obtained are too complicated for direct analytical use in a classifier, so a Markov chain Monte Carlo (MCMC) algorithm is used to provide samples from the distributions. These samples are then used to make classifications of future data.

Classifier Design for Population and Sensor Drift

The basic assumption in classifier design is that the distribution from which the design sample is selected is the same as the distribution from which future objects will arise: i.e., that the training set is representative of the operating conditions. In many applications, this assumption is not valid. In this paper, we discuss sources of variation and possible approaches to handling it. We then focus on a problem in radar target recognition in which the operating sensor differs from the sensor used to gather the training data. For situations where the physical and processing models for the sensors are known, a solution based on Bayesian image restoration is proposed.

Automatic target recognition using both measurements from identity sensors and motion information from tracking sensors

The majority of automatic target recognition (ATR) studies are formulated as a traditional classification problem. Specifically, using a training set of target exemplars, a classifier is developed for application to isolated measurements of targets. Performance is assessed using a test set of target exemplars. Unfortunately, this is a simplification of the ATR problem. Often, the operating conditions differ from those prevailing at the time of training data collection, which can have severe effects on the obtained performance. It is therefore becoming increasingly recognised that development of robust ATR systems requires more than just consideration of the traditional classification problem. In particular, one should make use of any extra information or data that is available. The example in this paper focuses on a hybrid ATR system being designed to utilise both measurements from identity sensors (such as radar profiles) and motion information from tracking sensors to classify targets. The first-stage of the system uses mixture-model classifiers to classify targets into generic classes based upon data from (long range) tracking sensors. Where the generic classes are related to platform types (e.g. fast-jets, heavy bombers and commercial aircraft), the initial classifications can be used to assist the military commanders early decision making. The second-stage of the system uses measurements from (closer-range) identity sensors to classify the targets into individual target types, while taking into account the (uncertain) outputs from the first-stage. A Bayesian classifier is proposed for the second-stage, so that the first-stage outputs can be incorporated into the second-stage prior class probabilities.

Detection and estimation of general frequency-modulated signals using reversible jump MCMC methods

General frequency modulated signals can be used to characterize many vibrations in dynamic environments, with applications to engine monitoring and sonar. Most work in to parameter estimation of such signals assumes knowledge of the number of carrier frequencies present in the signal. In this paper, we make no such assumption, and use Bayesian techniques to address jointly the problem of model selection and parameter estimation. Following the work of Andrieu and Doucet, who addressed the problem of joint Bayesian model selection and parameter estimation for non-modulated sinusoids in white Gaussian noise, a posterior distribution for the parameter and model order is obtained. This distribution is to o complicated to evaluate analytically, so we use a reversible jump Markov chain Monte Carlo algorithm to draw samples for the distribution. Some simulated examples are presented to illustrate the algorithms performance.