Binary offset carrier (BOC) modulated signals are characterised by multi-peaked correlation functions which may lead to false peak locks that occur when a secondary correlation lobe is tracked instead of the main peak. To solve this problem, side-band processing (SBP) operates on the two main lobes of the BOC spectrum separately, in a binary phase shift keying like fashion. Although an unambiguous correlation function is obtained, the information provided by the BOC subcarrier is lost. This information is preserved by the double estimator and by the double phase estimator (DPE) which adopt an additional tracking loop to process the subcarrier component. In this study, the connection between SBP and independent subcarrier processing is shown and a novel SBP scheme, the coherent side-band (CSB) approach, is proposed. As in standard SBP, the two main lobes of the BOC spectrum are processed separately and upper and lower correlators are computed. These correlators are then combined to recover the subcarrier information. CSB provides subcarrier measurements and achieves the performance of the DPE. CSB tracking is thoroughly characterised and simulations and real-data processing are used to support theoretical findings. The CSB approach is an effective alternative to independent subcarrier processing.

The robustness of standard correlation-based Global Navigation Satellite System (GNSS) signal processing can be significantly improved by pre-processing the input samples with a zero-memory non-linearity (ZMNL). A paradigm for the design of ZMNLs is provided by the M-estimator framework where heavy-tailed probability density functions (pdfs) are used to model the impairments affecting the input samples. The myriad non-linearity, obtained considering a Cauchy pdf, is analysed for the acquisition and tracking of GNSS signals in the presence of pulsed interference. The impact of the myriad non-linearity is theoretically characterised and Monte Carlo simulations are used to support theoretical findings. Finally, real GNSS signals collected in the presence of jamming are processed: the myriad non-linearity provides a significant performance improvement with respect to standard GNSS signal processing which is unable to acquire and track the samples affected by interference.

Determining the attitude using GNSS carrier signals is studied. It features an analytical approach to get an estimate as initial guess for iterative algorithms, in three steps. First, baseline vectors are estimated by least-squares method. Second, the constraint of the direction cosine matrix (DCM) is ignored and the least-squares estimates of its 9 elements are solved. Third, a mathematically feasible DCM estimate is extracted from the above estimated free matrix. An error attitude, formulated using the Gibbs vector, is introduced to relate the previously estimated and the true attitude, and the measurement model becomes a nonlinear function of the Gibbs vector. The Gauss-Newton iteration is employed to solve the least-squares problem with this measurement model. The estimate of the roll-pitch-yaw angles and the variance covariance matrix of their estimation errors are extracted from the final solution. Numerical experiments are conducted. With 3 orthogonally mounted 3-meter baselines, 4 visible satellites, and 5-millimeter standard-deviation of the carrier measurements, the accuracy of the analytical solution can be less than 1° in the root mean squared error (RMSE) sense. The convergence of the iteration is rather fast, the RMSE converges after only one iteration, with the converged RMSE less than 0.1°.

This study presents a novel method for low angle estimation in diffuse multipath environment by the time-reversal (TR) minimum-norm-like (MNL) technique. In recent studies, the diffuse multipath is always regarded as the interference which is tried to be eliminated or weakened in low angle estimation for very high-frequency radar. However, it is difficult to establish the accurate model of the multipath environment. The common methods usually ignore the diffuse multipath and use the mirror reflection as the approximate model, but the ideal assumption would cause great errors. The proposed method makes the radar array working in the TR setup and the MNL technique is applied to estimate the low angle. In the proposed method, the exact model of the multipath environment does not need to be established completely but the accuracy performance of low angle estimation can be improved by making use of the multipath. Simulation results are presented to demonstrate the effectiveness of the proposed method. In addition, the performance degradation with respect to target motion is also shown in simulation results.

