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In this paper, an efficient power allocation (PA) strategy is developed for maneuvering target tracking (MTT) in the collocated MIMO radar. The mechanism of our strategy is to implement the optimal PA based on the prior target maneuvering information in the tracking cycle. The predicted conditional Cramer–Rao lower bound (PC-CRLB) is derived, normalized and adopted as the optimization criterion, since the PC-CRLB is based on the most recently realized measurement and provides a more accurate lower bound than the standard posterior CRLB (PCRLB). We fully demonstrate that the established optimization model is convex. By exploiting the monotonic decreasing property of the objective function, an efficient sequential relaxation-based solver is proposed for the solution, where the PA for one target is identified that whether should be fixed on the minimum level at each iteration. Simulation results show better tracking performance compared with the uniform allocation, and improved efficiency, compared with convex optimization tools.

In this paper, we consider the distributed target detection problem with unknown signal signatures in Gaussian noise with unknown covariance matrix. Two adaptive detectors are proposed by using the persymmetry of the noise covariance matrix. We derive analytical expressions for the probabilities of false alarm of the proposed detectors, which indicate their constant false alarm rate properties against the noise covariance matrix. All the theoretical expressions are confirmed by Monte Carlo simulations. Numerical examples demonstrate that the proposed detectors have better detection performance than their counterparts, especially in the case of limited training data.

In this paper, we investigate the anomaly detection problem for widespread targets with known spacial patterns under a local Gaussian model when training data are available. Three adaptive detectors are proposed based on the principles of the generalized likelihood ratio test, the Rao test, and the Wald test, respectively. We prove that these tests are statistically equivalent to each other. In addition, analytical expressions for the probability of false alarm and probability of detection of the proposed detectors are obtained, which are verified through Monte Carlo simulations. It is shown that these detectors have a constant false alarm rate against the covariance matrix. Finally, numerical examples using synthetic and real hyperspectral data demonstrate that these training data assisted detectors have better detection performance than their counterparts without training data.

This letter investigates the problem of distributed target detection with signal mismatch in homogeneous environment. Precisely, the actual signal steering vector is not aligned with the nominal one which is assumed by radar system. Within this framework, we propose a tunable detector which can adjust its directivity (robustness or selectivity) flexibly and effectively by changing a tunable parameter. Moreover, this tunable detector encompasses the generalized Kelly's generalized likelihood ratio test (GKGLRT) and the generalized adaptive matched filter (GAMF) as its two special cases. Finally, to test the effectiveness of this detector, the real data received by the IPIX radar are used for experiments. The results illustrate the superiority of the proposed detector both in simulation environment and realistic environment.

Due to the complex nature of open-pit mining rock mass, multiple variables has a significant impact on slope stability, which is difficult to evaluate under disaster conditions. The damaged rock slope stability analysis using fundamental fuzzy model is established using the concept of fuzzy measurements upon the basis of statistical analysis on large amount of measured data in Geo-Spatial study. Because of the marked “fuzziness” of the variables is analyzed in this research, the slope stability issues under disaster conditions has been analyzed using Fuzzy Mathematical Theory (FMT) which examines damaged rock slope deformation failure at the open-pit mining. The fuzzy probability formula for rock mass deformation failure, and a numerical method for calculating the fuzzy probability, is derived by applying the theory of variation probability measurements in open pit mining. Here the damaged rock slope under disaster conditions in open-pit mine area has been analyzed and The fuzzy based disaster data management concept has been proposed for analyzing the disaster in open-pit mine area for the damaged rock due to disasters. Finally, the formulation of the Gauss–Legendre is a three-point technical illustration of damaged rock slope which has been used in the open pit. The practical calculation demonstrates that the technique is used for evaluating the slope stability problems in the metal mine opencast under disaster conditions.

This paper considers the target detection problem in multiple-input multiple-output radar where the disturbance covariance matrix is unknown. Based on the Rao criterion, a persymmetric Rao test is designed by exploiting the persymmetric structure of the disturbance covariance matrix. Particularly, the proposed detector does not require training data, and exhibits strong selectivity to mismatched signals. Another contribution in this paper is to propose a two-stage detector whose second stage coincides with the proposed persymmetric Rao test. The selectivity or robustness of the two-stage detector can be tuned by selecting different threshold pairs.

