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The availability of accurate estimates of the delay or time of arrival (TOA) of the incoming signals is of paramount importance for the position estimation in passive radars with multiple receivers. This correspondence aims at improving estimation of the delays by multiple detectors exploiting the cross-correlation between the cross-correlation estimates (say cross-cross-correlation) of the received signals. The resulting equation system is formulated as a least squares (LS) minimization problem, whose solution is efficiently found computing the pseudo-inverse of the model matrix. In fact, the cross-cross-correlation implicitly performs a filtering operation on the considered signal, approximating the generalized cross-correlator behavior, without using statistical information about the signal spectra. The proposed method is numerically validated in comparison with classic counterparts and theoretical bounds.

Space-time adaptive processing (STAP) is a well-known and effective method to detect targets, obscured by interference, from airborne radars that works by coherently combining signals from a phased antenna array (spatial domain) with multiple radar pulses (temporal domain). As widely demonstrated, optimum STAP, in the sense of maximizing the output signal to interference plus noise ratio (SINR), is a coherent, linear, transversal filter (i.e., tapped delay line), that can be synthesized by a complex-valued weight vector. This paper extends previous work that focused on adaptive spatial-only nulling; it derives the optimum phase-only STAP, namely, the optimal weight vector that maximizes the SINR subject to the constraint it belongs to the $N$ -torus of phase-only complex vectors, where $N$ is the number of spatio-temporal degrees of freedom. Because this problem does not admit a closed-form solution, it is solved numerically using the phase-only conjugate gradient method (CGM). The effectiveness of phase-only STAP is demonstrated using both SINR values and receiving beampattern shape, comparing it with the optimum fully-adapted STAP and the nonadapted beam former responses as well as other possible counterparts. Additionally, several analyses of practical utility also demonstrate the benefits provided by phase-only STAP.

This letter proposes a coregistration algorithm to compensate for the possible inaccuracy of trajectory sensor during the synthetic aperture radar (SAR) image acquisition process. Such a misalignment can be modeled as a pure displacement in range and azimuth directions and a rotation effect due to different angles of sight. The approach is formalized as a constrained least squares (CLS) optimization problem enforcing a constraint of the absence of a zooming effect between the two SAR images. Moreover, the system equations can optionally be weighted according to local properties between the extracted patches within the quoted couple. Interestingly, the solution can be obtained in closed form, therefore, with a low computational cost. The results of the tests conducted on the 9.6-GHz Gotcha SAR data demonstrate the capability of the strategy to properly register the imagery.

This letter considers the design of a two-stage direction of arrival (DOA) scheme for radar systems. Precisely, at the first stage a sparse recovery approach is used to obtain both DOA and complex amplitude estimates of the incoming signal. Since the DOA is evaluated on a predefined grid of bins sampling the antenna azimuth mainbeam, at the second stage, a closed-form complex-valued parabolic interpolation is performed to refine it. By doing so, the angle accuracy is improved, but at the same time maintaining fixed the overall computational complexity. Numerical results show the enhancement provided by the proposed procedure to the initial sparse recovery method.

This paper devises a tunable detection architecture to deal with mismatched signals embedded in Gaussian interference with unknown covariance matrix based on a sparse recovery technique. Specifically, a sparse learning method is exploited to estimate the amplitude and angle of arrival of the possible targets, which are then employed to design detectors relying on the two-stage detection paradigm. Remarkably, the new decision scheme exhibits a bounded-constant false alarm rate property. The performance assessment, carried out through Monte Carlo simulations, shows that the new detectors can outperform classic counterparts in terms of rejecting mismatched signals, while retaining reasonable detection performance for matched signals.

This paper considers the problem of censoring outliers from the secondary dataset in a radar scenario where the sample support is limited. To this end, the generalized regularized likelihood function (GRLF) criterion is used and the corresponding regularized maximum likelihood (RML) estimate of the outlier subset is derived. Since the exact RML estimate involves the solution of a combinatorial optimization problem, a reduced complexity but approximate RML (ARML) procedure is also designed. As to the selection of the regularization parameter, both the expected likelihood (EL) principle and the cross-validation (CV) technique are exploited. At the analysis stage, the performance of the RML and ARML procedure is evaluated based on simulated data in comparison with some previously proposed methods. The results highlight that the RML and ARML algorithm achieves, in general, a satisfactory performance level whereas the previously proposed techniques often experience some performance degradation when the volume of training data is dramatically limited.

