Direction of arrival (DOA) estimation of a gunshot is an important issue in shooter localisation. As the distance between the firing position and the sensor array increases, the signal-to-noise ratio decreases, which degrades the accuracy of the DOA estimation. Strong noise may lead to false peaks in cross-correlation functions, which may result in spurious time difference of arrival (TDOA) estimates and hence spurious DOA estimates. The proposed gunshot DOA estimation algorithm [exhaustive search-searching consistent fundamental loop (ES-SCFL)] reduces this problem by combining the methods of standard estimation, ES, and SCFL. The ES-SCFL method looks for the best set of microphone pairs and the correct peaks of their cross-correlation functions, and uses the time lags of these peaks as the TDOA estimates for DOA estimation. The performance of the proposed algorithm is evaluated using real gunshot data recorded from a field experiment.

The present study focuses on the acoustical detection and localisation of shots using a network of wireless asynchronous acoustic nodes. The first sections describe the detection and classification schemes of the developed real-time acoustic nodes and the asynchronous shooter localisation principle. This localisation method is evaluated in free field and in complex propagation conditions, where obstacles affect the propagation of the muzzle blast and shock waves. More than 600 shots with calibre 5.56 to 12.7 mm weapons at distances varying from 100 to 800 m constitute the database used for the evaluation of the localisation performance. It shows that the localisation of shooters in complex environments is possible when the group of acoustic nodes is near to the shot trajectory.

This study evaluates and compares the accuracies of five different ballistic models in predicting the speed profile of a supersonic bullet using radar measured speed data for 36 types of bullets. Each of the five ballistic models is parameterised by a ballistic constant and the muzzle speed of the bullet. In practice, each of these two parameters spans a wide range of values because of the large number of different bullet types that are available for use in a variety of applications. For a given bullet type, the bullet's ballistic constant and muzzle speed are determined by fitting the ballistic model to the data in a least-squares (LS) sense, and the root-mean-square (RMS) and maximum absolute (MA) deviations of the LS fit of the model from the data are computed. The best ballistic model (out of the five) is the one that has the smallest RMS and MA errors for the maximum number of bullet types. This ballistic model has been applied to accurate ranging of small arms fire using a single sensor node, with and without a priori knowledge of the model parameters, and its effectiveness for both cases is demonstrated using real data recorded from a field experiment.

A method for tomographically reconstructing atmospheric temperature and wind velocity profiles from measurements of acoustic travel time between two or more unmanned aerial vehicles is presented. The approach avoids the explicit transmission of signals between aircraft, thus lending itself to use in smaller disposable aircraft. As a result, observation of hazardous, remote and hard-to-reach environments, otherwise unjustifiable on the basis of cost or risk, becomes possible; and preparation of ground sites is no longer a requirement. The mobility offers the potential for observing dynamically moving atmospheric structures and thus exploitation of dynamic meteorological environments through energy harvesting. An error analysis is provided based on simulations of a daytime convective planetary boundary layer modelled using large eddy simulation. The estimated atmospheric temperature and wind fields, represented as the weighted sum of radial basis functions, are compared to the target data to examine the potential performance envelope of the approach. The accuracy requirements are compared to those of ground-based acoustic tomography.

Three passive acoustic data processing applications using a non-linear least squares (NLS) approach are reviewed for parameter estimation of a variety of aero-acoustic emitters and observables: (i) flight motion parameter estimation of a turboprop aircraft using a sequence of instantaneous frequency measurements from a single microphone, (ii) flight motion parameter estimation of a jet aircraft using the multipath time delay measurements from a single microphone located above the ground, and (iii) target motion parameter estimation of a ground vehicle using time difference of arrival measurements of its broadband radiated noise at pairs of microphones configured as a cross array. However, the results of processing acoustic sensor data using conventional methods such as time-frequency analysis of narrowband signals and passive ranging by wavefront curvature of broadband signals show that both approaches to source parameter estimation are comparable. Conventional methods, which use basic data processing to extract source parameter information, are suited to implementation in embedded computers with limited data processing resources such as those found in networked wireless miniature sensing devices. Moreover, conventional methods can be used for initial estimation of the NLS parameter vectors.

