The issue of extended target multipath tracking has been studied. Based on the geometry model on the sea surface, a novel extended target multipath tracking algorithm is proposed under the random finite sets (RFS) framework. In the algorithm, extended target probability hypothesis density (ET-PHD) filter is used as a pre-processor, and multipath Bernoulli filter (MPBF) is used as main processor. The outputs of the ET-PHD filter are treated as pseudo-measurements and fed into the MPBF. At last, probability of existence and target state are estimated from the outputs of MPBF. In contrast with the existing extended target filter and multipath filter, the proposed algorithm does not attempt to get the rigorous solution and avoids the high computational complexity. In order to get the solution of the algorithm, its particle filter implementation has been proposed. Results of simulation show that the proposed algorithm estimates target state accurately. Comparing with extended target Bernoulli filter, the proposed algorithm has good tracking performance at the presence of multipath effect.

This study deals with the multipaths suppression problem in a shielded environment with a through-wall imaging radar. The authors propose a similarity-based algorithm to eliminate the multipath ghosts for the scenario where some targets overlap with other targets’ multipath ghosts. Specifically, the authors first extract the connected domains of the radar image after binarisation, and then put them into a vector in ascending order based on the distances between their average coordinates and the array centre. Second, they divide the vector into two sub-vectors and calculate the distances between each sub-vector and all sensor locations along different paths. Third, they construct the similarity matrix using these two sub-vectors and further derive the matrix elements larger than the similarity threshold. Finally, decision rules are designed to eliminate the multipath ghosts without losing true targets. At the analyse stage, the authors assess the effectiveness of the proposed approach through simulation results showing its ability of well removing multipath ghosts.

This study proposes a novel approach to solve the source localisation problem with noisy range measurements. Since the objective function of the range-based least square problem is non-convex and non-smooth, it is challenging to achieve an accurate estimation. Unlike previous methods that took non-convexity property of the objective function into account, this approach addresses the problem considering the non-smoothness property of the objective function. The problem is solved by a two-stage local optimisation technique which is based on a smooth non-convex approximation of the original objective function. First, the least square method is utilised to obtain a coarse estimation of the problem. Then, the estimation is refined by the trust region method which converges quadratically. Simulation results are presented to show that the proposed approach outperforms other existing methods in terms of the mean squared localisation error and convergence speed.

Covariance, one of the most widely accepted mathematical tool for similarity measurement relies heavily on the assumption of Gaussian distribution noise model. Along with many other second-order statistics based methods, its performance deteriorates significantly in the presence of impulsive noise. Therefore, in this study, a generalised covariance function named bounded non-linear covariance (BNC) is put forward to handle relative problems in the presence of noise with non-Gaussian and heavy-tailed distribution. Meanwhile, the projection approximation subspace tracking-like algorithm based on BNC is proposed as well. Simulations have verified its performances over existing methods, especially the robustness to impulsive noise.

In this study, the problem of detecting and finding the location of a low probability of intercept (LPI) radar is investigated. A method based on using two electronic support antennas mounted on a moving aircraft is proposed and it is proved that the phase difference between the signals received by the two antennas can be used to detect and localise an LPI radar. In addition, the effect of the aircraft random displacements on the proposed method performance is discussed and a modification to compensate for unwanted motions is introduced. Simulation results show the effectiveness of the method for detecting very low signal-to-noise ratio signals, and the proposed method performance is compared with the short-time Fourier transform method.

The temporal variations of ionospheric total electron content (TEC) due to space weather events compromise the precision of the global navigation satellite system (GNSS) measurements. The vulnerability of GNSS services to ionospheric delay can be studied using TEC datasets. Hence, in this study, the ionospheric TEC measured during 1 January 2013–31 December 2013 from global positioning system receiver located at a low-latitude station, KL University, Vaddeswaram, Guntur, India (16.31°N, 80.37°E) has been processed and analysed using synchrosqueezing transform (SST). SST is a wavelet-based adaptive time–frequency analysis tool. The performance of SST with an autoregressive moving average (ARMA) model is analysed and validated. Its potential in decomposing and forecasting ionospheric delay for an hour in advance has been exploited. It is observed that the hybrid ARMA with SST, i.e. the SST-ARMA model is 4% more accurate in forecasting ionospheric variations than the model ARMA and 46% more accurate than the wavelet transform-ARMA model for the 91 days of TEC dataset (April–June 2013). The forecast results during various geomagnetic conditions of 24th solar maximum period (2013) indicate that SST-ARMA has the potential to be a useful tool to set up early warning systems for ionospheric disturbances.