In this paper, we propose a space-time allocation strategy for collocated multiple-input multiple-output (MIMO) radar to determine the beam directions to multiple targets, to be tracked. The transmit beams are allocated to different targets with distinct time units in one illumination. The basis of our strategy is to achieve the optimal probing through the feedback information in the tracking recursion cycle, with the objective of improving the overall tracking accuracy of multiple targets. We derive the posterior Cramer-Rao lower bound (PCRLB), used as the optimization criterion, to quantify the target state estimate accuracy. By introducing the illumination probability in each time unit, the space-time allocation problem is converted to a convex one. Therefore, a sufficient solution is provided, which aims at the real-time demand of radar system. Simulation results demonstrate the superiority of the proposed strategy to the uniform allocation, space-only allocation and time-only allocation methods.

It is known that accurate motion parameter estimation makes significant benefits to radar target tracking, imaging and recognition. However, maneuvering targets usually cause across-range-unit and across-Doppler-unit effects, which make it difficult to accurately estimate the motion parameters of the target. The generalized Radon-Fourier transform (GRFT) has been proposed to estimate the motion parameter vector of maneuvering targets, but only the noise scenario is considered. In this paper, the normalized adaptive GRFT (NAGRFT) is first proposed for motion parameter estimation, which is proven to be the maximum likelihood estimator (MLE) of the motion parameter vector in Gaussian clutter. Then, we derive the Cramer-Rao lower bound (CRLB) for the motion parameter vector as a comparison of the estimation mean square error (MSE) of the NAGRFT. In this derivation, the target motion is described by a high-order polynomial model, and a Gaussian-shaped function is adopted to characterize the power spectrum density of the homogenous clutter. Finally, to demonstrate the optimal estimation performance of the proposed NAGRFT, numerical experiments are provided, which show that the estimation MSE of the NAGRFT can reach the CRLB. Experiments are also provided to analyze the relationship between the CRLB and clutter parameters.

We exploit persymmetric structures to design a generalized likelihood ratio test for detecting subspace signals in homogeneous Gaussian clutter with unknown covariance matrix. The subspace model is employed to account for mismatches in the target steering vector. An exact but finite-sum expression for the probability of false alarm of the proposed detector is derived, which is verified using Monte Carlo simulations. This expression is irrelevant to the clutter covariance matrix, indicating that the proposed detector exhibits a constant false alarm rate property against the clutter covariance matrix. Numerical examples show that the proposed detector has strong robustness to the target steering vector mismatch.

This paper investigates the problem of adaptive detection of a range-spread target in colored Gaussian disturbance. The range-spread target is described by a multi-rank subspace model, which lies in a subspace but with unknown coordinates. The disturbance, usually including clutter and thermal noise, has an unknown covariance matrix. Under the above assumption, we design the Rao and generalized likelihood ratio test (GLRT) detectors by the two-step procedure, which incorporates persymmetric structure of received data. The two detectors are shown to coincide with each other. Remarkably, the proposed detector ensures constant false alarm rate property. Experimental results conducted by both simulation and real data verify that the proposed detector outperforms the existing counterparts in training-limited scenarios.

This paper considers the problem of suppressing complex-jamming, which contains sidelobe blanket jammings (SLJs), multiple near-mainlobe blanket jammings (multiple-NMLJs) and self-defensive false target jamming (SDJ). We propose a blind source separation (BSS)-based space–time multi-channel algorithm for complex-jamming suppression. The space–time multi-channel consists of spatial multiple beams and temporal multiple adjacent pulse repetition intervals (PRIs). The source signals can be separated by the BSS, owing to their statistical independence. The real target and SDJ can then be obtained by the pulse compression approach, distinguished by echo identification simultaneously. A remarkable feature of the proposed approach is that it does not require prior knowledge about real target or jammings, and it is easy to implement for engineering applications.