The following study presents the acoustic aircraft detection system designed for automated detection, classification and tracking of low-flying aircraft using a network of passive acoustic sensors. The system consists of multiple autonomously powered sensor nodes, each equipped with a microphone cluster, cameras and electronics that perform pre-processing and transmit the results wirelessly to a central processing station. The station fuses the data from sensors for finding the direction of arrival (DOA) of aircraft sounds then uses triangulation techniques for the target localisation. The calculated tracks were used for steering the cameras to the acoustically tracked target to capture pictures. The extended test spanning more than two years has uncovered many challenges that are part of such deployment including the impact of the weather, natural and man-made interfering sources of noise, effects of terrain and the variety of types and modes of operation of the targets of interest. During the deployment period, the system detected a significant number of targets of interest. Several control tests with different aircraft providing ground truth GPS for comparison with the acoustic tracking was also conducted.

This study describes a three-component decomposition of Stokes vector representing the hybrid-polarimetry (hybrid-pol) data. The three components are single-bounce, double-bounce and volume scattering. At the outset, the received backscattered wave is decomposed into completely polarised (CP) and completely depolarised (CD) parts based on Born and Wolf's wave dichotomy theorem. Then, the CP part is further decomposed into three independent components which indicate the contribution of three basic scattering mechanisms. In the proposed method, the CD part is considered as random noise and no physical meaning is attached to it. Whereas in existing hybrid-pol decomposition techniques such as m − δ and m − α, this component has been considered as volume scattering. This results in volume scattering being overestimated by these techniques. The authors demonstrated that the performance of the proposed decomposition technique is better than these existing decomposition techniques.

In this study a comparative analysis is performed between a novel Viterbi based and multiple hypothesis based track stitching algorithms. The track fragments in the Viterbi based track stitching algorithm are modelled as nodes in a trellis structure. A sequential Viterbi data association algorithm is then used to solve the trellis and associate track fragments with each other. A Kalman filter is used to determine the possible associations as well as the probabilities of the associations between the track fragments. In the multiple hypothesis track stitching algorithm, the hypothesis based multiple hypothesis tracking (MHT) algorithm is extended to perform track fragment to track fragment associations, rather than associating observations to tracks. Aspects of the developed multiple hypothesis algorithm are compared with implementations of a similar nature. Novel aspects of this research include the modification of the sequential Viterbi algorithm, as well as the extension of the MHT algorithm to solve the track stitching problem. It was found that the sequential Viterbi track stitching algorithm performed somewhat better than the multiple hypothesis track stitching algorithm for similar execution times. The Viterbi based track stitching algorithm is also shown to produce more consistently acceptable results.

This study addresses the waveform design problem of multiple-input–multiple-output (MIMO) radar. The goal is to improve the detection performance for the Rician targets. The authors first establish a general signal model, which can describe the returns by both statistical and colocated MIMO radar systems. Then they derive the associated optimal Neyman–Pearson detector and find the difficulty of optimising the waveforms that maximise the probability of detection (for a fixed probability of false alarm). Alternatively, they employ the relative entropy associated with the detection problem as the design metric. In order to tackle the non-convex waveform optimisation problem, they propose a minorisation-maximisation-based design method. They prove that the proposed method can increase the relative entropy (of the devised waveforms) at each iteration and guarantees convergence. Finally, they include several numerical examples to demonstrate the effectiveness of the proposed method.

With the combined multiscale Gaussian kernel and Morlet wavelet kernel, two multiscale kernel sparse coding-based classifiers (MKSCCs) are proposed for radar target recognition using high-resolution range profiles (HRRPs). The kernel trick can make samples more clustered in higher-dimensional space. Moreover, the multiscale kernels at different scales have advantages of good generalisation and primary signature capturing ability for target's HRRP, which are helpful to improve the target recognition accuracy and robustness of MKSCC further. Numerous experiments are conducted on five types of ground vehicles’ HRRP data and the authors also make comparisons with the KSCC and some related recognition methods. The results demonstrate the effectiveness of the proposed method.

