Direction detector for distributed targets in unknown noise and interference

Adaptive detection of distributed radar targets in homogeneous Gaussian noise plus subspace interference is addressed. It is assumed that the actual steering vectors lie along a fixed and unknown direction of a preassigned and known subspace, while interfering signals are supposed to belong to an unknown subspace, with directions possibly varying from one resolution cell to another. The resulting detection problem is formulated in the framework of statistical hypothesis testing and solved using an ad hoc algorithm strongly related to the generalised likelihood ratio test. A performance analysis, carried out also in comparison to natural benchmarks, is presented

Adaptive Radar Detection of a Subspace Signal Embedded in Subspace Structured plus Gaussian Interference Via Invariance

This paper deals with adaptive radar detection of a subspace signal competing with two sources of interference. The former is Gaussian with unknown covariance matrix and accounts for the joint presence of clutter plus thermal noise. The latter is structured as a subspace signal and models coherent pulsed jammers impinging on the radar antenna. The problem is solved via the Principle of Invariance which is based on the identification of a suitable group of transformations leaving the considered hypothesis testing problem invariant. A maximal invariant statistic, which completely characterizes the class of invariant decision rules and significantly compresses the original data domain, as well as its statistical characterization are determined. Thus, the existence of the optimum invariant detector is addressed together with the design of practically implementable invariant decision rules. At the analysis stage, the performance of some receivers belonging to the new invariant class is established through the use of analytic expressions

A Unified Theory of Adaptive Subspace Detection. Part I: Detector Designs

This paper addresses the problem of detecting multidimensional subspace signals, which model range-spread targets, in noise of unknown covariance. It is assumed that a primary channel of measurements, possibly consisting of signal plus noise, is augmented with a secondary channel of measurements containing only noise. The noises in these two channels share a common covariance matrix, up to a scale, which may be known or unknown. The signal model is a subspace model with variations: the subspace may be known or known only by its dimension; consecutive visits to the subspace may be unconstrained or they may be constrained by a prior distribution. As a consequence, there are four general classes of detectors and, within each class, there is a detector for the case where the scale between the primary and secondary channels is known, and for the case where this scale is unknown. The generalized likelihood ratio (GLR) based detectors derived in this paper, when organized with previously published GLR detectors, comprise a unified theory of adaptive subspace detection from primary and secondary channels of measurements

Adaptive radar detection of distributed targets in homogeneous and partially homogeneous noise plus subspace interference

This paper addresses adaptive radar detection of distributed targets in noise plus interference assumed to belong to a known or unknown subspace of the observables. At the design stage we resort to either the GLRT or the so-called two-step GLRT-based design procedure and assume that a set of noise-only data is available (the so-called secondary data). Detection algorithms have been derived modeling noise vectors, corresponding to different range cells, as independent, zero-mean, complex normal ones, sharing either the same covariance matrix (homogeneous environment) or the same covariance matrix up to possibly different (mean) power levels between primary data, i.e., range cells under test, and secondary ones (partially homogeneous environment). The performance assessment has been conducted by Monte Carlo simulation, also in comparison to previously proposed detection algorithms, and confirms the effectiveness of the newly proposed ones

Adaptive radar detection of distributed targets in homogeneous and partially homogeneous noise plus subspace interference

This paper addresses adaptive radar detection of distributed targets in noise plus interference assumed to belong to a known or unknown subspace of the observables. At the design stage we resort to either the GLRT or the so-called two-step GLRT-based design procedure and assume that a set of noise-only data is available (the so-called secondary data). Detection algorithms have been derived modeling noise vectors, corresponding to different range cells, as independent, zero-mean, complex normal ones, sharing either the same covariance matrix (homogeneous environment) or the same covariance matrix up to possibly different (mean) power levels between primary data, i.e., range cells under test, and secondary ones (partially homogeneous environment). The performance assessment has been conducted by Monte Carlo simulation, also in comparison to previously proposed detection algorithms, and confirms the effectiveness of the newly proposed ones

Adaptive Radar Detection of Distributed Targets in Homogeneous and Partially-Homogeneous Noise plus Subspace Interference

This paper addresses adaptive radar detection of distributed targets in noise plus interference assumed to belong to a known or unknown subspace of the observables. At the design stage we resort to either the GLRT or the so-called two-step GLRT-based design procedure and assume that a set of noise-only data is available (the so-called secondary data). Detection algorithms have been derived modeling noise vectors, corresponding to different range cells, as independent, zero-mean, complex normal ones, sharing either the same covariance matrix (homogeneous environment) or the same covariance matrix up to possibly different (mean) power levels between primary data, i.e., range cells under test, and secondary ones (partially homogeneous environment). The performance assessment has been conducted by Monte Carlo simulation, also in comparison to previously proposed detection algorithms, and confirms the effectiveness of the newly proposed ones

Informative Data Fusion: Beyond Canonical Correlation Analysis

Multi-modal data fusion is a challenging but common problem arising in fields such as economics, statistical signal processing, medical imaging, and machine learning. In such applications, we have access to multiple datasets that use different data modalities to describe some system feature. Canonical correlation analysis (CCA) is a multidimensional joint dimensionality reduction algorithm for exactly two datasets. CCA finds a linear transformation for each feature vector set such that the correlation between the two transformed feature sets is maximized. These linear transformations are easily found by solving the SVD of a matrix that only involves the covariance and cross-covariance matrices of the feature vector sets. When these covariance matrices are unknown, an empirical version of CCA substitutes sample covariance estimates formed from training data. However, when the number of training samples is less than the combined dimension of the datasets, CCA fails to reliably detect correlation between the datasets. This thesis explores the the problem of detecting correlations from data modeled by the ubiquitous signal-plus noise data model. We present a modification to CCA, which we call informative CCA (ICCA) that first projects each dataset onto a low-dimensional informative signal subspace. We verify the superior performance of ICCA on real-world datasets and argue the optimality of trim-then-fuse over fuse-then-trim correlation analysis strategies. We provide a significance test for the correlations returned by ICCA and derive improved estimates of the population canonical vectors using insights from random matrix theory. We then extend the analysis of CCA to regularized CCA (RCCA) and demonstrate that setting the regularization parameter to infinity results in the best performance and has the same solution as taking the SVD of the cross-covariance matrix of the two datasets. Finally, we apply the ideas learned from ICCA to multiset CCA (MCCA), which analyzes correlations for more than two datasets. There are multiple formulations of multiset CCA (MCCA), each using a different combination of objective function and constraint function to describe a notion of multiset correlation. We consider MAXVAR, provide an informative version of the algorithm, which we call informative MCCA (IMCCA), and demonstrate its superiority on a real-world dataset.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113419/1/asendorf_1.pd