This paper considers the design of tunable decision schemes capable of rejecting with high probability mismatched signals embedded in Gaussian interference with unknown covariance matrix. To this end, a sparse recovery technique is exploited to enhance the resolution at which the target angle of arrival is estimated with the objective to obtain high-selective detectors. The outcomes of this estimation procedure are used to devise detection architectures relying on either the twostage design paradigm or heuristic design procedures based upon the generalized likelihood ratio test. Remarkably, the new decision rules exhibit a bounded-constant false alarm rate property and allow for a tradeoff between the matched detection performance and the rejection of undesired signals by tuning a design parameter. At the analysis stage, the performance of the newly proposed detectors is assessed also in comparison with existing selective competitors. The results show that the new detectors can outperform the considered counterparts in terms of rejection of unwanted signals, while retaining reasonable detection performance of matched signals., 13 pages, 13 figures

The ability to discriminate between ballistic missile warheads and confusing objects is an important topic from different points of view. In particular, the high cost of the interceptors with respect to tactical missiles may lead to an ammunition problem. Moreover, since the time interval in which the defense system can intercept the missile is very short with respect to target velocities, it is fundamental to minimize the number of shoots per kill. For this reason, a reliable technique to classify warheads and confusing objects is required. In the efficient warhead classification system presented in this paper, a model and a robust framework is developed, which incorporates different micro-Doppler-based classification techniques. The reliability of the proposed framework is tested on both simulated and real data.

This letter studies the conformity with the reciprocity theorem on the measured polarimetric synthetic aperture radar (SAR) data. The problem is formalized via a binary hypothesis test where the reciprocity assumption is tested versus its alternative (absence of reciprocity). The generalized likelihood ratio (GLR) is used as design criterion and the resulting decision rule ensures the constant false alarm rate (CFAR) property. At the analysis stage, the performance of the GLR statistic is analyzed on the simulated data as well as on two different measured data sets (collected by two systems) thus highlighting the effectiveness of the approach.

This paper describes a new framework that, exploiting the Kullback-Leibler Divergence, allows to address the design of one-stage adaptive detectors for multiple hypothesis testing problems. Precisely, at the design stage, the problem is formulated in terms of multiple alternative hypotheses competing with the null hypothesis. Then, a one-stage decision scheme is derived in the context of both known model and unknown parameters as well as for the most general case of unknown model and parameters. Interestingly, the resulting detectors are given by the sum of the compressed log-likelihood ratio based on the available data and a penalty term depending on the number of unknown parameters. This general architecture is then particularized to the problem of subspace target detection, and its effectiveness is assessed through simulations also in comparison with its counterpart based on the two-stage paradigm.

This paper is focused on noncooperative target position estimation via the joint use of two-dimensional (2-D) hyperbolic and elliptic passive location techniques based on time difference of arrival (TDOA) and passive coherent locator (PCL) measurements, respectively. A fusion strategy is laid down at the signal processing level to obtain a reliable estimate of the current target position. With reference to the scenario with a single transmitter of opportunity, the mathematical model for joint exploitation of TDOA and PCL strategies is formulated. Then, the Cramer-Rao lower bound (CRLB) for the Cartesian coordinates of the target is established and the theoretical performance gains achievable over the localization technique using only TDOA or PCL observations are assessed. Finally, TDOA-PCL hybrid 2-D localization algorithms are provided and their performance in terms of root-mean-square error is compared with the square root of the CRLB.

A new algorithm for Passive Bistatic Radar (PBR) localization exploiting multiple illuminators of opportunity is proposed. To capitalize a-priori information on the receiving antenna main-lobe extent, specific constraints are forced to the target localization process. At the estimator design process the elliptic positioning problem is formulated according to the constrained Least Squares (LS) framework. Hence, the resulting non-convex optimization problem is globally solved providing a closed-form estimate to the target Cartesian coordinates. At the analysis level, the performance of the new estimator is assessed in terms of Root Mean Square Error (RMSE) behavior. The results highlight that interesting MSE improvements with respect to some counterparts available in the open literature can be achieved especially at low Signal to Noise Ratio (SNR) values.