State-of-the-art space-time adaptive processing (STAP) algorithms devised in the beam-Doppler domain are confined by fixing the beam-Doppler cells used for adaptation, which may suffer from performance degradation. To overcome this drawback, a novel STAP algorithm in the beam-Doppler domain is proposed. The proposed algorithm adopts a generalized sidelobe canceller structure, and the filter design is formulated as a sparse representation problem by imposing a sparse constraint on the weight vector. As the sparse constraint enforces most of the elements in the weight vector to be zero (or sufficiently small in amplitude), the proposed algorithm can adaptively select the best beam-Doppler cells for adaptation, and thus it falls under the category of reduced-dimension approach. Simulation results illustrate that the proposed algorithm outperforms the existing STAP approaches with fixed beam-Doppler localized processing.

In this paper, we examine the normalized output signal-to-interference-plus-noise ratio (SINR) of a sample matrix inversion beamformer exploiting the persymmetry of the received data. The persymmetry commonly exists in the received data, when a symmetrically spaced linear array and/or symmetrically spaced pulse trains are utilized. An exact expression for the probability density function (PDF) of the normalized output SINR is derived in the mismatched case. This PDF is verified using Monte Carlo simulations. Numerical examples indicate that the exploitation of persymmetry is equivalent to doubling the training data size, and hence can greatly alleviate the requirement of training data in adaptive processing.

In this paper, we consider the distributed target detection problem in Gaussian clutter with unknown covariance matrix. By exploiting the persymmetry of the covariance matrix, an adaptive detector is proposed according to the two-step design method. The probabilities of detection and false alarm of the proposed detector are derived in closed form, which are verified through Monte Carlo simulations. The expression for the probability of false alarm reveals that the proposed detector bears constant false alarm rate against the covariance matrix. Numerical examples illustrate that the proposed detector outperforms its counterparts, especially in the limited training data environment.

In order to alleviate the effect of the limited secondary data in the non-Gaussian clutter, a knowledge aided adaptive detector is proposed. The covariance matrix estimation is modeled as a general linear combination of prior covariance matrix and sample covariance matrix. Within this consideration, we obtain an adaptive detector based on the generalized likelihood ratio test. Experimental results on simulation and real data demonstrate that the proposed detector achieves better performance than the existing one-step GLRT (1S-GLRT) detectors when the secondary data are insufficient.

For multichannel signal filtering or detection in unknown noise, it is usually difficult to obtain sufficient independent and identically distributed (IID) training data in real-world applications, which considerably degrades the performance of adaptive algorithms. In this paper, we consider the problem of subspace signal filtering and detection in sample-starved environment. A simple reduced-dimension approach is adopted, which alleviates the requirement of IID training data. First, the test and training data are projected onto the signal subspace. Then we adopt the criterion of the generalized likelihood ratio test (GLRT) to devise a detector, which can also serve as a filter. The resulting detector can properly work in sample-starved environment, where the number of IID training data is less than the dimension of the test data. Moreover, the devised approach is superior to the existing adaptive subspace processor in filtering and detection, even in some sample-abundant situations. Analytical expressions for the probabilities of detection and false alarm are derived for the proposed approach. Numerical examples are given to verify its effectiveness.

The presence of mutual coupling usually causes space-time steering vector distortion for space-time adaptive processing (STAP) in airborne radar, thereby causing significant performance degradation. In this paper, a robust STAP approach was proposed against mutual coupling based on middle subarray clutter covariance matrix reconstruction. To address the space-time steering vector distortion caused by the mutual coupling, the training snapshots of middle subarray were obtained using the spatial-temporal selection matrix, and they were collected to compute the sample covariance matrix (SCM). Thus, the clutter-plus-noise covariance matrix (CNCM) of middle subarray was reconstructed by utilizing the clutter Capon spectrum of middle subarray to integrate over the possible clutter spatial-temporal domain. Moreover, the target covariance matrix of middle subarray was calculated by employing the target Capon spectrum of middle subarray to integrate over the possible target region, and the space-time steering vector of the target was estimated with the eigenvector corresponding to its maximum eigenvalue. Finally, the proposed robust STAP weight vector of middle subarray was built. The proposed method is capable of simultaneously mitigating the mutual coupling, target components in the SCM, and target space-time steering vector mismatch. The simulation results verified the effectiveness of the proposed approach.

