A bayesian approach to adaptive detection in nonhomogeneous environments

We consider the adaptive detection of a signal of interest embedded in colored noise, when the environment is nonhomogeneous, i.e., when the training samples used for adaptation do not share the same covariance matrix as the vector under test. A Bayesian framework is proposed where the covariance matrices of the primary and the secondary data are assumed to be random, with some appropriate joint distribution. The prior distributions of these matrices require a rough knowledge about the environment. This provides a flexible, yet simple, knowledge-aided model where the degree of nonhomogeneity can be tuned through some scalar variables. Within this framework, an approximate generalized likelihood ratio test is formulated. Accordingly, two Bayesian versions of the adaptive matched filter are presented, where the conventional maximum likelihood estimate of the primary data covariance matrix is replaced either by its minimum mean-square error estimate or by its maximum a posteriori estimate. Two detectors require generating samples distributed according to the joint posterior distribution of primary and secondary data covariance matrices. This is achieved through the use of a Gibbs sampling strategy. Numerical simulations illustrate the performances of these detectors, and compare them with those of the conventional adaptive matched filter

Auto-regressive model based polarimetric adaptive detection scheme part II: Performance assessment under spectral model mismatch

This work addresses the problem of target detection in coherent radar systems equipped with multiple polarimetric channels. In “Part I” of this two-part study, a multi-channel auto-regressive model based polarimetric detection scheme has been developed and its performance has been studied against clutter with characteristics exactly matching the adopted parametric model. In this second part of the study, the performance assessment is extended, by means of theoretical and simulated analyses, to include the case of disturbance components with diverse spectral characteristics. Consequently, an appropriate modification is introduced to the detection scheme to make it robust to typical spectral mismatches occurring in practical situations. Finally, the effectiveness of the resulting detection scheme is proved against simulated and experimental data

Detector CFAR de promediación con corrección del factor de ajuste a través del método de los momentos para la distribución Log-Normal

The new LN-MoM-CA-CFAR detector is introduced, exhibiting a reduced deviation of the operational false alarm probability from the value conceived in the design. The solution solves a fundamental problem of CFAR processors that has been ignored in most proposals. Indeed, most of the previously proposed schemes deal with sudden changes in the clutter level, whereas the new solution has an improved performance against slow statistical changes that occur in the background signal. It has been proven that these slow changes have a remarkable influence on the selection of the CFAR adjustment factor, and consequently in maintaining the false alarm probability. The authors took advantage of the high precision achieved by the MoM (Method of Moments) in the estimation of the Log-Normal (LN) shape parameter, and the wide application of this distribution to radar clutter modeling, to create an architecture that offers precise results and it’s computationally inexpensive at the same time. After an intensive processing, involving 100 million Log-Normal samples, a scheme, which operates with excellent stability reaching a deviation of only 0,2884 % for the probability of false alarm of 0,01, was created, improving the classical CA-CFAR detector through the continuous correction of its scale factor.Se presenta el nuevo detector LN-MoM-CA-CFAR que tiene una desviación reducida en la tasa de probabilidad de falsa alarma operacional con respecto al valor concebido de diseño. La solución corrige un problema fundamental de los procesadores CFAR que ha sido ignorado en múltiples desarrollos. En efecto, la mayoría de los esquemas previamente propuestos tratan con los cambios bruscos del nivel del clutter mientras que la presente solución corrige los cambios lentos estadísticos de la señal de fondo. Se ha demostrado que estos tienen una influencia marcada en la selección del factor de ajuste multiplicativo CFAR, y consecuentemente en el mantenimiento de la probabilidad de falsa alarma. Los autores aprovecharon la alta precisión que se alcanza en la estimación del parámetro de forma Log-Normal con el MoM, y la amplia aplicación de esta distribución en la modelación del clutter, para crear una arquitectura que ofrece resultados precisos y con bajo costo computacional. Luego de un procesamiento intensivo de 100 millones de muestras Log-Normal, se creó un esquema que, mejorando el desempeño del clásico CA-CFAR a través de la corrección continua de su factor de ajuste, opera con una excelente estabilidad alcanzando una desviación de solamente 0,2884 % para la probabilidad de falsa alarma de 0,01

Unit Circle Roots Based Sensor Array Signal Processing

As technology continues to rapidly evolve, the presence of sensor arrays and the algorithms processing the data they generate take an ever-increasing role in modern human life. From remote sensing to wireless communications, the importance of sensor signal processing cannot be understated. Capon\u27s pioneering work on minimum variance distortionless response (MVDR) beamforming forms the basis of many modern sensor array signal processing (SASP) algorithms. In 2004, Steinhardt and Guerci proved that the roots of the polynomial corresponding to the optimal MVDR beamformer must lie on the unit circle, but this result was limited to only the MVDR. This dissertation contains a new proof of the unit circle roots property which generalizes to other SASP algorithms. Motivated by this result, a unit circle roots constrained (UCRC) framework for SASP is established and includes MVDR as well as single-input single-output (SISO) and distributed multiple-input multiple-output (MIMO) radar moving target detection. Through extensive simulation examples, it will be shown that the UCRC-based SASP algorithms achieve higher output gains and detection probabilities than their non-UCRC counterparts. Additional robustness to signal contamination and limited secondary data will be shown for the UCRC-based beamforming and target detection applications, respectively