The problem of high range resolution profile (HRRP) estimation is considered in this paper. In particular, stepped frequency waveforms are devised to enhance the target range profile (RP) estimation accuracy. The basic idea relies on the dynamic optimization of the probing waveform accounting for some feedback information to minimize the profile estimation error. The transmitted frequency hopping pattern is selected so as to minimize the predicted Cramer–Rao lower bound (CRLB) associated with the amplitudes and locations of the scattering centers falling in the coarse range bin under test (i.e., the target profile). Specifically, it is assumed that the target imaging is initially performed via a conventional linear stepped frequency transmission, hence, based on the collected data, an initial prediction of the target profile is derived (perception). Then, the RP estimation is enhanced progressively according to the cognitive paradigm, via a specific frequency pattern selection at the next transmission (action). The results highlight the capabilities of the cognitive approach to provide interesting benefits with respect to the classic linear stepped frequency strategy.

In this study, authors address high-range-resolution (HRR) profile reconstruction, when stepped-frequency waveforms are eventually used to maintain a narrow instantaneous bandwidth, resorting to the sparse learning via iterative minimisation (SLIM) paradigm, a regularised minimisation approach with an l(q)-norm constraint (for 0 < q

This paper deals with the problem of censoring outliers in a class of complex multivariate elliptically contoured distributed radar data, which is a vital issue in radar signal processing applications, such as adaptive radar detection and space-time adaptive processing. The maximum likelihood (ML) estimate of the outlier subset is derived resorting to the generalized likelihood function (GLF) criterion. Since the ML estimate involves the solution of a combinatorial problem, a reduced complexity but approximate ML (AML) procedure is also considered. At the analysis stage, the performance of the AML method is evaluated in the presence of both simulated and real radar data, also in comparison with the conventional generalized inner product (GIP) and the reiterative censored GIP (RCGIP) algorithms. The results highlight that the AML technique achieves a satisfactory performance level and can outperform both GIP and RCGIP in some situations.

In this paper, we describe novel techniques for automatic classification of the dominant scattering mechanisms associated with the pixels of polarimetric SAR images. Specifically, we investigate two operating scenarios. In the first scenario, it is assumed that the polarimetric image pixels locally share the same covariance (homogeneous environment), whereas the second scenario considers polarimetric pixels with different power levels and the same covariance structure (heterogeneous environment). In the second case, we invoke the Principle of Invariance to get rid of the dependence on the power levels. For both scenarios, we formulate the classification problem in terms of multiple hypothesis tests which is addressed by applying the model-order selection rules. The performance analysis is conducted on both simulated and measured data and demonstrates the effectiveness of the proposed approach. © 2019 IEEE.

The problem of High Resolution Range Profile (HRRP) estimation is considered in this paper. In particular, stepped frequency waveforms are devised to enhance target Range Profile (RP) estimation accuracy. The basic idea relies on the dynamic optimization of the probing waveform accounting for some feedback information to minimize the profile estimation error. The results highlight the capabilities of the cognitive approach to provide significant benefits with respect to the classic linear stepped frequency strategy. © 2017 IEEE.

In this chapter, cognition about the surrounding environment has been exploited to adapt the system to the interfering environment. Precisely, the robust joint optimization of the transmit signal and receive filter bank in the presence of signal-dependent interference has been considered. The Doppler shift of the moving target has been assumed unknown, and the worst case SINR at the output of the filter bank has been employed as figure of merit. By doing so, the effectiveness of the cognitive architecture has been investigated when the target Doppler frequency is a-priori unknown. In fact, while a rough Doppler knowledge is very reasonable during the detection confirmation or for an already tracked target, it is usually not available during the standard search radar operation and suitable cognitive algorithms are required.

A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample covariance matrix projection into a specific set of structured covariance matrices. Regardless of the considered norm, an efficient solution technique to handle the resulting constrained optimization problem is developed. Specifically, it is shown that the new family of distribution-free estimators shares a shrinkagetype form; besides, the eigenvalues estimate just requires the solution of a one-dimensional convex problem whose objective function depends on the considered unitary norm. For the two most common norm instances, i.e., Frobenius and spectral, very efficient algorithms are developed to solve the aforementioned one-dimensional optimization leading to almost closed form covariance estimates. At the analysis stage, the performance of the new estimators is assessed in terms of achievable Signal to Interference plus Noise Ratio (SINR) both for a spatial and a Doppler processing assuming different data statistical characterizations. The results show that interesting SINR improvements with respect to some counterparts available in the open literature can be achieved especially in training starved regimes., Comment: submitted for journal publication