The problem of target detection in colocated multiple-input multiple-output radar with unknown disturbance covariance matrix is considered. According to the generalized likelihood ratio test, we design an adaptive detector by exploiting the persymmetric structure of the covariance matrix. In particular, training data are not required in the proposed adaptive detector. Analytical expressions for the probability of false alarm and detection probability are derived, which are confirmed by Monte Carlo simulations. The expression for the probability of false alarm shows that the proposed detector exhibits a constant false alarm rate property against the disturbance covariance matrix. Numerical examples based on both simulated and experimental data confirm that the proposed detector has better detection performance than its counterparts.

This paper addresses the state estimation problem in the presence of unknown time-varying non-Gaussian measurement noise (NGMN) modeled by Gaussian mixture distribution(GMD). Recently, the variational Bayesian (VB)-based estimators have been successfully used in the state estimation problem in the presence of unknown measurement noise. However, we reveal that when the state-space model is non-Gaussian, exploiting the traditional VB method, the joint posterior probability density function of the state and parameters of non-Gaussian measurement noise has no analytical result. To fill this gap, a fixed-point iteration Gaussian sum filtering (FPI-GSF) estimator is proposed to jointly estimate the state and the unknown time-varying NGMN online. The proposed estimator utilizes a fixed-point iteration scheme to iteratively calculate the state posterior distribution through the GSF and noise parameters posterior distribution via the VB method, thus it avoids calculating the joint posterior distribution. Simulation results demonstrate the effectiveness of the proposed estimator.

The problem of detecting a subspace signal in colored Gaussian noise with unknown covariance matrix is investigated by incorporating persymmetric structure of received data. The signal of interest is described with a subspace model, namely, it belongs to a subspace spanned by the columns of a known matrix, but with unknown coordinates. We propose a persymmetric detector with two tunable parameters, which includes many existing persymmetric detectors as special cases. Approximate expressions for the probabilities of false alarm and detection of the proposed detector are derived, which are verified via Monte Carlo simulations. Numerical results reveal that the exploitation of the persymmetric structure leads to a significant gain in the detection performance, especially in the case of limited training data. In addition, a further gain in the detection performance can be obtained by optimally selecting the tunable parameters.

We consider the problem of detecting a distributed target in compound-Gaussian sea clutter with Gamma distributed texture components. We design the Rao, Wald, and generalized likelihood ratio test (GLRT) detectors according to the two-step method: the first step is to obtain the Rao, Wald tests and GLRT on the assumption that the texture or/and covariance matrix structure are known; then the maximum a posteriori probability estimate of the clutter texture and the fixed point estimate of covariance matrix exploiting persymmetry are employed to replace the known texture and covariance matrix in the tests derived in the first step. Remarkably these proposed detectors ensure constant false alarm rate with respect to the covariance matrix structure. The effectiveness of the proposed detectors is verified by using simulated and real sea clutter data.

We consider the problem of detecting subspace signals embedded in subspace interference and Gaussian noise with unknown covariance matrix. According to the criterion of generalized likelihood ratio test, we exploit persymmetry to propose an adaptive detector. Moreover, the statistical characterization of the proposed detector in the absence of target signals is obtained, which exhibits a constant false alarm rate property against the noise covariance matrix. Numerical examples illustrate that the proposed detector outperforms its counterparts, especially when the number of training data is small.

This paper deals with the problem of detecting range-spread targets in Gaussian noise with unknown covariance matrix. We model the received signal under the signal-plus-noise hypothesis as the sum of noise, useful target echoes and fictitious signals, which makes the signal-plus-noise hypothesis more plausible in the mismatched case. An adaptive detector is designed according to the Rao test. We prove the proposed Rao test exhibits constant false alarm rate property against the covariance matrix. Numerical examples show that the proposed Rao outperforms its counterparts in the mismatched case.

In this paper, we investigate the anomaly detection problem for multi-pixel targets in hyperspectral imagery when training data are available. We derive the generalized likelihood ratio test and obtain its analytical expressions of the probability of false alarm and probability of detection. The performance of the proposed detector is evaluated by using simulated and real data. The results demonstrate that this training data assisted detector outperforms its counterpart without training data.

Passive multistatic radar is of great interest in both civilian and military applications due to its numerous advantages. We focus on the target detection problem in passive multistatic radar consisting of a non-cooperative illuminator of opportunity, and several spatially separated surveillance receivers. Two F-test based detectors are proposed for target detection in this passive multistatic radar. They both exhibit a constant false alarm rate with respect to noise power. We drive closed-form expressions for the probability of false alarm of the proposed detector for the case of equal noise power in each receivers. Simulation results illustrate that the proposed detectors achieve satisfactory detection performance without requirement of knowledge about noise power.

