The adaptive coherence estimator is the generalized likelihood ratio test for a class of heterogeneous environments

The adaptive coherence estimator (ACE) is known to be the generalized likelihood ratio test (GLRT) in partially homogeneous environments, i.e., when the covariance matrix Ms of the secondary data is proportional to the covariance matrix Mp of the vector under test (or Ms = gamma/Mp). In this letter, we show that ACE is indeed the GLRT for a broader class of nonhomogeneous environments, more precisely when Ms is a random matrix, with inverse complex Wishart prior distribution whose mean only is proportional to Mp. Furthermore, we prove that, for this class of heterogeneous environments, the ACE detector satisfies the constant false alarm rate (CFAR) property with respect to gamma and Mp

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

Knowledge-aided bayesian detection in heterogeneous environments

We address the problem of detecting a signal of interest in the presence of noise with unknown covariance matrix, using a set of training samples. We consider a situation where the environment is not homogeneous, i.e., when the covariance matrices of the primary and the secondary data are different. A knowledge-aided Bayesian framework is proposed, where these covariance matrices are considered as random, and some information about the covariance matrix of the training samples is available. Within this framework, the maximum a priori (MAP) estimate of the primary data covariance matrix is derived. It is shown that it amounts to colored loading of the sample covariance matrix of the secondary data. The MAP estimate is in turn used to yield a Bayesian version of the adaptive matched filter. Numerical simulations illustrate the performance of this detector, and compare it with the conventional adaptive matched filter

Synthèse des traitements STAP pour la détection en environnement hétérogène

Cet article synthétise les différents algorithmes spatio-temporels adaptatifs (STAP) développés et/ou utilisés pour la détection en environnement non-homogène. Nous rappelons en premier lieu les causes principales qui peuvent conduire à un environnement hétérogène. Puis nous présentons les stratégies STAP les plus communément utilisées dans de tels environnements

Detection of Gaussian Signal Using Adaptively Whitened Data

The adaptive matched filter, like many other adaptive detection schemes, uses in its test statistic the data under test whitened by the sample covariance matrix S of the training samples. Actually, it is a generalized likelihood ratio test (GLRT) based on the conditional (i.e., for given S) distribution of the adaptively whitened data. In this letter, we investigate detection of a Gaussian rank-one signal using the marginal (unconditional) distribution of the adaptively whitened data. A first contribution is to derive the latter and to show that it only depends on a scalar parameter, namely the signal to noise ratio. Then, a GLRT is formulated from this unconditional distribution and shown to have the constant false alarm rate property. We show that it bears close resemblance with the plain GLRT based on the whole data set (data under test and training samples). The new detector performs as well as the plain GLRT and even better with multiple cells under test and low training sample support

Change Detection Techniques with Synthetic Aperture Radar Images: Experiments with Random Forests and Sentinel-1 Observations

This work aims to clarify the potential of incoherent and coherent change detection (CD) approaches for detecting and monitoring ground surface changes using sequences of synthetic aperture radar (SAR) images. Nowadays, the growing availability of remotely sensed data collected by the twin Sentinel-1A/B sensors of the European (EU) Copernicus constellation allows fast mapping of damage after a disastrous event using radar data. In this research, we address the role of SAR (amplitude) backscattered signal variations for CD analyses when a natural (e.g., a fire, a flash flood, etc.) or a human-induced (disastrous) event occurs. Then, we consider the additional pieces of information that can be recovered by comparing interferometric coherence maps related to couples of SAR images collected between a principal disastrous event date. This work is mainly concerned with investigating the capability of different coherent/incoherent change detection indices (CDIs) and their mutual interactions for the rapid mapping of "changed" areas. In this context, artificial intelligence (AI) algorithms have been demonstrated to be beneficial for handling the different information coming from coherent/incoherent CDIs in a unique corpus. Specifically, we used CDIs that synthetically describe ground surface changes associated with a disaster event (i.e., the pre-, cross-, and post-disaster phases), based on the generation of sigma nought and InSAR coherence maps. Then, we trained a random forest (RF) to produce CD maps and study the impact on the final binary decision (changed/unchanged) of the different layers representing the available synthetic CDIs. The proposed strategy was effective for quickly assessing damage using SAR data and can be applied in several contexts. Experiments were conducted to monitor wildfire's effects in the 2021 summer season in Italy, considering two case studies in Sardinia and Sicily. Another experiment was also carried out on the coastal city of Houston, Texas, the US, which was affected by a large flood in 2017; thus, demonstrating the validity of the proposed integrated method for fast mapping of flooded zones using SAR data

On Detection and Ranking Methods for a Distributed Radio-Frequency Sensor Network: Theory and Algorithmic Implementation

A theoretical foundation for pre-detection fusion of sensors is needed if the United States Air Force is to ever field a system of distributed and layered sensors that can detect and perform parameter estimation of complex, extended targets in difficult interference environments, without human intervention, in near real-time. This research is relevant to the United States Air Force within its layered sensing and cognitive radar/sensor initiatives. The asymmetric threat of the twenty-first century introduces stressing sensing conditions that may exceed the ability of traditional monostatic sensing systems to perform their required intelligence, surveillance and reconnaissance missions. In particular, there is growing interest within the United States Air Force to move beyond single sensor sensing systems, and instead begin fielding and leveraging distributed sensing systems to overcome the inherent challenges imposed by the modern threat space. This thesis seeks to analyze the impact of integrating target echoes in the angular domain, to determine if better detection and ranking performance is achieved through the use of a distributed sensor network. Bespoke algorithms are introduced for detection and ranking ISR missions leveraging a distributed network of radio-frequency sensors: the first set of bespoke algorithms area based upon a depth-based nonparametric detection algorithm, which is to shown to enhance the recovery of targets under lower signal-to-noise ratios than an equivalent monostatic radar system; the second set of bespoke algorithms are based upon random matrix theoretic and concentration of measure mathematics, and demonstrated to outperform the depth-based nonparametric approach. This latter approach shall be shown to be effective across a broad range of signal-to-noise ratios, both positive and negative