When the sea surface is illuminated by a radar sufficiently far away and in the absence of a coherent target, the scattered electromagnetic signal, called ‘sea clutter’ is unpredictable and can be represented by a stochastic process. A model based on stochastic differential equations and consistent with previous statistical models (K distribution) has been proposed. It depends on three parameters: , , and . To estimate them, maximum likelihood estimators for and , and an estimator based on the hypothesis of ergodicity for are proposed in this study. The authors compare three expressions for the transition probabilities: the exact one, Euler's approximation, and Nowman's approximation. By regenerating the trajectories from the same Brownian increments, they can quantify the typical error made on the sea clutter from the typical error made on the estimated parameters. Though the exact transition probabilities minimise the error on the sea clutter, they show that an approximation such as Euler's is sufficient.

This study reports the development of a coherent dual-band radar system consisting of a frequency selective surface (FSS)-based dual-band focal-point/Cassegrain parabolic antenna and a single photonics-based transceiver. The proposed antenna enables to simultaneously operate in the S and X bands due to the use of an FSS-based sub-reflector. Numerical and experimental results of the antenna reflection coefficient, radiation pattern and gain have been shown in excellent agreement for both frequency bands. Furthermore, the proposed dual-band antenna has been applied in conjunction with a photonics-based coherent dual-band radio-frequency transceiver operating in the same bands. The authors’ innovative radar system has been properly validated by the detection and ranging of a commercial aircraft and a helicopter on a building roof, using S and X bands concurrently.

In this study, authors address high-range-resolution (HRR) profile reconstruction, when stepped-frequency waveforms are eventually used to maintain a narrow instantaneous bandwidth, resorting to the sparse learning via iterative minimisation (SLIM) paradigm, a regularised minimisation approach with an -norm constraint (for ), providing a variant to the original method. Particularly, the proposed method resorts to the regularised maximum-likelihood estimation paradigm including a term promoting the sparsity of the profile and related to the -norm of the vector containing the scatterers’ reflectivities. A priori information on the interference power level is also accounted for, at the design stage, and, assuming that each range cell under test contains at most one scatterer, the actual active scatterers composing the target are determined by exploiting the Bayesian information criterion (BIC). BIC is also used to automatically select the optimised q, so as to make the procedure adaptive with respect to q. Once the location of the active scatterers has been determined, a least-squares approach is also used to obtain even more precise HRR reconstruction. Furthermore, an efficient algorithm to define optimised frequency hopping patterns, in the presence of a continuous and coordinated feedback between the transmitter and receiver, is presented and assessed. The carried out analysis shows that the SLIM-based procedure presents higher accuracy in the HRR profile recovery than other widely used techniques, i.e. the iterative adaptive approach (IAA). Moreover, results demonstrate that the target range profile estimation capabilities are enhanced, both for SLIM and IAA, when the cognitive paradigm is employed.

The Weibull and K-distributions are shown to be very similar over a range of shape parameters ( for the K-distribution), and the mapping gives a means of converting between the shape parameter of the K-distribution to the shape parameter k for the Weibull distribution. The Weibull distribution is very like a truncated normal distribution when , so that a power transform to the power can transform any Weibull distribution to a good approximation of a truncated normal distribution. The transformation was found to transform K-distributed samples to the normal distribution, where is the maximum value after clipping at the 0.9995 quantile level.

This study gives explicit closed-form expressions of the stochastic Cramer–Rao bounds (STO-CRBs) on direction-of-departure and direction-of-arrival estimation accuracies for collocated multiple-input–multiple-output (MIMO) radar with unknown spatially coloured noise. In some special cases, i.e. the CRB of direction estimation accuracy for monostatic MIMO radar, the white noise scenario is discussed. Theoretical comparisons between the STO-CRBs and the deterministic ones are presented. Finally, these bounds are numerically compared.