This paper investigates the problem of detecting a distributed target in the presence of signal mismatch in a partially homogeneous environment. To design a selective detector, we modify the original hypothesis test by injecting a fictitious interference under the null hypothesis test. The fictitious interference is assumed to be orthogonal to the nominal signal in the whitened subspace. Then, according to the generalized likelihood ratio criterion, we obtain a detector that has the constant false alarm rate property and is more selective than existing detectors. However, the proposed detector works only in the case of large number of training data. To overcome this limitation, we introduce a tunable detector, which is parameterized by a tunable parameter. It can work under a very loose constraint on a number of training data. More importantly, the directivity property (robustness and selectivity) of the tunable detector can be flexibly adjusted through the tunable parameter. In addition, the tunable detector can achieve roughly the same detection performance as the corresponding generalized likelihood ratio test when no signal mismatch occurs. Numerical examples are given to demonstrate the effectiveness of the proposed detectors.

In this paper, we investigate the problem of detecting a multichannel signal in nonhomogeneous environment. The nonhomogeneity is assumed to be caused by the generalized eigenrelation (GER). According to three common detector design criteria, namely, the generalized likelihood ratio (GLRT), Rao test, and Wald test, we derive three adaptive detectors, which are the generalizations of the existing ones. Numerical examples show that the detection performance of the detectors are significantly affected by the GER structure nonhomogeneity. Moreover, the GLRT provides better detection performance than the other two detectors.

The number of training data is usually limited for moving target detection in airborne radar, which can significantly degrade the performance of detectors. In this study, the authors propose a detector for detecting moving targets based on the random matrix theory (RMT). The clutter subspace is first estimated through the RMT. Then the data under test are projected onto the orthogonal complement space of the clutter subspace for whitening. Finally, the generalised energy accumulation detection of the whitened data is carried out. Simulation results show that the proposed detector can detect moving targets effectively even when the number of training data is extremely small and the detector has a fast rate of convergence and constant false alarm rate.

In this study, a novel method for overcomplete dictionary construction for sparse recovery (SR) space-time adaptive processing (STAP) is proposed, which can effectively mitigate the off-grid effect. The proposed method utilises the clutter ridge, calculated via some prior knowledge such as radar system parameters and modern inertial navigation system information, to discretise the grids in the angle-Doppler plane. The authors also investigate the accuracy of clutter ridge in the presence of several typical non-ideal factors such as array errors, intrinsic clutter motion and aircraft crab. In particular, a parameter is introduced to adaptively adjust the grid interval to avoid the strong column coherence of the dictionary. The simulation results show that the signal-to-clutter-plus-noise ratio for the SR STAP with the proposed dictionary is significantly improved, compared with the one utilising conventional dictionary. Moreover, it is shown that the novel method not only works more robustly for the side-looking array, but also has better performance for other array orientations.

This paper devises a new constant false alarm rate (CFAR) detection scheme to deal with the problem of radar target detection in heterogeneous environment. The proposed scheme, called “clustering-CFAR detector,” is data dependent and composed of three stages: an adaptive clustering procedure that, exploiting the recorded measurements of the clutter environment, divides the detection area into different classes to provide auxiliary information, a dynamic reference cell selector that chooses appropriate secondary data according to the classes, and a conventional CFAR processor to make the final decision about the target presence. The performance of “clustering-CFAR detector” is analyzed by computer simulation and public radar measured data (IPIX data and MSTAR data), and compared with existing CFAR detectors. The results show that the new detector achieves a better performance in the aspects of terrain classification, control of false alarm points, and probability of detection.

This paper investigates the statistical performance of three adaptive detectors in the presence of subspace interference and Gaussian noise. The interference is deterministic and lies in a known subspace but with unknown coordinates, while the noise is Gaussian distributed with unknown covariance matrix. For performance evaluation, we consider a more general case, namely, the case of subspace signal mismatch, where the actual signal does not completely lie in the presumed signal subspace. We derive the exact statistical distributions of the detectors, and then obtain analytical expressions for probabilities of detection and false alarm. The theoretical study reveals that the interference and signal mismatch affects the detection performance through two angles, which are the angle between the interference subspace and actual signal, and the angle between the actual signal and presumed signal subspace after they are both projected onto the interference-orthogonalized subspace. Numerical examples are provided to verify the theoretical results.