This paper deals with detection of oil spills from multipolarization synthetic aperture radar images. The problem is cast in terms of a composite hypothesis test aimed at discriminating between the polarimetric covariance matrix (PCM) equality (absence of oil spills in the tested region) and the situation where the region under test exhibits a PCM with at least an ordered eigenvalue smaller than that of a reference covariance. This last setup reflects the physical condition where the backscattering associated with the oil spills leads to a signal, in some eigendirections, weaker than the one gathered from a reference area where the absence of any oil slicks is a priori known. A multifamily generalized likelihood ratio test approach is pursued to come up with an adaptive detector ensuring the constant false alarm rate property. At the analysis stage, the behavior of the new architecture is investigated in comparison with a benchmark (but nonimplementable) structure and some other suboptimum adaptive detectors available in the open literature. This study, which is conducted in the presence of both simulated and real data, confirms the practical effectiveness of the new approach.

The authors consider the problem of covariance matrix estimation in heterogeneous environments for radar signal processing applications, where the secondary data exhibit heterogeneity in local power and share the same covariance structure. Without resorting to the complete statistical characterisation of the sample support, a class of estimators, each of them defined as the geometric barycenter of a set of basic covariances estimates (obtained from the available secondary data) with a specific distance employed, is proposed. The basic estimates are obtained by exploiting the characteristics of positive-definite matrix space and a condition number upper bound constraint. Finally, they evaluate the detection capabilities of an adaptive normalised matched filter with the proposed estimators in the presence of compound-Gaussian disturbance comparing it with existing alternatives.

This paper deals with detection from multipolarization SAR images. The problem is cast in terms of a composite hypothesis test aimed at discriminating between the Polarimetric Covariance Matrix (PCM) equality (absence of target in the tested region) and the situation where the region under test exhibits a PCM with at least an ordered eigenvalue smaller than that of a reference covariance. This last setup reflects the physical condition where the back scattering associated with the target leads to a signal, in some eigen-directions, weaker than the one gathered from a reference area where it is apriori known the absence of targets. A Multi-family Generalized Likelihood Ratio Test (MGLRT) approach is pursued to come up with an adaptive detector ensuring the Constant False Alarm Rate (CFAR) property. At the analysis stage, the behaviour of the new architecture is investigated in comparison with a benchmark (but non-implementable) and some other adaptive sub-optimum detectors available in open literature. The study, conducted in the presence of both simulated and real data, confirms the practical effectiveness of the new approach. © 2016 IEEE.

Phase modulation induced by target micro-motions introduces side-bands 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 is capable of uniquely describing the micro-motion. 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 in 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.

In this paper we deal with the problem of detecting extended targets embedded in Gaussian interference with structured covariance matrix. We model the target echo from each range bin as a deterministic signal with an unknown scaling factor that accounts for the target response. We also exploit some a-priori knowledge about the operating environment at the design stage. Specifically, we assume that inverse disturbance covariance matrix belongs to a set described through a family of unitary invariant convex functions. Hence, we derive a class of Generalized Likelihood Ratio Tests (GLRT's) for the resulting hypothesis test. At the analysis stage, we assess the performance of some detectors, lying in the aforementioned class, in terms of Detection Probability (PD). The results highlight that the better the covariance uncertainty characterization, the better the detection performance. © 2013 IEEE.

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 semidefinite 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 detection capability of an Adaptive Matched Filter (AMF) receiver with the proposed estimator in place of the sample covariance matrix, for a spatial processing. The results show that the AMF with the structured constrained covariance matrix estimator can achieve higher Detection Probabilities (PD), than some counterparts available in open literature. © 2012 IEEE.

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. © 2012 IEEE.

A high-contrast inpainting scheme based on the Complex Ginzburg-Landau equation recently applied successfully to image restoration is applied to SAR interferograms to improve their quality and therefore final quality of Digital Elevation Models (DEMs). The new technique attempts to recover the phase values in low coherence regions through diffusion and inpainting. After phase unwrapping low coherence regions are masked and discarded and a Complex Ginzburg-Landau (CGL) inpainting scheme is applied to regions where phase values are missing. We demonstrate that the residues reduce and the proposed algorithm leads to a higher Signal-to-Noise Ratio (SNR) if compared with MCF algorithm. The restoration technique has been applied to ERS-1 and ERS-2 data sets acquired on July 1995. Results appear to be very promising: the proposed algorithm provides good performances especially in presence of strong noise level and low coherence areas with relatively small dimensions. © 2010 IEEE.