This paper studies sky-wave time-difference-of-arrival (TDOA) localisation in passive-radar systems, and the focus is on two-dimensional localisation on the earth surface. Signals are reflected by the ionosphere layer before arriving at sensors, making the localisation problem very complicated. Parametric methods are found to be inefficient in this case; therefore, grid-based methods are studied. However, conventional grid-based methods are not guaranteed to find the nearest grid point (NGP) of target, even when the grid map is dense and the measurements are noise-free. Hence, this paper derives the sufficient condition for NGP selection in noiseless environments. Based on it, an ellipsoid-norm method (ENM) is proposed to promise optimal results with noise-free measurements, which consists of a test phase and a search phase. If a given grid map passes the offline test phase, the search phase produces a close-form estimate at a low computational complexity. The impact of noise on ENM is also theoretically analysed. Additionally, ENM is extended to handle cases with inaccurately known ionosphere layer heights. Numerical results show that for different sensor networks, the test phase is feasible by adjusting grid densities; and ENM is superior to the current state-of-the-art in terms of estimation accuracy and computational complexity.

Any sensing task is constrained by the resources that the sensor has at its disposal. For example, a radar system can only allocate a certain amount of transmit energy per unit time to track all necessary target parameters. When multiple dynamic parameters must be tracked over time, a common approach is to schedule updates at regular intervals, subject to all of the tasks assigned to the radar timeline. However, with the advent of much more agile sensors, such as all-digital apertures, it is possible to conceive of increasingly adaptive and dynamic resource allocation strategies that will yield better performance in target-dense, resource-constrained scenarios. In this study, the authors investigate adaptive resource allocation in a canonical scenario by assuming a parallel, linear channel model, and derive various allocation strategies and compare their short- and long-term performance. The authors also investigate effectiveness as a function of varying circumstances, such as varying signal-to-noise ratio and strength of the target dynamics, and relate the results to adaptive allocation strategies for phased arrays and all-digital apertures.

Target vibration or rotation produces special phase modulation of synthetic aperture radar azimuth echo signals, referred to as the micro-Doppler effect, which can provide favourable information for target detection and recognition. However, the pulse repetition frequency will be lower than the azimuth bandwidth of azimuth echo signal when the micro-motion amplitude is too large, resulting in spectral aliasing, which invalidates the conventional detection and estimation algorithm. This study proposes a new target detection and estimation algorithm for large micro-motion targets. First, the authors perform time–frequency (TF) transform on the azimuth echo signals of micro-motion targets. Then extract the TF curves in the TF distribution. After modifying the analytical expression of large micro-motion target TF curves, the target detection and parameter estimation are realised by Hough transform. The algorithm proposed in this study is applicable to the detection of both large and small micro-motion targets. It is capable of detecting multiple micro-motion targets in a single range cell simultaneously and is featured with high parameter estimation precision even if there is strong noise. Simulation results and field experimental data prove the effectiveness of the proposed algorithm and its superiority compared with the inverse radon transform algorithm.

Owing to the exponentially increasing spectrum demand for commercial communication, radar and communication are increasingly encouraged to share spectrum. One approach is to incorporate information bearing communication sequences into radar waveforms. However, the varying radar/communication waveforms in a coherent processing interval lead to a range sidelobe modulation (RSM) that cause a loss of coherence when the Doppler processing operation is applied, thus leading to reduced target visibility. In this study, a new approach of embedding communication into radar waveform is proposed. Based on the scheme of constant envelope orthogonal frequency division multiplexing phase modulation (CE-OFDM-PM) and the orthogonality among trigonometric function, information bearing sequences are implemented using CE-OFDM-PM signal and then phase attached to a radar modulation term with a weighted coefficient. Also, the radar modulation term is synthesised by multiple sinusoidal functions where the coefficients of each sinusoidal modulation function are generated using random variables to achieve a thumbtack-like ambiguity function. The weighted coefficient of a communication modulation term provides a direct control of the degree of RSM. Theoretic analysis and simulation results show that a satisfactory communication bit error rate performance can be achieved without sacrificing the radar performance.

In this study, the authors propose a new constant false alarm rate detection algorithm in the non-homogeneous Weibull clutter caused by point-like targets interference. In their algorithm, sparsity regularisation is imposed on the target, which makes use of the target minority in detection background. On the basis of the regularised estimate of outliers, the indicator function is introduced to select the clean samples out of the background to estimate the distribution parameters, which further improves the robustness of the proposed detector. Simulation and experimental results verify the performance of the proposed detector which illustrates its superiority by making a comparison with the conventional detectors.

