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Plagued by heterogeneous clutter, it is a serious challenge for airborne radars to detect low-altitude, weak targets. To overcome this problem, a novel matrix information geometry detector for airborne multi-channel radar is proposed in this paper. The proposed detector applies the given steering vector and array structure information to the matrix information geometry detection method so that it can be used for space–time adaptive detection. While improving the detection performance, the matrix information geometry detector's original anti-clutter advantage is enhanced as well. The simulation experiment results indicate that the proposed detector has advantages in several of the properties related to space–time adaptive detection, while its computational complexity does not increase significantly. Moreover, experiment results based on the measured data verify the superior performance of the proposed method. Sea-detecting data-sharing-program data, mountaintop data, and phased-array radar data are employed to verify the performance advantage of the proposed method in heterogeneous clutter and the ability for weak target detection. [ABSTRACT FROM AUTHOR]

The generalized likelihood ratio test (GLRT) for composite hypothesis testing problems is studied from a geometric perspective. An information-geometrical interpretation of the GLRT is proposed based on the geometry of curved exponential families. Two geometric pictures of the GLRT are presented for the cases where unknown parameters are and are not the same under the null and alternative hypotheses, respectively. A demonstration of one-dimensional curved Gaussian distribution is introduced to elucidate the geometric realization of the GLRT. The asymptotic performance of the GLRT is discussed based on the proposed geometric representation of the GLRT. The study provides an alternative perspective for understanding the problems of statistical inference in the theoretical sense. [ABSTRACT FROM AUTHOR]

Information divergences are commonly used to measure the dissimilarity of two elements on a statistical manifold. Differentiable manifolds endowed with different divergences may possess different geometric properties, which can result in totally different performances in many practical applications. In this paper, we propose a total Bregman divergence-based matrix information geometry (TBD-MIG) detector and apply it to detect targets emerged into nonhomogeneous clutter. In particular, each sample data is assumed to be modeled as a Hermitian positive-definite (HPD) matrix and the clutter covariance matrix is estimated by the TBD mean of a set of secondary HPD matrices. We then reformulate the problem of signal detection as discriminating two points on the HPD matrix manifold. Three TBD-MIG detectors, referred to as the total square loss, the total log-determinant and the total von Neumann MIG detectors, are proposed, and they can achieve great performances due to their power of discrimination and robustness to interferences. Simulations show the advantage of the proposed TBD-MIG detectors in comparison with the geometric detector using an affine invariant Riemannian metric as well as the adaptive matched filter in nonhomogeneous clutter. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the connections between information geometry and performance of sensor networks for target tracking are explored to pursue a better understanding of placement, planning and scheduling issues. Firstly, the integrated Fisher information distance (IFID) between the states of two targets is analyzed by solving the geodesic equations and is adopted as a measure of target resolvability by the sensor. The differences between the IFID and the well known Kullback–Leibler divergence (KLD) are highlighted. We also explain how the energy functional, which is the “integrated, differential” KLD, relates to the other distance measures. Secondly, the structures of statistical manifolds are elucidated by computing the canonical Levi–Civita affine connection as well as Riemannian and scalar curvatures. We show the relationship between the Ricci curvature tensor field and the amount of information that can be obtained by the network sensors. Finally, an analytical presentation of statistical manifolds as an immersion in the Euclidean space for distributions of exponential type is given. The significance and potential to address system definition and planning issues using information geometry, such as the sensing capability to distinguish closely spaced targets, calculation of the amount of information collected by sensors and the problem of optimal scheduling of network sensor and resources, etc., are demonstrated. The proposed analysis techniques are presented via three basic sensor network scenarios: a simple range-bearing radar, two bearings-only passive sonars, and three ranges-only detectors, respectively. [Copyright &y& Elsevier]

This paper presents a covariance matrix estimation method based on information geometry in a heterogeneous clutter. In particular, the problem of covariance estimation is reformulated as the computation of geometric median for covariance matrices estimated by the secondary data set. A new class of total Bregman divergence is presented on the Riemanian manifold of Hermitian positive-definite (HPD) matrix, which is the foundation of information geometry. On the basis of this divergence, total Bregman divergence medians are derived instead of the sample covariance matrix (SCM) of the secondary data. Unlike the SCM, resorting to the knowledge of statistical characteristics of the sample data, the geometric structure of matrix space is considered in our proposed estimators, and then the performance can be improved in a heterogeneous clutter. At the analysis stage, numerical results are given to validate the detection performance of an adaptive normalized matched filter with our estimator compared with existing alternatives. [ABSTRACT FROM AUTHOR]

This paper proposes a class of covariance estimators based on information divergences in heterogeneous environments. In particular, the problem of covariance estimation is reformulated on the Riemannian manifold of Hermitian positive-definite (HPD) matrices. The means associated with information divergences are derived and used as the estimators. Without resorting to the complete knowledge of the probability distribution of the sample data, the geometry of the Riemannian manifold of HPD matrices is considered in mean estimators. Moreover, the robustness of mean estimators is analyzed using the influence function. Simulation results indicate the robustness and superiority of an adaptive normalized matched filter with our proposed estimators compared with the existing alternatives. [ABSTRACT FROM AUTHOR]

This paper proposes a radar target detection algorithm based on information geometry. In particular, the correlation of sample data is modeled as a Hermitian positive-definite (HPD) matrix. Moreover, a class of total Jensen–Bregman divergences, including the total Jensen square loss, the total Jensen log-determinant divergence, and the total Jensen von Neumann divergence, are proposed to be used as the distance-like function on the space of HPD matrices. On basis of these divergences, definitions of their corresponding median matrices are given. Finally, a decision rule of target detection is made by comparing the total Jensen-Bregman divergence between the median of reference cells and the matrix of cell under test with a given threshold. The performance analysis on both simulated and real radar data confirm the superiority of the proposed detection method over its conventional counterparts and existing ones. [ABSTRACT FROM AUTHOR]