Détection de bateaux dans les images de radar à ouverture synthétique

Le but principal de cette thèse est de développer des algorithmes efficaces et de concevoir un système pour la détection de bateaux dans les images Radar à Ouverture Synthetique (ROS.) Dans notre cas, la détection de bateaux implique en premier lieu la détection de cibles de points dans les images ROS. Ensuite, la détection d'un bateau proprement dit dépend des propriétés physiques du bateau lui-même, tel que sa taille, sa forme, sa structure, son orientation relative a la direction de regard du radar et les conditions générales de l'état de la mer. Notre stratégie est de détecter toutes les cibles de bateaux possibles dans les images de ROS, et ensuite de chercher autour de chaque candidat des évidences telle que les sillons. Les objectifs de notre recherche sont (1) d'améliorer 1'estimation des paramètres dans Ie modèle de distribution-K et de déterminer les conditions dans lesquelles un modèle alternatif (Ie Gamma, par exemple) devrait être utilise plutôt; (2) d'explorer Ie modèle PNN (Probabilistic Neural Network) comme une alternative aux modèles paramétriques actuellement utilises; (3) de concevoir un modèle de regroupement flou (FC : Fuzzy Clustering) capable de détecter les petites et grandes cibles de bateaux dans les images a un seul canal ou les images a multi-canaux; (4) de combiner la détection de sillons avec la détection de cibles de bateaux; (5) de concevoir un modèle de détection qui peut être utilisé aussi pour la détection des cibles de bateaux en zones costières.Abstract: The main purpose of this thesis is to develop efficient algorithms and design a system for ship detection from Synthetic Aperture Radar (SAR) imagery. Ship detection usually involves through detection of point targets on a radar clutter background.The detection of a ship depends on the physical properties of the ship itself, such as size, shape, and structure; its orientation relative to the radar look-direction; and the general condition of the sea state. Our strategy is to detect all possible ship targets in SAR images, and then search around each candidate for the wake as further evidence.The objectives of our research are (1) to improve estimation of the parameters in the K-distribution model and to determine the conditions in which an alternative model (Gamma, for example) should be used instead; (2) to explore a PNN (Probabilistic Neural Networks) model as an alternative to the commonly used parameteric models; (3) to design a FC (Fuzzy Clustering) model capable of detecting both small and large ship targets from single-channel images or multi-channel images; (4) to combine wake detection with ship target detection; (5) to design a detection model that can also be used to detect ship targets in coastal areas. We have developed algorithms for each of these objectives and integrated them into a system comprising six models.The system has been tested on a number of SAR images (SEASAT, ERS and RADARSAT-1, for example) and its performance has been assessed

CFAR Ship Detection in Polarimetric Synthetic Aperture Radar Images Based on Whitening Filter

Polarimetric whitening filter (PWF) can be used to filter polarimetric synthetic aperture radar (PolSAR) images to improve the contrast between ships and sea clutter background. For this reason, the output of the filter can be used to detect ships. This paper deals with the setting of the threshold over PolSAR images filtered by the PWF. Two parameter-constant false alarm rate (2P-CFAR) is a common detection method used on whitened polarimetric images. It assumes that the probability density function (PDF) of the filtered image intensity is characterized by a log-normal distribution. However, this assumption does not always hold. In this paper, we propose a systemic analytical framework for CFAR algorithms based on PWF or multi-look PWF (MPWF). The framework covers the entire log-cumulants space in terms of the textural distributions in the product model, including the constant, gamma, inverse gamma, Fisher, beta, inverse beta, and generalized gamma distributions (GΓDs). We derive the analytical forms of the PDF for each of the textural distributions and the probability of false alarm (PFA). Finally, the threshold is derived by fixing the false alarm rate (FAR). Experimental results using both the simulated and real data demonstrate that the derived expressions and CFAR algorithms are valid and robust