Jamming in defence applications is increasingly difficult because of advanced signal processing countermeasures. The jamming power allocation techniques for MIMO radar are investigated based on two criteria, namely the minimum mean square error (MMSE) for target estimation and the mutual information (MI) between the radar echo and the target impulse response. Different jamming power allocation strategies are obtained using the two criteria, respectively. Furthermore, the robust jamming power allocation strategies are studied when the target, environment or waveform information are not perfectly known. The worst case performance is optimised considering two cases of uncertainty. The analysis indicates that the least favourable sets (LFSs) of the MMSE- and MI-based robust jamming are different if the radar waveform power and the target power spectral density (PSD) lie in the uncertainty sets which are confined by known upper and lower bounds. The LFSs of the MMSE- and MI-based robust jamming are the same if the target PSD and the noise PSD lie in the uncertainty sets. Results are useful for the implementation of cognitive jammer.

Distributed coherent aperture radar (DCAR) can realise N ³ times signal-to-noise ratio promotion, as well as achieve high accuracy angle estimation since it has an equivalent large aperture. However, due to its sparse array, grating lobes are emerged in antenna pattern, which will lead to ambiguous angle estimation. Based on the various degrees of freedom of DCAR, this study proposes a multi-scale combination method to disambiguate the correct angle from the ambiguous ones. Firstly, it combines the antenna in different scale, so each combination has different equivalent phase centre spacings. Secondly, phase comparison monopulse is employed to measure the angles under each combination with relatively low computational complexity, even in the single snapshot scenario. Thirdly, the high accuracy unambiguous angle can be resolved from the low accuracy unambiguous angle step by step. Moreover, the estimation accuracy and design criterion on correct angle extraction are also analysed, providing an array geometry and combination design approach to guarantee the disambiguity process a success. Finally, DCAR with two radars and eight radars are properly designed, respectively, and simulations and field experiments validate the effectiveness of the proposed method.

In critical tracking problems, it is important to follow fast manoeuvring targets and use each measurement at disposal to best estimate a fast curvilinear trajectory. The turn rate is important to that end, but it is not generally available for measurements in radar systems. This study develops a method that uses the information of the range rate, typically a fairly accurate measurement, together with the coordinate point measurement, in order to improve the turn rate estimation. It introduces an estimation method that applies a compatibility check between the range rate measurement and the estimated velocity projection on the range direction. Disagreement between these quantities indicates a turn rate change, leading to one step corrections. The particle filter combined with best linear unbiased estimator filters is used to improve state estimations and likelihood functions and the corrections are introduced independently to each particle. For comparisons, a method from the literature and the proposed method are implemented, tested and compared. Performance error analysis indicates the effectiveness of the present method for fast manoeuvrers.

Multi-sensor fusion for multiple target tracking in cluttered environments is needed for improving tracking accuracy and track maintenance over single sensor target tracking in real target tracking applications. A track quality measure, such as the probability of target existence, can be used when fusing local sensor tracks for false track discrimination at the fusion centre and to improve the performance of the track-to-track association. The track quality measure is a highly effective tool for track maintenance and lowers the computational load by sending tracks with a high probability of target existence to the track centre. In this study, the authors utilise the iterative joint-integrated probabilistic data association technique for multi-sensor distributed fusion systems. Track-to-track fusion performance also depends on distributed fusion architecture. The track-to-track fusion algorithm is evaluated in distributed fusion systems without memory, with memory, and with feedback. The track confirmation rates and position errors are simulated and compared with low-level centralised fusion, which is theoretically optimal.

Through-the-wall radar imaging (TWRI) based on the ultra-wide band (UWB) technology plays an important role in military and civil applications due to its powerful penetration and high down-range resolution. As a result, it has acquired great interest in the research of synthetic aperture radar (SAR) or multiple-input and multiple-output radar. Most of the existing algorithms for TWRI assume that the antenna array is parallel to the front wall. Therefore, they cannot guarantee an idea effect in real applications. The unknown tilt angle between the antenna array and the wall may induce an inevitable imaging distortion and even may lead to a false detection. To solve this problem, the authors propose a new datum correction algorithm based on backward propagation of electromagnetic wave in reverse time. Firstly, according to the time delay of echo signals, the tilt angle and stand-off distance are estimated to determine the coordinates of antenna elements. A datum plane consequently is determined as well. Secondly, a wave equation inversion problem is solved for giving a set of echo signals collected by the virtual parallel array along with the datum plane. Simulation shows that their proposed algorithm is effective and has robust stability against the noise.

This study considers the problem of deception electronic counter-countermeasure (ECCM) in distributed multiple-radar architectures. To discriminate deception targets from the detected targets, a two-block detection/discrimination ECCM scheme is proposed. The first block is devoted to the detection task, which is achieved by the non-coherent accumulation detector. If a target is declared, the second block is performed to discriminate between radar targets and deception jamming, exploiting the difference that the jamming signal vectors always exist in a rank one subspace and that the target signal vectors randomly distribute in the whole space. The target discriminator in the Neyman–Pearson sense is developed based on the generalised likelihood ratio test in classical linear models. Furthermore, the analytical expression for the probability of correctly discriminating radar targets is derived. An iteratively censored procedure is established to estimate the jamming subspace in real time. Finally, simulation results verify the feasibility of the new discriminator, and its performance due to the spatial correlation of radar targets, the signal-to-noise ratio, and the geometric spread are covered.