The joint integrated probabilistic data association (JIPDA) filter is effective for automatic multi-target tracking in cluttered environment. At each time step, the posterior probability density function (PDF) is approximated by a Gaussian PDF to estimate track states. However, JIPDA suffers from the track coalescence problem. When targets are closely spaced, their tracking gates may overlap, so that the track state estimates become biased and tend to coalesce. The authors note that the covariance can influence both the size of the tracking gate and the accuracy of the Gaussian approximation. Therefore, in this study, the posterior PDF is optimised by controlling the covariance to improve the accuracy of the track state estimates. A cost function measuring the track estimate error covariance is developed as the optimisation criterion, and an iterative strategy is adopted for minimising it. Finally, the posterior PDF with the minimal cost function is derived as the desired one. The theoretical analysis and example show that the proposed approach can reduce the extent of tracking gate overlap and improve the accuracy of the Gaussian approximation. Simulation results show that the new approach can handle track coalescence and performs better than the traditional methods.

Dealing with low probability of intercept (LPI) radar signals in very low signal-to-noise ratio (SNR) stages requires reconnaissance systems to employ an effectively practical method for detecting and fully characterising the received signals. Following the aim of LPI signal detection, in this study, a novel method based on concentrating the energy of the signal in one particular row of the time–frequency domain matrix is proposed. It is shown that the proposed method enables to detect and estimate the parameters of multiple low-power linear-frequency-modulated signals. A comparison has been made between the performance of the matched filter and the proposed method, and it is shown the proposed method has approximately the same performance and low computational complexity as matched filters. This method is also able to detect the poly-phase signals such as Frank-coded signals and also non-linear-frequency-modulated signals, as well. To show the effectiveness of the method, extensive simulations are carried out with different LPI radar waveforms corrupted with additive white Gaussian noise of SNR down to −25 dB.

A Bayesian approach to multiple moving extended targets tracking is proposed for estimating the shape approximation of the extended targets in addition to their kinematics. Within this approach, the extended target extensions are modelled with random hypersurface models, and a new variant of probabilistic multi-hypothesis tracking is used for modelling assignments of measurements to extended targets. Moreover, an approximate measurement update that arises directly from the analytical techniques of the variational Bayesian framework is derived to simultaneously estimate the posterior states iteratively including the shape and kinematics of each extended target. The performance of the proposed algorithm is demonstrated with simulated data.

In this study, the authors propose two knowledge-aided detection schemes based on prior structured clutter information for airborne collocated multiple-input multiple-output (MIMO) radars. Based on a first-order representation of the clutter spectrum, they propose the first-order generalised likelihood ratio test (FO-GLRT) detector. Meanwhile, Based on a second-order representation of the clutter spectrum, they propose the second-order GLRT (SO-GLRT) detector. They also analyse and compare the detection performance of those two detectors in different situations. The FO-GLRT detector can achieve acceptable performance without any secondary data, and thus immune to the clutter heterogeneity. The SO-GLRT detector that exploits the structured clutter covariance matrix is able to achieve a nearly optimal performance in certain cases. Both the proposed detectors are suitable for the collocated MIMO radars, which have a high signal dimension and a large demand for independent identically distributed training samples. Simulations validate those results.

The analysis of hybrid-polarimetric (pol) data can be performed using any of the well-established full-pol decomposition techniques through reconstruction of pseudo quad-pol data. This reconstruction requires estimation of cross-polarisation () information from the hybrid-pol measurements. In this study, the authors established a direct relationship to estimate from hybrid-pol entropy. This proposed reconstruction approach overcomes the limitations related to the iterative based procedure implemented in the conventional Souyris’ reconstruction method. The proposed method also circumvents a non-linear co- and cross-pol linking used in Souyris’ method that holds only for volume scattering dominated areas. The comparative analysis over four different datasets indicates that the proposed method can perform better for the application of landcover classification, in comparison with conventional Souyris’ as well as recently reported Espeseth's reconstruction methods.

