Two-dimensional multivariate parametric models for radar applications-Part I: Maximum-entropy extensions for Toeplitz-block matrices

Copyright © 2008 IEEEIn a series of two papers, a new class of parametric models for two-dimensional multivariate (matrix-valued, space-time) adaptive processing is introduced. This class is based on the maximum-entropy extension and/or completion of partially specified matrix-valued Hermitian covariance matrices in both the space and time dimensions. This first paper considers the more restricted class of Toeplitz Hermitian covariance matrices that model stationary clutter. If the clutter is stationary only in time then we deal with a Toeplitz-block matrix, whereas clutter that is stationary in time and space is described by a Toeplitz-block-Toeplitz matrix. We first derive exact expressions for this new class of 2-D models that act as approximations for the unknown true covariance matrix. Second, we propose suboptimal (but computationally simpler) relaxed 2-D time-varying autoregressive models (ldquorelaxationsrdquo) that directly use the non-Toeplitz Hermitian sample covariance matrix. The high efficiency of these parametric models is illustrated by simulation results using true ground-clutter covariance matrices provided by the DARPA KASSPER Dataset 1, which is a trusted phenomenological airborne radar model, and a complementary AFRL dataset.Yuri I. Abramovich, Ben A. Johnson, and Nicholas K. Spence

Adaptive Illumination Patterns for Radar Applications

The fundamental goal of Fully Adaptive Radar (FAR) involves full exploitation of the joint, synergistic adaptivity of the radar\u27s transmitter and receiver. Little work has been done to exploit the joint space time Degrees-of-Freedom (DOF) available via an Active Electronically Steered Array (AESA) during the radar\u27s transmit illumination cycle. This research introduces Adaptive Illumination Patterns (AIP) as a means for exploiting this previously untapped transmit DOF. This research investigates ways to mitigate clutter interference effects by adapting the illumination pattern on transmit. Two types of illumination pattern adaptivity were explored, termed Space Time Illumination Patterns (STIP) and Scene Adaptive Illumination Patterns (SAIP). Using clairvoyant knowledge, STIP demonstrates the ability to remove sidelobe clutter at user specified Doppler frequencies, resulting in optimum receiver performance using a non-adaptive receive processor. Using available database knowledge, SAIP demonstrated the ability to reduce training data heterogeneity in dense target environments, thereby greatly improving the minimum discernable velocity achieved through STAP processing

Mitigating Interference with Knowledge-Aided Subarray Pattern Synthesis and Space Time Adaptive Processing

Phased arrays are essential to airborne ground moving target indication (GMTI), as they measure the spatial angle-of-arrival of the target, clutter, and interference signals. The spatial and Doppler (temporal) frequency is utilized by space-time adaptive processing (STAP) to separate and filter out the interference from the moving target returns. Achieving acceptable airborne GMTI performance often requires fairly large arrays, but the size, weight and power (SWAP) requirements, cost and complexity considerations often result in the use of subarrays. This yields an acceptable balance between cost and performance while lowering the system’s robustness to interference. This thesis proposes the use of knowledge aided adaptive radar to institute adaptive subarray nulling in concert with digital space-time adaptive processing to improve performance in the presence of substantial interference. This research expands previous work which analyzed a clutter-free airborne moving-target indication (AMTI) application of knowledge-aided subarray pattern synthesis (KASPS) [1] and updates this previous research by applying the same concept to the GMTI application with clutter and STAP

Regularized Covariance Matrix Estimation in Complex Elliptically Symmetric Distributions Using the Expected Likelihood Approach - Part 1: The Over-Sampled Case

In \cite{Abramovich04}, it was demonstrated that the likelihood ratio (LR) for multivariate complex Gaussian distribution has the invariance property that can be exploited in many applications. Specifically, the probability density function (p.d.f.) of this LR for the (unknown) actual covariance matrix $\R_{0}$ does not depend on this matrix and is fully specified by the matrix dimension $M$ and the number of independent training samples $T$. Since this p.d.f. could therefore be pre-calculated for any a priori known $(M,T)$, one gets a possibility to compare the LR of any derived covariance matrix estimate against this p.d.f., and eventually get an estimate that is statistically ``as likely'' as the a priori unknown actual covariance matrix. This ``expected likelihood'' (EL) quality assessment allows for significant improvement of MUSIC DOA estimation performance in the so-called ``threshold area'' \cite{Abramovich04,Abramovich07d}, and for diagonal loading and TVAR model order selection in adaptive detectors \cite{Abramovich07,Abramovich07b}. Recently, a broad class of the so-called complex elliptically symmetric (CES) distributions has been introduced for description of highly in-homogeneous clutter returns. The aim of this series of two papers is to extend the EL approach to this class of CES distributions as well as to a particularly important derivative of CES, namely the complex angular central distribution (ACG). For both cases, we demonstrate a similar invariance property for the LR associated with the true scatter matrix \mSigma_{0}. Furthermore, we derive fixed point regularized covariance matrix estimates using the generalized expected likelihood methodology. This first part is devoted to the conventional scenario ($T \geq M$) while Part 2 deals with the under-sampled scenario ($T \leq M$)

An Approach to Ground Moving Target Indication Using Multiple Resolutions of Multilook Synthetic Aperture Radar Images