A solution for multi-radar bias estimation without a priori association is provided for a decentralized multi-radar tracking system. We describe the systematic bias of radar with random finite sets by a pseudo-measurement of bias, which is derived at the measurement level to decouple the bias estimation and target tracking. The Gaussian mixture probability hypothesis density filter is applied for estimating the systematic bias recursively in multi-target tracking scene without a priori association. The numerical results show that the proposed method provides similar performance to the maximum likelihood estimator with the perfect known association and improved performance to the maximum likelihood estimator combined with probabilistic data association.

Conventional space-time adaptive processing (STAP) technique can achieve perfect performance when applied to side-looking airborne radar (SLAR), where the clutter is relatively stationary, whereas it suffers significant degradation for non-SLAR due to severe range dependence, especially when range ambiguity is present. In theory, the range-dependent clutter is mainly located at the near range and can be eliminated via elevation non-adaptive or adaptive beamforming. However, the pure near-range clutter portion utilized for calculating elevation adaptive weights cannot be obtained due to range ambiguity in practice. In this paper, a novel method to adaptive extract the near-range clutter via sparsity-based technique is presented and the non-stationary clutter potion can be effectively eliminated by elevation adaptive beamforming. With this technique, the residual clutter becomes stationary, and thus, the corresponding STAP performance will be significantly improved.

Space–time adaptive processing (STAP) for airborne radar has recently been enriched owing to the development of methods based on sparse recovery techniques. These methods have shown advantages over the conventional ones. However, there are still difficulties in practical situations, for example, when many clutter components are not located on the discretized sampling grids of the dictionary, which will result in significant performance loss. To deal with such off-grid problem, this paper proposes a sparse Bayesian learning-based STAP (SBL-STAP) with an off-grid self-calibration method, which can effectively mitigate the off-grid effect. In the proposed method, the clutter plus noise covariance matrix is estimated via SBL. Meanwhile, we construct a small-scale complementary dictionary with an adaptive approach to calibrate the uniformly discretized dictionary. In each iteration of the SBL, the atoms of the complementary dictionary renew themselves by an approach based on weighted least squares. In this way, the atoms of complementary dictionary can converge to the clutter ridge adaptively when off-grid occurs. The simulation results show that the clutter ridge spreading caused by off-grid can be mitigated effectively, and the output signal-to-clutter-plus-noise ratio of the STAP is significantly improved. The benefits come at the cost of negligible increase of computational complexity.

We present a novel sparsity-based space-time adaptive processing (STAP) technique based on the alternating direction method to overcome the severe performance degradation caused by array gain/phase (GP) errors. The proposed algorithm reformulates the STAP problem as a joint optimization problem of the spatio-Doppler profile and GP errors in both single and multiple snapshots, and introduces a target detector using the reconstructed spatio-Doppler profiles. Simulations are conducted to illustrate the benefits of the proposed algorithm.

For the problem of detecting a subspace signal in the presence of signal mismatch, we propose a two-stage detector, referred to as the AESD. The AESD is constructed by cascading two detectors, namely, the adaptive energy detector (AED) and the adaptive subspace detector (ASD). The AESD offers great flexibility in controlling the detection performance for mismatched subspace signals, since the AED is very robust, while the ASD is very selective. We derive the analytical expressions for the probabilities of detection and false alarm, which are verified by Monte Carlo simulations.

This paper investigates the problem of detecting a multichannel signal when subspace signal mismatch occurs. A new detector is proposed, which is obtained by weighting two existing detectors, namely, the subspace-based adaptive matched filter and adaptive subspace detector. The proposed weighted detector has flexibility in controlling its capability of rejection mismatched subspace signals. Specifically, its robustness (or selectivity) for mismatched subspace signals improves as the weight value increases (or decreases). Closed-form expressions for the probabilities of detection and false alarm are derived. The theoretical results are confirmed by Monte Carlo simulations.