The authors generalise the construction of Doppler-tolerant Golay complementary waveforms by Pezeshki–Calderbank–Moran–Howard to complementary code sets having more than two codes, which they call Doppler-null codes. This is accomplished by exploiting number-theoretic results involving the sum-of-digits function and a generalisation to more than two symbols of the classical two-symbol Thue–Morse sequence. Two approaches are taken to establish higher-order nulls of the composite ambiguity function: one by rewriting it in terms of equal sums of powers (ESP) and the other by factoring it in product form to reveal a higher-order zero, analogous to spectral-null codes. They conclude by describing an application of minimal ESP sets to multiple-input–multiple-output radar.

This study presents an exploratory comparative study for learning the priors of synthetic aperture radar (SAR) images, using the Fields of Experts approach, a filter-based higher-order Markov random fields model, which has substantially improved the learning capability of the entire image priors. First, the authors provide new insights into prior learning for despeckling SAR images, which commonly exhibits a variety of the likelihood functions due to the complex physical process of the scattering. Second, the authors introduce a prior learning framework using a bi-level optimisation algorithm. Third, some interesting experiments are conducted to learn the priors of SAR images. Finally, the authors validate the learned priors on despeckling SAR images. It suggests that the representation of the prior is more accurate by using the training samples from the filtered real SAR images themselves than from both the optical images of the Earth's surface and the natural images.

The conventional sidelobe blanking system, known as the Maisel sidelobe blanker, uses two receiving channels with different gains to detect the presence of a jammer. The Maisel system is an ad-hoc detector without any optimality properties. Yet, it has been successfully utilised in numerous operational systems. Here, the authors study the optimum Neyman–Pearson type sidelobe blanking (SLB) detectors for the Swerling target models to assist the design of Maisel blankers. The authors note that the optimal sidelobe blankers are of theoretical interest, since they require the knowledge of target and jammer parameters, which are typically not available at the radar site. The main goals of the present study are (i) to derive the optimal Neyman–Pearson detectors for SLB, (ii) to examine the performance gap between the optimal and Maisel detectors, and (iii) to develop objective criteria for the design of Maisel blankers that provides a guarantee on the gap to the optimality. Ready-to-use computer programs to assist the design process are also provided.

A method for selecting auxiliary channels in reduced-dimension space-time adaptive processing (STAP) is proposed for airborne multiple-input multiple-output radar. The auxiliary channel selection of the proposed approach is data dependent. Based on maximum cross-correlation energy metric, the significance of each spatial-Doppler channel is evaluated, and the auxiliary channels are selected step-by-step through utilising iteration. For the sake of achieving better performance as much as possible, the proposed approach will select two auxiliary channels at the first step, and select one channel at the next each step. Due to that the explicit physical meaning is very important for a STAP algorithm, the physical meaning of the maximum cross-correlation energy metric is discussed, and the fact that the local optimal output signal-to-interference-noise (SINR) performance can be assured by the maximum cross-correlation energy metric is proved theoretically. The simulations demonstrated that the output SINR loss of the proposed approach is about −1.9 dB when only two auxiliary channels are selected. Consequently, the proposed approach can reduce the requirement of the sample support dramatically. This will be more obvious advantage for the practical application in heterogeneous clutter environments where the number of secondary samples is extremely limited.

