Adaptive detection of distributed targets in compound-Gaussian noise without secondary data: A Bayesian approach

In this paper, we deal with the problem of adaptive detection of distributed targets embedded in colored noise modeled in terms of a compound-Gaussian process and without assuming that a set of secondary data is available.The covariance matrices of the data under test share a common structure while having different power levels. A Bayesian approach is proposed here, where the structure and possibly the power levels are assumed to be random, with appropriate distributions. Within this framework we propose GLRT-based and ad-hoc detectors. Some simulation studies are presented to illustrate the performances of the proposed algorithms. The analysis indicates that the Bayesian framework could be a viable means to alleviate the need for secondary data, a critical issue in heterogeneous scenarios

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

A novel approach to robust radar detection of range-spread targets

This paper proposes a novel approach to robust radar detection of range-spread targets embedded in Gaussian noise with unknown covariance matrix. The idea is to model the useful target echo in each range cell as the sum of a coherent signal plus a random component that makes the signal-plus-noise hypothesis more plausible in presence of mismatches. Moreover, an unknown power of the random components, to be estimated from the observables, is inserted to optimize the performance when the mismatch is absent. The generalized likelihood ratio test (GLRT) for the problem at hand is considered. In addition, a new parametric detector that encompasses the GLRT as a special case is also introduced and assessed. The performance assessment shows the effectiveness of the idea also in comparison to natural competitors.Comment: 28 pages, 8 figure

Clutter rejection for MTI radar using a single antenna and a long integration time

Moving Target Indicators (MTI) are airborne radar systems designed to detect and track moving vehicles or aircrafts. In this paper, we address the problem of detecting hazardous collision targets to avoid them. One of the best known solutions to solve this problem is given by the so-called Space-Time Adaptive Processing (STAP) algorithms which optimally filter the target signal from interference and noise exploiting the specific relationship between Direction Of Arrival (DOA) and Doppler for the ground clutter. However, these algorithms require an antenna array and multiple reception channels that increase cost and complexity. The authors propose an alternative solution using a single antenna only. In addition to the standard Doppler shift related to the radial speed, the orthoradial speed of any target can be estimated if using a long integration time. Dangerous targets and ground clutter have different signatures in the radial-orthoradial velocity plane. An optimal detector is then proposed based on the oblique projection onto the signal subspace orthogonal to the clutter subspace. The theoretical performances of this detector are derived and a realistic radar scene simulation shows the benefits of this new MTI detector

A novel target detection approach based on adaptive radar waveform design

AbstractTo resolve problems of complicated clutter, fast-varying scenes, and low signal-clutter-ratio (SCR) in application of target detection on sea for space-based radar (SBR), a target detection approach based on adaptive waveform design is proposed in this paper. Firstly, complicated sea clutter is modeled as compound Gaussian process, and a target is modeled as some scatterers with Gaussian reflectivity. Secondly, every dwell duration of radar is divided into several sub-dwells. Regular linear frequency modulated pulses are transmitted at Sub-dwell 1, and the received signal at this sub-dwell is used to estimate clutter covariance matrices and pre-detection. Estimated matrices are updated at every following sub-dwell by multiple particle filtering to cope with fast-varying clutter scenes of SBR. Furthermore, waveform of every following sub-dwell is designed adaptively according to mean square optimization technique. Finally, principal component analysis and generalized likelihood ratio test is used for mitigation of colored interference and property of constant false alarm rate, respectively. Simulation results show that, considering configuration of SBR and condition of complicated clutter, 9 dB is reduced for SCR which reliable detection requires by this target detection approach. Therefore, the work in this paper can markedly improve radar detection performance for weak targets

Regularized Covariance Matrix Estimation in Complex Elliptically Symmetric Distributions Using the Expected Likelihood Approach - Part 2: The Under-Sampled Case

In the first part of this series of two papers, we extended the expected likelihood approach originally developed in the Gaussian case, to the broader class of complex elliptically symmetric (CES) distributions and complex angular central Gaussian (ACG) distributions. More precisely, we demonstrated that the probability density function (p.d.f.) of the likelihood ratio (LR) for the (unknown) actual scatter matrix \mSigma_{0} does not depend on the latter: it only depends on the density generator for the CES distribution and is distribution-free in the case of ACG distributed data, i.e., it only depends on the matrix dimension $M$ and the number of independent training samples $T$, assuming that $T \geq M$. Additionally, regularized scatter matrix estimates based on the EL methodology were derived. In this second part, we consider the under-sampled scenario ($T \leq M$) which deserves a specific treatment since conventional maximum likelihood estimates do not exist. Indeed, inference about the scatter matrix can only be made in the $T$-dimensional subspace spanned by the columns of the data matrix. We extend the results derived under the Gaussian assumption to the CES and ACG class of distributions. Invariance properties of the under-sampled likelihood ratio evaluated at \mSigma_{0} are presented. Remarkably enough, in the ACG case, the p.d.f. of this LR can be written in a rather simple form as a product of beta distributed random variables. The regularized schemes derived in the first part, based on the EL principle, are extended to the under-sampled scenario and assessed through numerical simulations