In this paper, we reconsider the problem of detecting a matrix-valued rank-one signal in unknown Gaussian noise, which was previously addressed for the case of sufficient training data. We relax the above assumption to the case of limited training data. We re-derive the corresponding generalized likelihood ratio test (GLRT) and two-step GLRT (2S--GLRT) based on certain unitary transformation on the test data. It is shown that the re-derived detectors can work with low sample support. Moreover, in sample-abundant environments the re-derived GLRT is the same as the previously proposed GLRT and the re-derived 2S--GLRT has better detection performance than the previously proposed 2S--GLRT. Numerical examples are provided to demonstrate the effectiveness of the re-derived detectors., This manuscript is accepted by Signal Processing

The problem of detecting subspace signals in the presence of subspace interference and Gaussian noise is examined by using multiple observations collected from multiple range cells, bands, and/or coherent processing intervals. We exploit persymmetry to propose one-step and two-step detectors, according to the criterion of generalized likelihood ratio test (GLRT). Both the proposed detectors exhibit constant false alarm rate properties against the noise covariance matrix. Moreover, the statistical characterizations of the proposed one-step detector are obtained. We derive exact expressions for the probability of false alarm (PFA) of the proposed one-step detector in six cases where the signal subspace dimension is no more than 4 or the number of observations is no more than 2. In other cases, we derive an approximate expression for the PFA of the proposed one-step detector. Numerical examples illustrate that the proposed detectors outperform their counterparts, especially when the number of training data is small. In addition, the proposed one-step GLRT detector generally has better detection performance than the two-step detector.

For the problem of detecting a distributed target using a subspace model, we examine one nonadaptive detector and three adaptive detectors. The nonadaptive detector was proposed under the assumption that the noise covariance matrix is known a priori, i.e., the detector is the asymptotic optimum detector (AOD). We derive the statistical distribution of the AOD, according to which we obtain analytical expressions for the probabilities of detection and false alarm. Many kinds of simulations are carried out, from which useful results are obtained.

Sparse representation (SR)-based inverse synthetic aperture radar (ISAR) imaging method can achieve super-resolution image of a target. However, it is computationally expensive and sensitive to noise. To overcome these two drawbacks, the authors propose the coupled Nesterov linearised Bregman iteration algorithm based on two-dimensional (2D) real-valued dictionaries (CNLBI-TRD) for ISAR imaging. First, the ISAR echoes are taken as a 2D joint SR model in the range frequency-azimuth Doppler domain. Then the 2D complex-valued dictionaries are converted into real-valued ones through unitary transformations. The computational complexity is thus decreased by a factor of at least four. Finally, the CNLBI algorithm is proposed to reconstruct the 2D SR model directly. It combines the Nesterov's accelerated gradient method with the condition number optimisation of sensing matrices. An adaptive-adjustment strategy of the soft threshold parameter is presented. Thus the total iteration numbers can be greatly reduced. The simulation results and real data experiments verify the effectiveness of the proposed imaging algorithm.

This study addresses the problem of detecting a distributed target in interference and noise with low sample support. The target signal and interference lie in two linearly independent subspaces and the spectral property of the noise is unknown. The number of available training data is too small to form a non-singular sample covariance matrix. To overcome the difficulty, the authors resort to the Bayesian framework and design two generalised likelihood ratio tests. Both detectors can reduce training requirement by utilising the a prior knowledge of the noise covariance matrix. Numerical results show that the proposed detectors provide better detection performance than the conventional solutions in training-limited scenarios.

In this letter, we consider the problem of direction detection in deterministic interference and partially homogeneous noise. The target echoes, reflected by a distributed target, all come from the same direction. However, the signal steering vector is only known to lie in a subspace of dimension greater than one. The interference belongs to a subspace linearly independent of the signal subspace. We propose two effective detectors according to the two-step design criteria of the generalized likelihood ratio test and the Wald test. It is shown that the proposed detectors possess the constant false alarm rate property and have better detection performance than their counterparts.

In this study, the authors establish the general signal model for a moving target based on the multiple-input–multiple-output radar with arbitrary transmitting waveforms and arbitrary antenna configuration. It is shown that the existing signal models are special cases of the proposed one. According to the proposed general signal model, they devise several detectors, which are based on the criteria of the generalised likelihood ratio test, Rao test, and Wald test. Numerical examples show that the detection performance varies with different transmitting waveforms and different detectors. Hence, the general signal model is useful in choosing suitable transmitting waveforms and suitable detectors for different detection tasks.

