Most existing methods for direction-of-arrival (DOA) estimation are severely influenced by impulsive noise due to their Gaussian noise assumption. As a typical non-linear similarity measure, the maximum correntropy criterion (MCC) has been considered to restrain impulsive noise, because of its ability to exploit the high-order statistics of signal. However, Gaussian kernel-based MCC method is not always the optimal choice and is only suitable for the real-valued signal, which certainly limits its applications. To solve the aforementioned problems, in this study, the authors proposed a novel generalised maximum complex correntropy criterion (GMCCC)-based complex-valued quasi-Newton method to restrain impulsive noise. GMCCC adopts the generalised complex Gaussian density function as the kernel function with more flexible parameters. Besides, it can extend the benefit to the complex-valued signal. Furthermore, its properties are formalised. The complex-valued quasi-Newton method guarantees the positive definite Hessian matrix to achieve the alternate minimisation of signal subspace and signal matrix. GMCCC achieves the accurate DOA estimation from the received data which does not require the covariance matrix. Stability performance and convergence are analysed. Experiment results show that the proposed GMCCC algorithm possesses the robustness and outperforms the state-of-the-art algorithms.

Automatic modulation classification of radar signals, which plays a significant role in both civilian and military applications, is researched in this study through a deep learning network. In this study, a novel network combined a shallow convolution neural network (CNN), long short-term memory (LSTM) network and deep neural network (DNN) is proposed to recognise six types of radar signals with different signal-to-noise ratio (SNR) levels from −14 to 20 dB. First, raw signal sequences in the time domain, frequency domain and autocorrelation domain are as input for a shallow CNN. Then the features extracted by CNN will be the input of LSTM network. Finally, DNNs will output the signal modulation types directly. The simulation results demonstrate that the accuracies in autocorrelation domain are all more than 90% at −6 dB and close to 100% when SNR > −2 dB. The recognition performances of the three domains are compared. Compared with other recognition methods, the proposed method has higher average accuracy and better performance under low SNR condition. The measured results show that the proposed method has achieved high accuracies of common four kinds of measured radar signals.

Sparse representation displays remarkable characteristics when applied to image processing and classification. The critical point in the success of sparse representation-based classification is to learn an authentic dictionary. The present study proposes a virtual dictionary-based sparse representation for automatic target recognition. Based on the properties of the synthetic aperture radar (SAR) images, some low complexity modules including adding speckle noise, histogram equalisation mapping, and bicubic interpolation are applied to construct some virtual compact dictionaries using Fisher discriminative dictionary learning. These dictionaries have different discriminative information on targets, which are used independently in several sparse representation-based classifiers. The reconstruction error vectors of the latter classifiers are then combined to recognise the target using decision fusion. Based on experimental results obtained drawing upon moving and stationary target acquisition and recognition data set, the proposed method presents the highest accuracy in classification reported yet in the literature. Furthermore, the procedure improves the recognition robustness against most commonly extended operating conditions, e.g. speckle noise corruption, depression angle variation and reduced training set. Accordingly, the current study claims a robust parallel method of high real-time ability in the target recognition of SAR images applicable to practical situations.

In this study, the issue of power allocation in the statistical multiple-input–multiple-output (MIMO) radars is investigated to reduce the probability of interception. In MIMO radars, orthogonal waveforms are commonly used, in which waveforms are orthogonal frequency-diversity or phase-coded (PC) waveforms. Therefore, the low probability of intercept (LPI) optimisation problem is considered for different orthogonal signals separately. In the FD case, the LPI optimisation problem based on analysing signal processing applied to the conventional interceptor is formulated as a min–max problem. In the PC case, the problem is formulated as a sum power minimisation problem with non-convex and non-linear detection performance constraint. Some relaxations and innovations are applied to simplify the problem and to convert it to a convex-linear problem. In addition, by analysing the form of the proposed solution, the proposed algorithm is extended based on adaptive thresholding to improve the LPI performance as much as possible. Here, the original problem is solved by a standard log-barrier algorithm as a benchmark to verify the optimality of the proposed algorithms. Simulation results show that, the proposed algorithms guarantee not only the detection performances, but also the LPI performance is considerably better in comparison with traditional power allocation algorithms.