The adaptive subspace detector in system-dependent clutter background (SDC-ASD) is proved to be able to improve the detection performance for deterministic target detection in the authors’ previous study. However, the exact performance of the SDC-ASD for fluctuating target detection is still unknown. In this study, with the aid of matrix decomposition theory, the analytical performance of the SDC-ASD for detecting fluctuating target is considered and assessed. At the design stage, the rigorous mathematical derivation processes for the exact theoretical detection performance of the SDC-ASD for fluctuating target detection is derived. The theoretical results, which have explicitly expressions for both the false alarm probability and the detection probability, not only provide an effective mathematical method to analyse the fluctuating target detection performance, but also can further simplify the deterministic target detection assessments. At the analysis stage, Monte Carlo simulations are resorted to validate the analytical results. Numerical experiments are conducted to assess the effectiveness of the SDC-ASD for fluctuating target detection. Results show that the SDC-ASD, by dealing separately with the clutter and the noise, performs the best in comparison with its published counterparts, i.e. the generalised likelihood ratio detectors, the adaptive matched filters, the adaptive subspace detectors and the low-rank detectors based on sample covariance matrix.

Geolocation based on time differences of arrival measured by three sensors is studied. Closed-form analytical solutions are derived, even for the cases where one or more sensors are not located on the earth. Exploiting four sensors, full three-dimensional localisation is achieved as well. These numbers of sensors are minimal. The analytical results have been implemented in algorithms and tested by Monte Carlo simulations. The results are unbiased and comply with the theoretical Cramer–Rao lower bound.

Sidelobes of radar waveforms can cause many undesirable consequences. Inspirited by achievements in multiple-input–multiple-output radar, the authors study how to use and design a set of nearly orthogonal waveforms for monostatic radar with coherent accumulation operation to transmit at successive pulse repetition intervals (PRIs). As the range sidelobes at different PRIs cannot be coherently accumulated anymore during the coherent accumulation, the overall sidelobe level after coherent accumulation can be decreased significantly, which is verified by numerical results.

Frequency diverse array (FDA) produces a range–angle-dependent transmit beampattern and offers a potential solution to localise targets in two dimensions with respect to slant range and azimuth angle. However, it is difficult to unambiguously estimate the target location information by a standard FDA radar via conventional adaptive beamforming due to its coupling range–angle response. In this study, the authors propose two FDA and multiple-input multiple-output (MIMO) hybrid radar transmitter design schemes by minimising the Cramér–Rao lower bound (CRLB) for range-dependent target localisation, namely, FDA–MIMO radar and transmit subarray FDA–MIMO (TS-FDA) radar. The former uses a small frequency increment across the MIMO antennas, whereas the latter divides the FDA elements into multiple subarrays using the same waveform within each subarray and orthogonal waveforms in distinct subarrays. The formulated CRLB minimisation problem is solved by convex optimisation. Furthermore, the targets are localised using the beamspace-based multiple signal classification algorithm. The designed FDA–MIMO and TS-FDA radars are evaluated by comparing their mean square error and cumulative distribution function performance.

Coherent integration for high-speed multi-targets detection is a challenging task in radar applications. First, range migration (RM) and Doppler frequency migration (DFM) induced by target's complex motions (i.e. high speed, acceleration, etc.) would result in serious integration performance loss. Second, if the scattering intensities of different targets differ significantly, the weak one would be shadowed by the strong target and makes it difficult to achieve the coherent accumulation for weak target. Existing methods either perform poorly or are too computationally expensive for coherent integration of high-speed manoeuvring targets. Two contributions are made towards addressing these limitations. First, a method based on keystone transform, fold factor phase term compensation and generalised dechirp process is proposed to remove the migrations (RM and DFM) and realise the coherent accumulation. Compared with the generalised Radon Fourier transform algorithm, the proposed method can avoid the blind speed sidelobe and has a much lower computational cost. Second, two CLEAN techniques based on sinc-like point spread function (PSF) and modified PSF are presented to eliminate the strong target's effect and highlight the weak ones. By this way, the coherent integration of strong target and weak ones can be achieved iteratively. Several simulations are provided to demonstrate the effectiveness.