Ground moving target indication (GMTI) using multiple resolutions of synthetic aperture radar (SAR) images to estimate the clutter scattering statistics is shown to outperform conventional sample matrix inversion space-time adaptive processing GMTI techniques when jamming is not present. A SAR image provides an estimate of scattering from nonmoving targets in the form of a clutter scattering covariance matrix for the GMTI optimum processor. Since the homogeneity of the scattering statistics are unknown, using SAR images at multiple spatial resolutions to estimate the clutter scattering statistics results in more confidence in the final detection decision. Two approaches to calculating the multiple SAR resolutions are investigated. Multiple resolution filter bank smoothing of the full-resolution SAR image is shown to outperform an innovative approach to multilook SAR imaging. The multilook SAR images are calculated from a single measurement vector partitioned base on synthetic sensor locations determined via eigenanalysis of the radar measurement parameters

Estimation et détection en milieu non-homogène, application au traitement spatio-temporel adaptatif

Pour un radar aéroporté, la détection de cibles nécessite, de par la nature du fouillis de sol, la mise en place d'un filtre spatio-temporel adaptatif (STAP). Les détecteurs basés sur l'hypothèse d'un milieu homogène sont souvent mis à mal dans un environnement réel, où les caractéristiques du fouillis peuvent varier significativement en distance et en angle. Diverses stratégies existent pour contrer les effets délétères de l'hétérogénéité. La thèse propose d'approfondir deux de ces stratégies. Plus précisément, un nouveau modèle d'environnement est présenté dans un contexte Bayésien : il intègre à la fois une relation originale d'hétérogénéité et de la connaissance a priori. De nouveaux estimateurs de la matrice de covariance du bruit ainsi que de nouveaux détecteurs sont calculés à partir de ce modèle. Ils sont étudiés de manière théorique et par simulations numériques. Les résultats obtenus montrent que le modèle proposé permet d'intégrer de manière intelligente l'information a priori dans le processus de détection. ABSTRACT : Space-time adaptive processing is required in future airborne radar systems to improve the detection of targets embedded in clutter. Performance of detectors based on the assumption of a homogeneous environment can be severely degraded in practical applications. Indeed real world clutter can vary significantly in both angle and range. So far, different strategies have been proposed to overcome the deleterious effect of heterogeneity. This dissertation proposes to study two of these strategies. More precisely a new data model is introduced in a Bayesian framework ; it allows to incorporate both an original relation of heterogeneity and a priori knowledge. New estimation and detection schemes are derived according to the model ; their performances are also studied theoretically and through numerical simulations. Results show that the proposed model and algorithms allow to incorporate in an appropriate way a priori information in the detection schem

Single data set detection for multistatic doppler radar

The aim of this thesis is to develop and analyse single data set (SDS) detection algorithms that can utilise the advantages of widely-spaced (statistical) multiple-input multiple-output (MIMO) radar to increase their accuracy and performance. The algorithms make use of the observations obtained from multiple space-time adaptive processing (STAP) receivers and focus on covariance estimation and inversion to perform target detection. One of the main interferers for a Doppler radar has always been the radar’s own signal being reflected off the surroundings. The reflections of the transmitted waveforms from the ground and other stationary or slowly-moving objects in the background generate observations that can potentially raise false alarms. This creates the problem of searching for a target in both additive white Gaussian noise (AWGN) and highly-correlated (coloured) interference. Traditional STAP deals with the problem by using target-free training data to study this environment and build its characteristic covariance matrix. The data usually comes from range gates neighbouring the cell under test (CUT). In non-homogeneous or non-stationary environments, however, this training data may not reflect the statistics of the CUT accurately, which justifies the need to develop SDS methods for radar detection. The maximum likelihood estimation detector (MLED) and the generalised maximum likelihood estimation detector (GMLED) are two reduced-rank STAP algorithms that eliminate the need for training data when mapping the statistics of the background interference. The work in this thesis is largely based on these two algorithms. The first work derives the optimal maximum likelihood (ML) solution to the target detection problem when the MLED and GMLED are used in a multistatic radar scenario. This application assumes that the spatio-temporal Doppler frequencies produces in the individual bistatic STAP pairs of the MIMO system are ideally synchronised. Therefore the focus is on providing the multistatic outcome to the target detection problem. It is shown that the derived MIMO detectors possess the desirable constant false alarm rate (CFAR) property. Gaussian approximations to the statistics of the multistatic MLED and GMLED are derived in order to provide a more in-depth analysis of the algorithms. The viability of the theoretical models and their approximations are tested against a numerical simulation of the systems. The second work focuses on the synchronisation of the spatio-temporal Doppler frequency data from the individual bistatic STAP pairs in the multistatic MLED scenario. It expands the idea to a form that could be implemented in a practical radar scenario. To reduce the information shared between the bistatic STAP channels, a data compression method is proposed that extracts the significant contributions of the MLED likelihood function before transmission. To perform the inter-channel synchronisation, the Doppler frequency data is projected into the space of potential target velocities where the multistatic likelihood is formed. Based on the expected structure of the velocity likelihood in the presence of a target, a modification to the multistatic MLED is proposed. It is demonstrated through numerical simulations that the proposed modified algorithm performs better than the basic multistatic MLED while having the benefit of reducing the data exchange in the MIMO radar system