Simulation of radar cross-sections of pedestrians at automotive radar frequencies forms a key tool for software verification test beds for advanced driver assistance systems. Two commonly used simulation methods are the computationally simple scattering centre model of dynamic humans and the shooting and bouncing ray technique based on geometric optics. The latter technique is more accurate but computationally complex. Hence, it is usually used only for modelling scattered returns of still human poses. In this work, the authors combine the two methods in a linear regression framework to accurately estimate the scattering coefficients or reflectivities of point scatterers in a realistic automotive radar signal model which they subsequently use to simulate range-time, Doppler-time and range-Doppler radar signatures. The simulated signatures show a normalised mean square error <10% and a structural similarity >81% with respect to measurement results generated with an automotive radar at 77 GHz.

This study investigates the feasibility of pilot-based detection for passive coherent location (PCL) radars exploiting digital video broadcasting-terrestrial (DVB-T) signals. The DVB-T signal is formed by two parts: a data signal and a pilot signal. The parameters of the pilot signal are known thanks to the DVB-T standards that permit the generation (at the receiver) of the pilot signal. The pilot recovery technique, based on the known DVB-T standard, is utilised in DVB-T based PCL systems to reduce the number of the reception channels by considering a locally generated pilot signal as a reference signal. Consequently, no reference channel is required, which reduces the cost and the complexity of the resulting PCL system. In this work, the authors propose a signal processing method to achieve this goal. They consider theoretical analysis, simulations and real-data results to validate the feasibility of such a system.

The prevalent imaging method in inverse synthetic aperture radar (ISAR) system is range-Doppler (RD) method, which is implemented by the fast Fourier transformation (FFT). FFT is computationally efficient, but it comes with a price – the problems of wide main-lobes and high side-lobes, especially under the sparse apertures condition. In addition, the resolution of RD method is determined by the radar parameters, which poses limitation to super-resolution imaging, multi-tasking and cognitive reconfigurable applications. In this study, the authors propose a novel super-resolution ISAR imaging method based on the total least squares-estimation of signal parameters via rotational invariance technique (TLS-ESPRIT). The locations and intensities of the scatterers are obtained by employing the ESPRIT algorithm and the least squares technique. Then the ISAR image is formulated, having circumvented all of the above-mentioned limitations. Experiments based on simulated and real measured data validate the effectiveness of the proposed method.

The single-sensor Poisson multi-Bernoulli (MB) mixture (PMBM) filter has been developed for multi-target tracking (MTT). However, there is a lack of research on the multi-sensor (MS) extensions of this filter. Because the conjugate density of PMBM filter is a hybrid form, which makes it difficult to extend directly using existing methods. In this study, a general MS Poisson MB filter based on an MS measurement likelihood is derived for MS-MTT. The MB mixture in the PMBM conjugate posterior is approximated as a single MB after each measurement update step. The likelihood function is designed for the partitioned measurements. Firstly, the authors employ the greedy measurement partition algorithm to derive an efficient implementation method; a Gibbs sampler is used to solve the data association problem subsequently. Secondly, they design a novel partition mechanism based on the Gibbs sampling algorithm dealing with those measurements generated by close targets. Various performance simulation and analysis are given in Sections 5 and 6, respectively.

BPSK is the basis of current GNSS (Global Navigation Satellite System) signals. BDS (Beidou navigation satellite system) RDSS (Radio Determination Satellite Service) system also adopts BPSK to realize communication and ranging simultaneously. To realize higher system capacity, RDSS signals overlap in time and frequency domain. The signal performance is heavily determined by the MAI (Multiple Access Interference) between overlapping signals. In this paper, SSMSK (spread spectrum MSK) is proposed. The signal performance is investigated under four conditions considering the main lobe bandwidth and the receiver bandwidth. The maximum number of overlapping signals for SSMSK is 11.7% higher than BPSK when the receiver bandwidth is for the side subcarrier. And the value is 10.6% when the receiver bandwidth is. SSMSK can be received utilizing BPSK local signal. When the receiving bandwidth is , the correlation peak of SSMSK_BPSK is identical to BPSK. The tracking accuracy of SSMSK is higher than BPSK when the correlation interval is between 0.2-1 chips. The accuracy of SSMSK_BPSK is higher than BPSK when the correlation interval is 0.5 chips. The disadvantage of SSMSK is larger quantization word length. SSMSK is a better modulation for RDSS based on the comprehensive performance.

