Luca Pallotta

Maximum Likelihood Estimation of a Structured Covariance Matrix With a Condition Number Constraint

In this paper, we deal with the problem of estimating the disturbance covariance matrix for radar signal processing applications, when a limited number of training data is present. We determine the maximum likelihood (ML) estimator of the covariance matrix starting from a set of secondary data, assuming a special covariance structure (i.e., the sum of a positive semi-definite matrix plus a term proportional to the identity), and a condition number upper-bound constraint. We show that the formulated constrained optimization problem falls within the class of MAXDET problems and develop an efficient procedure for its solution in closed form. Remarkably, the computational complexity of the algorithm is of the same order as the eigenvalue decomposition of the sample covariance matrix. At the analysis stage, we assess the performance of the proposed algorithm in terms of achievable signal-to-interference-plus-noise ratio (SINR) both for a spatial and a Doppler processing. The results show that interesting SINR improvements, with respect to some existing covariance matrix estimation techniques, can be achieved.

Radar Detection of Distributed Targets in Homogeneous Interference Whose Inverse Covariance Structure is Defined via Unitary Invariant Functions

In this paper we deal with the problem of detecting an extended target embedded in homogeneous Gaussian interference with unknown but structured covariance matrix. We model the possible target echo, from each range bin under test, as a deterministic signal with an unknown scaling factor accounting for the target response. At the design stage, we exploit some a-priori knowledge about the operating environment enforcing the inverse interference plus noise covariance matrix to belong to a set described via unitary invariant continuous functions. Hence, we derive the constrained Maximum Likelihood (ML) estimates of the unknown parameters, under both the H0 and H1 hypotheses, and design the Generalized Likelihood Ratio Test (GLRT) for the considered decision problem. At the analysis stage, we assess the performance of the devised GLRT for some covariance matrix uncertainty sets of practical relevance both for spatial and Doppler processing. The results highlight that correct use of the a-priori knowledge can lead to a detection performance quite close to the optimum receiver which supposes the perfect knowledge of the interference plus noise covariance matrix.

A novel algorithm for radar classification based on doppler characteristics exploiting orthogonal Pseudo-Zernike polynomials

Phase modulation induced by target micromotions introduces sidebands in the radar spectral signature returns. Time-frequency distributions facilitate the representation of such modulations in a micro-Doppler signature that is useful in the characterization and classification of targets. Reliable micro-Doppler signature classification requires the use of robust features that are capable of uniquely describing the micromotion. Moreover, future applications of micro-Doppler classification will require meaningful representation of the observed target by using a limited set of values. In this paper, the application of the pseudo-Zernike moments for micro-Doppler classification is introduced. Specifically, the proposed algorithm consists of the extraction of the pseudo-Zernike moments from the cadence velocity diagram (CVD). The use of pseudo-Zernike moments allows invariant features to be obtained that are able to discriminate the content of two-dimensional matrices with a small number of coefficients. The analysis has been conducted both on simulated and on real radar data, demonstrating the effectiveness of the proposed approach for classification purposes.

Pseudo-Zernike based multi-pass automatic target recognition from multi-channel SAR

The capability to exploit multiple sources of information is of fundamental importance in a battlefield scenario. Information obtained from different sources, and separated in space and time, provides the opportunity to exploit diversities to mitigate uncertainty. In this study, the authors address the problem of automatic target recognition (ATR) from synthetic aperture radar platforms. The authors approach exploits both channel (e.g. polarisation) and spatial diversity to obtain suitable information for such a critical task. In particular they use the pseudo-Zernike moments (pZm) to extract features representing commercial vehicles to perform target identification. The proposed approach exploits diversities and invariant properties of pZm leading to high confidence ATR, with limited computational complexity and data transfer requirements. The effectiveness of the proposed method is demonstrated using real data from the Gotcha dataset, in different operational configurations and data source availability.