This study presents novel target altitude estimation schemes optimised for ground-based multiple-input multiple-output (MIMO) radars with widely separated antennae, where the antennae are located in a plane so that the altitudes of the antennae are close together. For the ground-based systems, existing target localisation methods based on linear least squares such as least square (LS) and bistatic range measurement (BRM) suffer from performance degradation in target altitude estimation and eventually fail in altitude localisation for a perfect ground-based system where the altitude of antennae are the same. The authors propose three target altitude estimation schemes based on linear least squares for the ground-based systems resolving the drawback of existing algorithms for the ground-based systems; extended BRM approach, which estimates the square of target altitude from the auxiliary parameters produced by BRM algorithm, ellipsoid fitting approach, which directly estimates the square of target altitude with other target position information, and extended ellipsoid fitting approach, which utilise the estimation results of ellipsoid fitting approach to improve the target altitude estimation performance. Performance improvement of the proposed algorithms is analysed in terms of mean squared error and simulation results verify the performance.

In this study, an improved cubature particle filter based on the artificial bee colony (ABC) algorithm is proposed and applied to target tracking via underwater wireless sensor networks (UWSNs). In the proposed method, the square root cubature Kalman filter is used to generate the proposal distribution and the ABC algorithm is employed to optimise the particles before resampling, which makes the particles move toward the high likelihood region and maintain the diversity of the particles. Moreover, linear minimum variance criterion is utilised to fuse local estimates together in distributed fusion architectures of UWSNs. The simulation results show that the proposed method outperforms other classical algorithms in tracking accuracy.

Mahdasht Satellite Receiving Station (MSRS) has been using 10 m reflector antenna to communicate with LEO satellite at S-band (2.2–2.3 GHz) and X-band (8–8.4 GHz). Presently, antenna pointing operates in program tracking. Pointing accuracy under program tracking conditions is in the neighbourhood of 0.2°. This is acceptable at S-band, but not enough at X-band. Due to the narrow beamwidth at X-band, it is important to improve pointing accuracy significantly (0.05°). Monopulse antenna tracking is one approach that provides tracking accuracy at high-frequency bands. This study presents mathematical model and simulation of monopulse pointing system using a novel analytic approach. Monopulse error signals are calculated using the proposed model while considering the kinematic equations with the assumption of the Gaussian radiation pattern for reflector antenna. The simulation results are verified by using a real (MSRS antenna) monopulse tracking system in X-band frequency (8.2 GHz). The measurement and simulation results demonstrated the azimuth and elevation pointing errors are valid in 3 dB beamwidth.

Long-time coherent integration is an effective method to implement low-observable target detection in a complex scenario. Radon-fractional Fourier transform (RFRFT) can compensate the range and Doppler migration simultaneously and obviously improve the signal-to-clutter-noise ratio (SCNR) via long-time coherent integration. However, RFRFT uses a combination of moving parameters, i.e. initial range, velocity and acceleration, to search targets, increasing the computational burden. In this study, a novel two-stage RFRFT is proposed to detect low-observable targets. In the first stage, by calculating the spectrum similarity between adjacent bins, regions of interest (ROIs) can be detected in the range–Doppler domain. The processing in the first stage reduces the global search to a limited number of ROIs. In the second stage, based on the extraction of moving parameters, a refined search is performed to realise target detection and false alarm discrimination. To verify the effectiveness of the proposed two-stage method, both a simulation scenario and real radar dataset are applied. The theoretical analysis and experiment results show that the novel method is effective for the detection of dim targets with far less computation than standard RFRFT.

The accurate distance and speed estimates of train and individual coaches are necessary for the safe operation of the high-speed train system. Often, the train system does not rely on a single sensor for its distance and speed measurements as the sensors are susceptible to diverse operating conditions such as snow, rain, fog, tunnel, hilly region, slip, slide, etc. Hence, the information from a combination of sensors which can complement each other under certain operating conditions is required for the correct estimation. For distance measurements, Global Navigation Satellite System (GNSS) and balise are generally used. For speed sensing, the combination of wheel sensor, radar and GNSS are chosen. The diversity of sensors in terms of sampling rate and noise characteristics, etc. greatly affect the overall estimation accuracy and reliability if the measurements are used directly. Hence, this work presents a probabilistic weighted fusion algorithm which is based on the nonlinear longitudinal train dynamic model. The fusion algorithm combines the state estimates from distributed and sensor-specific extended Kalman filters. The effectiveness of the proposed fusion algorithm is demonstrated on the simulated sensor measurements along with a wide range of noises, spurious measurements, train operating conditions and track environmental disturbances.