In this study, by employing the intra-pulse cross-correlation (IPCC) operation, an unambiguous velocity estimation method is proposed for narrow-band long-range radars with high carrier frequency and low pulse repetition frequency. This estimation algorithm is simple and could be easily implemented in existing radar systems without changing the radar hardware or the pulse transmitting scheme. Comparing with the slow time dimension correlation algorithm, the accuracy of the proposed intra-pulse frequency domain method is greatly improved, and the brute-force search for the unknown motion parameters is also unnecessary. By first setting a small frequency offset of the IPCC operation, the unambiguous velocity region could be significantly enlarged. Using the relatively coarse but unambiguous estimates and increasing the frequency offset step by step, the IPCC is repeatedly applied to obtain more accurate estimates. Note that the estimation results of the IPCC algorithm could be used in the maximum-likelihood estimator for ambiguity resolution. The Cramér-Rao bound for the proposed algorithm is derived, and the optimal frequency offset in the sense of estimation accuracy is also analysed. Through numerical simulations for both synthetic and real radar data, the effectiveness of the proposed estimation algorithm is verified.

In this paper, a novel prediction-discrepancy based on innovative particle filter (PDIPF) is proposed to solve the unmanned aerial vehicle (UAV) positioning problem in the presence of the global positioning system (GPS) spoofing attack, supposing that the GPS spoofing effects are in the form of unknown but bounded errors. To cope with the GPS spoofing attacks as unknown sudden changes of system state variables, the compensation of the GPS spoofing effects is adaptively done in two basic parts of PDIPF algorithm including particle weighting and covariance matrix adaption. In addition, a theorem is developed which verifies that the output estimation error is upper bounded by a given probability with the help of the adapted covariance matrix. Besides, the particle weight calculation in PDIPF is done with respect to the prediction discrepancy of generated particles from the GPS measurements. The proposed PDIPF is used to decrease the effects of any GPS spoofing errors with different probability density functions and estimate true position of UAV in the presence of the GPS spoofing attacks. The algorithm is applied to the inertial navigation system/GPS/Loran-C integration systems. Simulation results demonstrate the effectiveness of the proposed PDIPF algorithm in terms of accuracy and redundancy.

To apply the Ramanujan filter bank based on the compressed sensing theory to the period estimation of multiple sets of radar pulses, alternatives to period data and the Ramanujan Subspace are proposed in this study. First, the rationality of alternatives to the TOA (time of arrival) model is illustrated by comparing the advantages and disadvantages of the time-point model and the TOA model. Next, by clarifying the zero-sum energy property of the Ramanujan Subspace, the possibility of finding an alternative to the discrete Fourier transform sequence with smaller data is proved. On this basis, a new algorithm for estimating the stagger period of mixed pulses is proposed, which introduces the initial phase of the stagger pulses. The results of the experiments show that the algorithm can accurately estimate the hidden stagger periods of mixed pulses, and it is adept at dealing with false and missing mixed pulses.

Magnetron-based marine radar technology is mature, affordable, reliable, and very effective for maritime safety applications. Commercial systems may be procured at a modest cost as compared to fully coherent solid-state systems. Magnetron oscillators inherently generate random phase signals. Phase instability on a pulse-to-pulse basis impedes this class of marine radars from success in applications requiring coherency such as moving target indication (MTI) or in generating target imagery. This limitation may be overcome by incorporating radio frequency sampling and cross-correlation of the transmit and receive signal technology to augment the current capability of available systems. In this research, the pulse train on transmit and receive is correlated in order to reject interference and detect image targets. Sampling the transmit signal and target echo on receive permits fully coherent processing. Marine radars traditionally operate non-coherently, and as such, offer limited surveillance in clutter rich environments. In this study, the authors report on a non-coherent marine radar that has been modified to produce a pseudo-coherent or coherent-on-receive sensor system. This is crucial to MTI and target image formation. In laboratory experiments, they employed a magnetron oscillator-based system to generate an inverse synthetic aperture radar image. The image was formed using four different algorithms: filtered back-projection (FBP), time domain back-projection (TDBP), an algebraic reconstruction technique, and frequency domain back-projection. In their research, TDBP produces exquisite imagery of steel rods, and it is the standard developed in this study. FBP performed poorly as compared to all other algorithms.