The authors present an algorithm that allows an interceptor aircraft equipped with an airborne radar to meet another air target (the intercepted) by developing a guidance law and automatically adapting and optimising the transmitted waveform on a pulse-to-pulse basis. The algorithm uses a Kalman filter to predict the relative position and speed of the interceptor with respect to the target. The transmitted waveform is automatically selected based on its ambiguity function and accuracy properties along the approaching path. For each pulse, the interceptor predicts its position and velocity with respect to the target, takes a measurement of range and radial velocity and, with the Kalman filter, refines the relative range and range rate estimates. These are fed into a linear quadratic Gaussian controller that ensures the interceptor reaches the target automatically and successfully with minimum error and with the minimum guidance energy consumption.

A novel scheduling algorithm was proposed aiming at the time resource allocation in the air-defence phased array radar. The algorithm colligated the threat density of the target and the deadline of the task to calculate the task synthetic priority. Through establishing the threat model of targets and designing the dynamic priority table, the threat level of the target, the task dwell time and the deadline of the task were colligated to calculate the task synthetic priority. Thereby all radar task synthetic priorities were dynamic, and the most important and urgent task could be prior scheduled. In addition, the notion of the threat ratio of execution was put forward to reflect the algorithm performance on scheduling the important tasks. The simulation results show the significant improvement of the proposed algorithm compared with the earliest deadline first algorithm.

In early warning surveillance domain, frequent behaviours could be mined from historical trajectories. Based on the mined frequent behaviours, online classification technology could be used to classify the continuously updated target trajectories. Online classification of frequent behaviours is of great significance for situation assessment, threat assessment and command decision. There are a lot of researches on trajectory classification. However, they cannot distinguish behaviours whose space position is similar but the moving speed and direction are quite different. The online classification performances of them are also not appropriate for early warning surveillance application. The authors propose a conformal multi-class classifier based on conformal predictor and propose a multi-factor non-conformity measure based on multidimensional trajectories firstly. Then, they present a sequential multi-factor Hausdorff nearest neighbour conformal multi-class classifier, which could online learn and classify frequent behaviours. Experiments in both simulated military scenario and realistic civilian scenario show the presented algorithm has a good performance to online classify frequent behaviours and would have a wide prospect in early warning surveillance systems.

The optimal radar detection of miniature unmanned aerial vehicles (UAVs) requires that the radar cross-section (RCS) of the UAVs be known. Although RCS estimates may be obtained from computer simulation and conventional static RCS measurements, the results may not be accurate given that the dynamic effects of the UAV, such as propeller motion, are absent. In this study, an X-band tracking radar is developed and used to measure the RCS of a mini-UAV while the UAV is in flight. Statistical methods are then applied to obtain models of the dynamic RCS for each aspect bin and for the UAV as a whole. For the particular quadcopter considered herein, the results indicate that the dynamic RCS is significantly higher than its static RCS. As a result, a target model developed from the dynamic RCS leads to a 15% increase of the 50% probability of detection range compared with a model based on static RCS measurements.

Nowadays, antenna arrays have been widely used in global navigation satellite system (GNSS) receivers to suppress interference. However, its performance of interference suppression is inevitably limited by channel mismatch. Under channel mismatch, the performance of interference suppression is affected by reference element selection, while selecting a different reference element has a different performance. Hence, it is indispensable to select the optimal reference element to make the maximum of the interference cancellation ratio. A novel method is proposed to select the optimal reference element. In comparison to the former methods, the proposed method only needs to calculate the self-correlation power of each channel and cross-correlation power of cross channel, while the parameters of channel mismatch is unnecessary. Simulations and experiments are executed, the proposed method always select the optimal reference element during the whole period, which assures the validity of the proposed method.

To enable the smoothed ℓ ₀-norm (SL0) algorithm to offer accurate estimates of the target parameters in three dimensions of range, angle, and Doppler, the fine discretisation of the potential target space is required for multiple-input multiple-output (MIMO) radars, which results in the ill-conditioned sensing matrix. Unfortunately, the SL0 algorithm will provide unacceptable results since the large errors occur in computing initial value and performing projection onto the feasible set through the use of the pseudo-inverse of the ill-conditioned sensing matrix. In this study, the authors present a robust SL0 approach for MIMO radars to provide accurate angle–range–Doppler estimates. The appropriate permutation matrix, which takes the place of the pseudo-inverse of the sensing matrix in implementing SL0 algorithm, can be pre-computed by taking advantage of the bi-conjugate gradient stabilised approach and the singular value decomposition (SVD) of the sensing matrix. Simulation results show that the proposed algorithm not only has lower computational cost, but provides better performance in estimation of range–angle–Doppler parameters, compared with the regularised iterative reweighted minimisation approach, SL0 algorithm and its modified versions in combination with Tikhonov and truncated SVD methods.