Modified GLRT and AMF framework for adaptive detectors

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE."This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder."The well-known general problem of signal detection in background interference is addressed for situations where a certain statistical description of the interference is unavailable, but is replaced by the observation of some secondary (training) data that contains only the interference. For the broad class of interferences that have a large separation between signal-and noise-subspace eigenvalues, we demonstrate that adaptive detectors which use a diagonally loaded sample covariance matrix or a fast maximum likelihood (FML) estimate have significantly better detection performance than the traditional generalized likelihood ratio test (GLRT) and adaptive matched filter (AMI') detection techniques, which use a maximum likelihood (ML) covariance matrix estimate. To devise a theoretical framework that can generate similarly efficient detectors, two major modifications are proposed for Kelly's traditional GLRT and AMF detection techniques. First, a two-set GLRT decision rule takes advantage of an a priori assignment of different functions to the primary and secondary data, unlike the Kelly rule that was derived without this. Second, instead of ML estimates of the missing parameters in both GLRT and AMF detectors, we adopt expected likelihood (EL) estimates that have a likelihood within the range of most probable values generated by the actual interference covariance matrix. A Gaussian model of fluctuating target signal and interference is used in this study. We demonstrate that, even under the most favorable loaded sample-matrix inversion (LSMI) conditions, the theoretically derived EL-GLRT and FL-AMF techniques (where the loading factor is chosen from the training data using the EL matching principle) gives the same detection performance as the loaded AMF technique with a proper a priori data-invariant loading factor. For the least favorable conditions, our EL-AMF method is still superior to the standard AMF detector, and may be interpreted as an intelligent (data-dep- endent) method for selecting the loading factor.Yuri I. Abramovich, Nicholas K. Spencer, Alexei Y. Gorokho

Contribuições analíticas para sistemas de radar modernos

Orientador: José Cândido Silveira Santos FilhoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Esta tese tem como objetivo avançar no campo de sistemas de radar ao lidar com os seguintes problemas centrais: (i) detecção de alvos distribuídos e pontuais imersos em ruído Gaussiano branco complexo; (ii) desempenho de sistemas de radar na presença de clutter terrestre do tipo Weibull; e (iii) estimação Doppler para alvos de alta velocidade sob ruído Gaussiano de fundo. A primeira parte da tese (Capítulos 2-4) ataca o primeiro problema, por meio do projeto e da análise de detectores phased array ótimos e subótimos para alvos distribuídos e alvos pontuais não-flutuantes. Para cada detector, as estatísticas da variável de decisão são analisadas sob a hipótese de algum - ou mesmo nenhum - conhecimento acerca dos parâmetros do alvo e da potência média do ruído. A partir daí, calculam-se a probabilidade de detecção e a probabilidade de falso alarme. A segunda parte da tese (Capítulos 5 e 6) confronta o segundo problema, fornecendo ferramentas matemáticas eficientes para avaliar o desempenho de um detector square-law operando em clutter terrestre do tipo Weibull. Aqui, as probabilidades de detecção e falso alarme são obtidas em forma fechada e em representação por séries de convergência rápida. Para isso, faz-se uso da função-H de Fox, bem como de um cálculo abrangente de resíduos. Finalmente, na terceira parte da tese (Capítulo 7), é fornecida uma análise estatística completa da estimação Doppler de alvos com alta velocidade sujeitos a ruído Gaussiano de fundo. A solução apresentada combina duas técnicas de processamento de sinais: o processamento de subpulso e o Teorema Chinês do Resto clássico. Além disso, o desempenho dessa técnica híbrida é avaliado em forma fechada. Vale ressaltar que todas as expressões supracitadas da tese são contribuições originais, com destaque para aquelas obtidas em representações por série, que se mostram atrativas pela ampla economia tanto de tempo de execução quanto de carga computacionalAbstract: This dissertation aims to advance in the field of radar systems by dealing with the following key problems: (i) detection of distributed and point-like targets embedded in complex white Gaussian noise; (ii) radar performance in the presence of Weibull-distributed ground clutter; and (iii) doppler estimation for high-velocity targets in background Gaussian noise. The first part of this dissertation (Chapters 2-4) addresses the first problem by designing and analyzing optimal and suboptimal phased-array detectors for distributed and non-fluctuating point-like targets. For each detector, the decision-variable statistics are investigated assuming a certain or no knowledge about the parameters of the target echoes and the average noise power. In each case, the probability of detection and the probability of false alarm are derived. The second part of this dissertation (Chapters 5 and 6) addresses the second problem by providing efficient mathematical tools to evaluate the performance of a square-law detector operating in Weibull-distributed ground clutter. In this case, the probabilities of detection and false alarm are expressed in terms of both closed-form expressions and fast convergent series. To do so, we rely upon the Fox H-function as well as a comprehensive calculus of residues. Finally, in the third part of this dissertation (Chapter 7), we provide a thorough statistical analysis for the Doppler estimation of high-speed targets in background Gaussian noise. The proposed solution combines two signal processing techniques: subpulse processing and the classic Chinese Remainder Theorem. Also, the performance of this hybrid technique is assessed in closed form. It is worth mentioning that all the aforementioned expressions from this dissertation are original contributions, with emphasis on those obtained in terms of series representations, which proved attractive for large savings in both execution time and computational loadDoutoradoTelecomunicações e TelemáticaCAPE