Adaptive detection in nonhomogeneous environments using the generalized eigenrelation

This letter considers adaptive detection of a signal in a nonhomogeneous environment, more precisely under a covariance mismatch between the test vector and the training samples, due to an interference that is not accounted for by the training samples, e.g., a sidelobe target or an undernulled interference. We assume that the covariance matrices of the test vector and the training samples verify the so-called generalized eigenrelation. Under this assumption, we derive the generalized likelihood ratio test and show that it coincides with Kelly’s detector

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

Enforcement of Regulation, Irregular Sector, and Firm Performance

In this paper we investigate how enforcement of regulation affects the size of irregular sector, firm perfomance and the exit rate to the market. Three kinds of enforcement policy will be tested in the model: control, punish and legitimacy. The first policy is based on the number of inspectors present in the economy; the second is defined by the magnitude of punish; the third is measured by the social legitimacy. Our results show the negligible influence of control to enforce irregularity; the strong effect of punish on irregular sector with a high exit rate; the good effect of legitimacy policy in promoting regularity with a low output performance.Irregular sector; enforcement policies; exit rate; firm perfomance

Adaptive Radar Detection of Dim Moving Targets in Presence of Range Migration

This paper addresses adaptive radar detection of dim moving targets. To circumvent range migration, the detection problem is formulated as a multiple hypothesis test and solved applying model order selection rules which allow to estimate the "position" of the target within the CPI and eventually detect it. The performance analysis proves the effectiveness of the proposed approach also in comparison to existing alternatives.Comment: 5 pages, 2 figures, submitted to IEEE Signal Processing Letter

A Unifying Framework for Adaptive Radar Detection in Homogeneous plus Structured Interference-Part II: Detectors Design

This paper deals with the problem of adaptive multidimensional/multichannel signal detection in homogeneous Gaussian disturbance with unknown covariance matrix and structured (unknown) deterministic interference. The aforementioned problem extends the well-known Generalized Multivariate Analysis of Variance (GMANOVA) tackled in the open literature. In a companion paper, we have obtained the Maximal Invariant Statistic (MIS) for the problem under consideration, as an enabling tool for the design of suitable detectors which possess the Constant False-Alarm Rate (CFAR) property. Herein, we focus on the development of several theoretically-founded detectors for the problem under consideration. First, all the considered detectors are shown to be function of the MIS, thus proving their CFARness property. Secondly, coincidence or statistical equivalence among some of them in such a general signal model is proved. Thirdly, strong connections to well-known simpler scenarios found in adaptive detection literature are established. Finally, simulation results are provided for a comparison of the proposed receivers.Comment: Submitted for journal publicatio

An improved adaptive sidelobe blanker

We propose a two-stage detector consisting of a subspace detector followed by the whitened adaptive beamformer orthogonal rejection test. The performance analysis shows that it possesses the constant false alarm rate property with respect to the unknown covariance matrix of the noise and that it can guarantee a wider range of directivity values with respect to previously proposed two-stage detectors. The probability of false alarm and the probability of detection (for both matched and mismatched signals) have been evaluated by means of numerical integration techniques

Theoretical performance analysis of the W-ABORT detector

In a recent paper we introduced a modification of the adaptive beaniformer orthogonal rejection test (ABORT) for adaptive detection of signals in unknown noise, by supposing under the null hypothesis the presence of signals orthogonal to the nominal steering vector in the whitened observation space. We will refer to this new receiver as the whitened adaptive beamformer orthogonal rejection test (W-ABORT). Through Monte Carlo simulations this new detector was shown to provide better rejection capabilities of mismatched (e.g., sidelobe) signals than existing ones, like ABORT or the adaptive coherence estimator (ACE), but at the price of a certain loss in terms of detection of matched (i.e., mainlobe) signals. The aim of this paper is to provide a theoretical validation of this fact. We consider both the case of distributed targets and point-like targets. We provide a statistical characterization of the W-ABORT test statistic, under the null hypothesis, and for matched and mismatched signals under the alternative hypothesis. For distributed targets, the probability of false alarm and the probability of detection can only be expressed in terms of multi-dimensional integrals, and are thus very complicated to obtain; in contrast, for point-like targets, such probabilities can be easily calculated by numerical integration techniques. The theoretical expressions derived herein corroborate the simulation results obtained previously

The classical Taub-Nut System: factorization, spectrum generating algebra and solution to the equations of motion

The formalism of SUSYQM (SUperSYmmetric Quantum Mechanics) is properly modified in such a way to be suitable for the description and the solution of a classical maximally superintegrable Hamiltonian System, the so-called Taub-Nut system, associated with the Hamiltonian: $$\mathcal{H}_\eta ({\mathbf{q}}, {\mathbf{p}}) = \mathcal{T}_\eta ({\mathbf{q}}, {\mathbf{p}}) + \mathcal{U}_\eta({\mathbf{q}}) = \frac{|{\mathbf{q}}| {\mathbf{p}}^2}{2m(\eta + |{\mathbf{q}}|)} - \frac{k}{\eta + |{\mathbf{q}}|} \quad (k>0, \eta>0) \, .$$ In full agreement with the results recently derived by A. Ballesteros et al. for the quantum case, we show that the classical Taub-Nut system shares a number of essential features with the Kepler system, that is just its Euclidean version arising in the limit $\eta \to 0$, and for which a SUSYQM approach has been recently introduced by S. Kuru and J. Negro. In particular, for positive $\eta$ and negative energy the motion is always periodic; it turns out that the period depends upon $\eta$ and goes to the Euclidean value as $\eta \to 0$. Moreover, the maximal superintegrability is preserved by the $\eta$-deformation, due to the existence of a larger symmetry group related to an $\eta$-deformed Runge-Lenz vector, which ensures that in $\mathbb{R}^3$ closed orbits are again ellipses. In this context, a deformed version of the third Kepler's law is also recovered. The closing section is devoted to a discussion of the $\eta<0$ case, where new and partly unexpected features arise.Comment: 11 pages, 6 figures. Version essentially extended: three new sections added, some notations changed, typos corrected and four new figures include