Optimization theory-based radar waveform design for spectrally dense environments

The radio frequency (RF) electromagnetic spectrum is a limited natural resource necessary for an ever-growing number of services and systems. It is used in several applications, such as mobile communications, radio and television broadcasting, as well as remote sensing. Together with oil and water, the RF spectrum now represents one of the most important, significant, crucial, and critical commodities due to the huge impact of radio services on society. Both high-quality/high-rate wireless services (4G and 5G) as well as accurate and reliable remote-sensing capabilities (air traffic control (ATC), Earth geophysical monitoring, defense and security applications) call for increased amounts of bandwidth [1], [2]. Besides, basic electromagnetic considerations, such as good foliage penetration [3], low path loss attenuation, and reduced sizes of the devices push some systems to coexist in the same frequency band [4] (for instance VHF and UHF). As a result, the RF spectrum congestion problem has been attracting the interest of many scientists and engineers during the last few years and is currently becoming one of the hot topics in both regulation and research fields [5], [6].

Pseudo-Zernike moments based radar micro-Doppler classification

Reliable micro-Doppler signature classification requires the use of robust features describing uniquely the micromotion. Moreover, future applications of micro-Doppler classification will require meaningful representation of the observed target by using a limited set of values. In this paper the application of the pseudo-Zernike moments for micro-Doppler classification is introduced demonstrating the effectiveness of the proposed approach by classifying real data. The use of pseudo-Zernike moments allows invariant features to be obtained that are able to discriminate the content of two-dimensional matrices with a small number of coefficients.

Automatic Target Recognition of Military Vehicles With Krawtchouk Moments

The challenge of automatic target recognition of military targets within a synthetic aperture radar scene is addressed in this paper. The proposed approach exploits the discrete-defined Krawtchouk moments, which are able to represent a detected extended target with few features, allowing its characterization. The proposed algorithm provides robust performance for target recognition, identification, and characterization, with high reliability in the presence of noise and reduced sensitivity to discretization errors. The effectiveness of the proposed approach is demonstrated using the MSTAR dataset.

On the Maximal Invariant Statistic for Adaptive Radar Detection in Partially Homogeneous Disturbance With Persymmetric Covariance

This letter deals with the problem of adaptive signal detection in partially homogeneous and persymmetric Gaussian disturbance within the framework of invariance theory. First, a suitable group of transformations leaving the problem invariant is introduced and the maximal invariant statistic (MIS) is derived. Then, it is shown that the (two-step) generalized-likelihood ratio test, Rao, and Wald tests can be all expressed in terms of the MIS, thus proving that they all ensure a constant false-alarm rate.

Performance prediction of the incoherent detector for a weibull fluctuating target

We deal with performance prediction of the incoherent radar receiver (i.e., squared law plus integrator) in the presence of independent nonidentically distributed (non-id)Weibull target echoes. First, we provide the probability density function (pdf) for the sum of independent but non-idWeibull random variables in terms of an infinite sum of Gamma pdfs. Then we develop an analytic expression for the detection probability as a fast converging series of functions. Finally, we study the approximation error and convergence rate of the quoted series, and evaluate the impacts on the detection performance of non-idWeibull target parameters.

Estimation of a structured covariance matrix with a condition number constraint for radar applications

In this paper we deal with the problem of estimating the disturbance covariance matrix for radar signal processing applications, when a limited number of training data is present. We determine the Maximum Likelihood (ML) estimator of the covariance matrix starting from a set of secondary data, assuming a special covariance structure (i.e. the sum of a positive semi-definite matrix plus a term proportional to the identity), and a condition number upper-bound constraint. We show that the formulated constrained optimization problem falls within the class of MAXDET problems and develop an efficient procedure for its solution in closed form. Remarkably, the computational complexity of the algorithm is of the same order as the eigenvalue decomposition of the sample covariance matrix. At the analysis stage, we assess the performance of the proposed algorithm in terms of achievable Signal to Interference plus Noise Ratio (SINR) for a spatial processing. The results show that interesting SINR improvements, with respect to other existing covariance matrix estimation techniques, can be achieved.