The frequency diverse array multiple-input multiple-output (FDA-MIMO) radar provides range estimation capability by exploiting a small frequency offset across the transmit sensors, which has been utilised in numerous applications. However, the estimation performance is basically limited by the array geometry and signal bandwidth. In this study, the authors propose a new FDA-MIMO framework, i.e. the unfolded coprime array with ‘unfolded’ coprime frequency offsets (UCA-UCFO) framework, for joint angle and range estimation without ambiguity. The array aperture and signal bandwidth are obviously expanded by employing UCA in the spatial domain and frequency domain, which results in significantly enhanced estimation accuracy and resolution. In addition, we construct the joint angle and range estimation problem as a two-dimensional (2D)-multiple signal classification spatial spectrum and transform 2D total spectrum search into a 1D local spectrum search by introducing a successive iteration (SUIT) algorithm. The SUIT algorithm can significantly relieve the computational burden but without performance degradation. The Cramér–Rao bounds of angle and range are provided as a performance benchmark. The analysis and simulations have validated the superiority and advantages of the UCA-UCFO framework and SUIT algorithm with respect to location accuracy, resolution, and computational complexity.

High-frequency surface-wave radar (HFSWR) is widely used in vessel and aircraft detection, sea-state sensing and wind-field mapping. Target detection suffers from the ionospheric clutter, which is reflected by the ionosphere. Adaptive beamforming (ABF) has been used for ionospheric clutter mitigation. However, the performance of ABF is limited by the heterogeneous ionospheric clutter and degrees of freedom (DOF) of the antennas array. In order to improve the performance, here, the one-dimensional ABF is expanded to two-dimensional fast-time space–time adaptive processing (STAP), which combines beam and range domains to obtain more DOFs than that in the ABF. In addition, the blind sources separation (BSS) method is also used to improve the spatial covariance matrix estimation accuracy of STAP in the heterogeneous ionospheric clutter background. The simulation and real data results demonstrate the effectiveness of the proposed BSS-STAP method in HFSWR.

This study handles the three-dimensional (3D) angle-only tracking (AOT) problem, which is calculating the target's location and velocity by measuring the target's elevation and azimuth angle. Nowadays, a non-civilian (unmanned) aircraft can accelerate in an unpredictable manner. This study presents a stochastic filter re-start strategy for tracking a target which can abruptly change its velocity in any 3D directions. Moreover, this study assumes that the target's destination information is known a priori. Using the target destination information, the authors can improve the filter accuracy as well as the time efficiency. As far as they know, this study is novel in using the target's destination information for manoeuvring target tracking in 3D AOT problem. The performance of the proposed stochastic filter re-start strategy based on the target's destination information is verified under MATLAB simulations.

The vector tracking structure is receiving growing attention due to its better tracking performance than the traditional scalar tracking structure. For the scalar tracking structure, signal quality monitoring (SQM) methods can effectively detect spoofing attacks based on the influence of correlation peaks overlap on the coherent integration results. However, the methods are invalid when the overlap is inexistent. While for the vector tracking structure, the authors find that because of the combined tracking of all received signals, the coherent integration results are affected by spoofing attacks regardless of whether the overlap exists. It implies that SQM techniques have a wider application range for the vector tracking structure. To this end, an SQM-based spoofing detection method for the vector tracking structure is proposed in this study. Analysis and simulation results demonstrate that the proposed method is useful even in the spoofing scenarios where the correlation peaks do not overlap. And it can detect spoofing attacks on both pseudo-code and carrier Doppler by using the existing observations in the tracking process, which is highly practical for the vector tracking structure.

An attractive and challenging problem in source localisation is to locate a target in three-dimensional (3D) space using a single station. To satisfy the observability requirements and achieve higher accuracy, the authors draw on the idea of the inverse synthetic aperture radar for single-station localisation, which leverages the mobility of target and a time serial measurements of angle of arrival (AoA) and time difference of arrival (TDoA). A closed-form pseudo-linear estimator (PLE) is developed to estimate both 3D position and velocity of mobile target through the linearisation of AoA–TDoA measurement equations. Furthermore, to suppress the large bias of PLE caused by the correlation of measurement noise, the authors propose a superior bias-reduced estimator (BRE), which imposes a quadratic constraint to minimise the noise correlation term. They prove that BRE is asymptotically efficient, attaining the Cramér-Rao lower bound (CRLB) over the moderate noise region. Extensive simulations show that both bias and mean square error of BRE are well predicted by theoretical analysis. Most importantly, in comparison with both PLE and two traditional bias reduction methods, namely weighted total least squares and weighted instrumental variables, BRE can approach the CRLB over a wider noise region and maintain a lower bias.