In this paper, we consider the problem of distributed target detection with subspace signal mismatch. Precisely, the echoes reflected by the distributed target all come from the same direction, and the signal steering vector is assumed to lie in a preassigned subspace. However, the actual signal steering vector does not completely belong to the presumed subspace, resulting in subspace signal mismatch. We focus on the design of selective detectors, which have good capabilities of mismatched signal rejection. To this end, we add a fictitious signal under the null hypothesis, which is orthogonal to the nominal signal subspace in the whitened or quasi-whitened subspace. According to the generalized likelihood ratio test criterion, we devise two effective detectors. Compared with the existing ones, the proposed detectors exhibit improved selectivity capabilities for signal mismatch at the price of a little bit performance loss in the case of no signal mismatch. Moreover, for the case of point-like target, which is a special case of distributed target, we derive analytical expressions for the probabilities of detection and false alarm. Simulation results illustrate the superiority of the proposed detectors and confirm our theoretical results.

We exploit persymmetry to study the adaptive detection problem with multiple observations in partially homogeneous environments where noise shares the same covariance matrix up to different power levels between the test and training data. A persymmetric subspace model is designed for taking into account steering vector mismatches. Based on the persymmetric subspace model, we propose a generalized likelihood ratio test in partially homogeneous environments. The proposed detector is proved to exhibit a constant false alarm rate property against both the covariance matrix structure and the scaling factor. Numerical examples show that the proposed detector, compared to its counterparts, is more robust to steering vector mismatches.

According to the structural characteristics of non-uniform dual circular array (NDCA), a new method is proposed to solve the problem of mutual coupling error. In this algorithm, solving the mutual coupling problem of NDCA can be equivalent to solving that of non-uniform linear array (NLA). Firstly, the mutual coupling matrix is divided into several blocks. Then, each sub-block can be decomposed into the sum of several matrices with special characteristics by matrix addition method. As a result, the signal angles and mutual coupling coefficients can be conveniently decoupled. Compared with the iterative self-calibration algorithm, the proposed algorithm has a small amount of calculation. Moreover, it neither requires any prior information nor has problem of local convergence. The new method can accurately estimate the signal directions and mutual coupling coefficients.

Radar coincidence imaging (RCI) is a recently developed staring imaging technique based on the wavefront random modulation and temporal–spatial stochastic radiation field. Before coincidence imaging processing, the RCI needs to compute the reference matrix accurately. Unfortunately, model error usually exists, which degrades the imaging performance considerably. In this article, by exploiting the sparse prior of target, the authors propose a sparsity-driven autofocus imaging via iterative maximum a posteriori (SA-MAP) algorithm for the RCI when model error exists. The algorithm performs well via simultaneous sparse imaging, self-calibration and parameters update. Simulation results demonstrate the validity of the proposed algorithm and performance improvement over the existing algorithms.

We consider the problem of detecting distributed targets in Gaussian noise with unknown covariance matrix. To make the signal-plus-noise hypothesis more plausible in the mismatched case, we model the received signal under the signal-plus-noise hypothesis as the sum of noise, useful target echoes and fictitious signals. Two adaptive detectors are designed according to the Rao test and Wald test. We prove the proposed Rao test and Wald test exhibit constant false alarm rate properties against the covariance matrix. Numerical examples show that the proposed Rao test has strong robustness against the steering vector mismatches.

We exploit persymmetry to study the adaptive detection problem with multiple observations in partially homogeneous environments where noise shares the same covariance matrix up to different power levels between the test and training data. A persymmetric subspace model is designed for taking into account steering vector mismatches. Based on the persymmetric subspace model, we propose adaptive detectors in partially homogeneous environments, according to the criteria of two-step generalized likelihood ratio test (GLRT), Wald test, and Rao test. It is found that the proposed GLRT and Wald test coincide, while the Rao test does not exist. The proposed detector is proved to exhibit a constant false alarm rate property against both the covariance matrix structure and the scaling factor. Numerical examples show that the proposed detector, compared to its counterparts, is more robust to steering vector mismatches.