Probabilistic models have been used extensively in the past to underpin classification algorithms in statistical pattern recognition. The most widely used model is the Gaussian distribution. However, signals of impulsive nature usually deviate from Gaussian and it is necessary to work with more realistic models. K-distribution is one of the long-tailed density which is known in the signal processing community for fitting the radar sea clutter accurately. The work presented in this thesis reflects the efforts made to model the background features, extracted from the sea images, by using a K-distribution. A novel approach for estimating the parameter of K-distribution is presented. The method utilises the empirical characteristic function, and is proven to perform better than any existing estimation technique. A classifier is then developed from the empirical characteristic function. This technique is applied to a problem of automatic target recognition with promising results.

Correlation filters (CFs) are well established and useful tools for a variety of tasks in signal processing and pattern recognition, including automatic target recognition and tracking, biometrics, landmark detection, and human action recognition. Traditionally, CFs have been designed and implemented efficiently in the frequency domain using the discrete Fourier transform (DFT). However, the element-wise multiplication of two DFTs in the frequency domain corresponds to a circular correlation, which results in aliasing (i.e., distortion) in the correlation output. Prior CF research has largely ignored these aliasing effects by making the assumption that linear correlation is approximated by circular correlation. In this work, we investigate in detail the topic of aliasing in CFs. First, we illustrate that the current formulation of CFs in the frequency domain is inherently flawed, as it unintentionally assumes circular correlation during the design phase. This means that existing CFs are not truly optimal. We introduce zero-aliasing correlation filters (ZACFs) which fix this formulation issue by ensuring that each CF formulation problem corresponds to a linear correlation rather than a circular correlation. By adopting the ZACF design modifications, we show that the recognition and localization performance of conventional CF designs can be significantly improved. We demonstrate these benefits using a variety of data sets and present solutions to the computational challenges associated with computing ZACFs. After a CF is designed, it is used for object recognition by correlating it with a test signal. We investigate the use of the well-known overlap-add (OLA) and overlap-save (OLS) algorithms to improve the computation and memory requirements of this correlation operation for high dimensional applications (e.g., video). Through this process, we highlight important tradeoffs between these two algorithms that have previously been undocumented. To improve the computation and memory requirements of OLA and OLS, we introduce a new block filtering scheme, denoted partial-aliasing OLA (PAOLA) that intentionally introduces aliasing into the output correlation. This aliasing causes conventional CFs to perform poorly. To remedy this, we introduce partial-aliasing correlation filters (PACFs), which are specifically designed to minimize this aliasing. We demonstrate through numerical results that PACFs outperform conventional CFs in the presence of aliasing.

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Pattern theory, a mathematical framework for representing knowledge of complex patterns developed by applied mathematician Ulf Grenander, has been shown to have potential uses in automatic target recognition (ATR). Prior research performed in the mid-1990s at Washington University in St. Louis resulted in ATR algorithms based on concepts in pattern theory for forward-looking infrared (FLIR) and laser radar (LADAR) imagery, but additional work was needed to create algorithms that could be implemented in real ATR systems. This was due to performance barriers and a lack of calibration between target models and real data. This work addresses some of these issues by exploring techniques that can be used to create practical pattern-theoretic ATR algorithms. This dissertation starts by reviewing the previous pattern-theoretic ATR research described above and discussing new results involving the unification of two previously separate outcomes of that research: multi-target detection/recognition and thermal state estimation in FLIR imagery. To improve the overall utility of pattern-theoretic ATR, the following areas are re-examined: 1) generalized diffusion processes to update target pose estimates and 2) the calibration of thermal models with FLIR target data. The final section of this dissertation analyzes the fundamental accuracy limits of target pose estimation under different sensor conditions, independent of the target detection/recognition algorithm employed. The Cramér-Rao lower bound (CRLB) is used to determine these accuracy limits.