In this study, a new input estimation method is proposed for targets with non-linear dynamics and unknown inputs (manoeuvres), where measurement model is corrupted with both additive and multiplicative noises. First, the authors proposed an innovative model by adding unknown inputs as a new state to the original state vector and constructed an augmented state vector. Therefore, manoeuvring model turns into a non-manoeuvring model. The proposed model does not need any manoeuvre detection stage procedure but it causes a correlation between the process and measurement noises. Subsequently, the authors modify the augmented model to deal with the cross-correlation problem. Finally an augmented extended Kalman filter scheme is proposed, which unlike the most existing literature, it can estimate unknown inputs as quickly as possible and copes with the multiplicative noises and the cross-correlation problem. The efficiency of the proposed method is demonstrated in computer simulations for a manoeuvring target with non-linear dynamics through Monte-Carlo simulation.

Uncertainty principle has made the inevitable trade-off between achieving better frequency resolution and better time resolution in signal parameter estimation. High dynamics could make this problem even more challenging. In this study, the authors propose a novel tracking method for Global Navigation Satellite System (GNSS) signal carrier. Different from the single-domain tracking methods or Strapdown Inertial Navigation System, the presented method works in the time–frequency (TF) image generated by Wigner–Ville distribution. It has the ability to restrict the TF uncertainty to a small number of pixels around instantaneous frequency (IF) curve, which almost completely avoids the effect of high dynamics in its time/frequency estimation. The clear curve of the IF in TF image makes it possible to accurately estimate the instantaneous Doppler frequency and acceleration. Moreover, this estimation can be improved by image enhancement technique and image space transforms. Its ability of GNSS signal tracking is proved by the real signal static experiments. Simulation results show that the authors’ method has the ability to track GNSS signal under at least 400 g dynamic stress in standard outdoor carrier-to-noise ratio.

This study analyses the use of human micro-Doppler signatures collected using a multistatic radar system to identify and classify unarmed and potentially armed personnel walking within a surveillance area. The signatures were recorded in a series of experimental tests and analysed through short time Fourier transform followed by feature extraction and classification. Features based on singular value decomposition and on the centroid of the micro-Doppler signature are proposed and their suitability for armed versus unarmed classification purposes discussed. It is shown that classification accuracy above 95% can be achieved using a single feature. Features based on the centroid of the signatures are shown to be also effective in cases where there are two people walking together in the same direction and at similar speed, and one of them may be armed or not, i.e. for targets not easily separable in range or in Doppler.

Low pulse repetition frequency waveforms inherently suffer from the Doppler ambiguity in inverse synthetic aperture radar (ISAR) imaging of group targets. In this study, a novel Doppler ambiguity removal method with sparse decomposition is presented for ISAR imaging of group targets. By solving a sparsity-driven optimisation problem, chirp signals corresponding to scattering centres of group targets are extracted in the azimuth time-domain, and the Doppler ambiguity number of each extracted chirp signal can be estimated simultaneously in the process of sparse decomposition. As a result, unambiguous ISAR image of group targets can be well reconstructed by a sophisticated compensation of migration through range cells and the time-varying Doppler. Extensive simulated experiments confirm the effectiveness of the proposal.

This study investigates the ability to invert synthetic aperture radar (SAR) measurement data in order to obtain unique estimates of the underlying motion parameters of targets within the imaged scene. In particular, this investigation reveals that ambiguities exist in estimating the kinematics parameters of surface targets for cases of general bistatic SAR collections. Specifically, the current study presents a detailed methodology for constructing any number of alternate target trajectories which yield the same set of SAR measurements as that corresponding to the true target motion. Additionally, the target trajectory ambiguities of the current investigation are shown to remain even if the radar system obtains bistatic range-rate or Doppler measurements. Unambiguous kinematics estimates can be obtained only through additional constraints, as with assumptions that a given surface target lies on the one-dimensional locus of a road. Thus, the ability to localise and estimate unambiguous target motion parameters relies on the energy intensity patterns of the transmission and reception beams of the radar system. Overall, the current analysis provides a simple, and yet powerful, exposition of the nature of target trajectory ambiguities in monostatic and bistatic SAR imagery.