Rather than emitting pulses, passive radar systems rely on illuminators of opportunity, such as TV and FM radio, to illuminate potential targets. These systems are attractive since they allow receivers to operate without emitting energy, rendering them covert. Until recently, most of the research regarding passive radar has focused on detecting and tracking targets. This dissertation focuses on extending the capabilities of passive radar systems to include automatic target recognition. The target recognition algorithm described in this dissertation uses the radar cross section (RCS) of potential targets, collected over a short period of time, as the key information for target recognition. To make the simulated RCS as accurate as possible, the received signal model accounts for aircraft position and orientation, propagation losses, and antenna gain patterns. An extended Kalman filter (EKF) estimates the target's orientation (and uncertainty in the estimate) from velocity measurements obtained from the passive radar tracker. Coupling the aircraft orientation and state with the known antenna locations permits computation of the incident and observed azimuth and elevation angles. The Fast Illinois Solver Code (FISC) simulates the RCS of potential target classes as a function of these angles. Thus, the approximated incident and observed angles allow the appropriate RCS to be extracted from a database of FISC results. Using this process, the RCS of each aircraft in the target class is simulated as though each is executing the same maneuver as the target detected by the system. Two additional scaling processes are required to transform the RCS into a power profile (magnitude only) simulating the signal in the receiver. First, the RCS is scaled by the Advanced Refractive Effects Prediction System (AREPS) code to account for propagation losses that occur as functions of altitude and range. Then, the Numerical Electromagnetic Code (NEC2) computes the antenna gain pattern, further scaling the RCS. A Rician likelihood model compares the scaled RCS of the illuminated aircraft with those of the potential targets. To improve the robustness of the result, the algorithm jointly optimizes over feasible orientation profiles and target types via dynamic programming.

This thesis focuses upon automatic target recognition (ATR) with radar sensors. Recent advancements in ATR have included the processing of target signatures from multiple, spatially-diverse perspectives. The advantage of multiple perspectives in target classification results from the angular sensitivity of reflected radar transmissions. By viewing the target at different angles, the classifier has a better opportunity to distinguish between target classes. This dissertation extends recent advances in multi-perspective target classification by: 1) leveraging bistatic target reflectivity signatures observed from multiple, spatially-diverse radar sensors; and, 2) employing a statistical distance measure to identify radar sensor locations yielding improved classification rates. The algorithms provided in this thesis use high resolution range (HRR) profiles – formed by each participating radar sensor – as input to a multi-sensor classification algorithm derived using the fundamentals of statistical signal processing. Improvements to target classification rates are demonstrated for multiple configurations of transmitter, receiver, and target locations. These improvements are shown to emanate from the multi-static characteristics of a target class’ range profile and not merely from non-coherent gain. The significance of dominant scatterer reflections is revealed in both classification performance and the “statistical distance” between target classes. Numerous simulations have been performed to interrogate the robustness of the derived classifier. Errors in target pose angle and the inclusion of camouflage, concealment, and deception (CCD) effects are considered in assessing the validity of the classifier. Consideration of different transmitter and receiver combinations and low signal-to-noise ratios are analyzed in the context of deterministic, Gaussian, and uniform target pose uncertainty models. Performance metrics demonstrate increases in classification rates of up to 30% for multiple-transmit, multiple-receive platform configurations when compared to multi-sensor monostatic configurations. A distance measure between probable target classes is derived using information theoretic techniques pioneered by Kullback and Leibler. The derived measure is shown to suggest radar sensor placements yielding better target classification rates. The predicted placements consider two-platform and three-platform configurations in a single-transmit, multiple-receive environment. Significant improvements in classification rates are observed when compared to ad-hoc sensor placement. In one study, platform placements identified by the distance measure algorithm are shown to produce classification rates exceeding 98.8% of all possible platform placements.

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The mathematical operation of correlation is a very simple concept, yet has a very rich history of application in a variety of engineering fields. It is essentially nothing but a technique to measure if and to what degree two signals match each other. Since this is a very basic and universal task in a wide variety of fields such as signal processing, communications, computer vision etc., it has been an important tool. The field of pattern recognition often deals with the task of analyzing signals or useful information from signals and classifying them into classes. Very often, these classes are predetermined, and examples (templates) are available for comparison. This task naturally lends itself to the application of correlation as a tool to accomplish this goal. Thus the field of Correlation Pattern Recognition has developed over the past few decades as an important area of research. From the signal processing point of view, correlation is nothing but a filtering operation. Thus there has been a great deal of work in using concepts from filter theory to develop Correlation Filters for pattern recognition. While considerable work has been to done to develop linear correlation filters over the years, especially in the field of Automatic Target Recognition, a lot of attention has recently been paid to the development of Quadratic Correlation Filters (QCF). QCFs offer the advantages of linear filters while optimizing a bank of these simultaneously to offer much improved performance. This dissertation develops efficient QCFs that offer significant savings in storage requirements and computational complexity over existing designs. Firstly, an adaptive algorithm is presented that is able to modify the QCF coefficients as new data is observed. Secondly, a transform domain implementation of the QCF is presented that has the benefits of lower computational complexity and computational requirements while retaining excellent recognition accuracy. Finally, a two dimensional QCF is presented that holds the potential to further save on storage and computations. The techniques are developed based on the recently proposed Rayleigh Quotient Quadratic Correlation Filter (RQQCF) and simulation results are provided on synthetic and real datasets.

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