The utilising of space-time adaptive processing (STAP) can effectively enhance the globe navigation satellite system (GNSS) receivers’ performance in suppressing harsh, sustained interference. However, STAP may introduce significant biases and distortions on the cross-correlation functions, which would deteriorate acquisition and tracking performance. To achieve high-accuracy GNSS applications in challenging environments, these biases and distortions must be mitigated. A novel distortionless space-time adaptive processor based on minimum variance disstortionless response (MVDR) beamformer is proposed. By combining the information of steering vector and constraining the taps number of tapped delay line to be odd, the proposed processor can maintain the linearity of space-time filter response and it introduces no biases into the code and carrier phase measurements. The effectiveness of the proposed processor is demonstrated by theoretical analysis and simulations.

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.

The intra-pulse phase change caused by frequency difference of arrival (FDOA) is very little and even omitted due to extremely short duration of emitter pulses that the joint location using time difference of arrival (TDOA) and FDOA cannot be realised. To solve this problem, a multi-pulse coherent accumulation algorithm of direct position determination (DPD) using the TDOA and FDOA is proposed in this study. Through establishing coherent signal model of short pulses which is deterministic but unknown, the maximum likelihood estimator for localisation of a stationary emitter using multiple moving receivers is derived by taking the DPD approach under additive Gaussian white noise environment. This study also derives a signal-specific Cramer–Rao lower bound (CRLB) of DPD, modelling the signal as a deterministic unknown. The CRLB is more applicable to some specific (non-stationary, non-Gaussian) signals, especially electromagnetic signals. Simulation results show that the proposed method achieves a significant performance improvement in locating accuracy over the existing methods and its accuracy is close to the CRLB in normal signal-to-noise ratio.

To generate a seamless mosaic of a forward-looking sonar (FLS) video sequence, this study proposes a novel fusion method for FLS image mosaic, which includes two main steps from coarse to fine. In the coarse fusion step, the source images are first decomposed into multi-scale sub-bands using the non-subsampled contourlet transform (NSCT), then the sub-bands of the source images are merged, based on the Gabor energy and the local contrast for low and high frequency sub-bands, respectively, to generate the fused sub-bands which are used to produce the fused image by inverse NSCT. In the fine fusion step, a decision map is used to choose the pixels of the fine fused image from the coarsely fused image or one of the source images. This decision map is first constructed by measuring the similarity of the coarsely fused image to the source images, and then processed by a morphological post-processing technique to ensure its continuity and smoothness. Extensive experiments on FLS image fusion and mosaic have been conducted to demonstrate the effectiveness and the superiority of the proposed technique using both a subjective evaluation and objective metrics.

A recent analysis reveals that any attempt to estimate the underlying two-dimensional (2D) motion of a surface target via general bistatic synthetic aperture radar yields ambiguities, so that alternate target trajectories can give the same measurement data. These ambiguities are of a continuous nature and are fundamentally distinct from the discrete ambiguities that arise in pulse-Doppler moving target indication radar. The current investigation relaxes the constraint that the mobile target lies on the surface of a ground plane, so that air targets with general 3D motion are considered. Specifically, the current paper develops methods for constructing alternate fictitious 3D target trajectory and speed profiles in time which yield identical radar measurements as that obtained from the true 3D target motion. These ambiguities are shown to remain even with the inclusion of bistatic range rate or Doppler measurements. Thus, the energy patterns of the radar transmission and reception beams determine the ability to localise and estimate the 3D target trajectory and speed profiles for general bistatic radar collections.

Conventional stepped-frequency (SF) waveform utilises the frequency step between pulses to span a wide bandwidth. However, the frequency step size is limited by the width of the pulse to prevent the grating lobes, and the first lobe is about −13 dB due to the uniformly sampling in frequency. Modulating the pulses [e.g. phase-coded (PC) modulation or linear frequency modulation] can increase the frequency step size and improve the performance of the sidelobes, but the sidelobes of the modulated SF waveform are still not the best. In this study, a PC frequency-hopping (PCFH) waveform to achieve optimal extend-range correlation sidelobes is presented. The presented waveform applies non-linear frequency evolution, optimal frequency order and different polyphase code to each pulse. In comparison to the SF waveform, the PCFH waveform has much higher degrees of freedom for suppressing extend-range correlation sidelobes. The authors propose a design scheme, which sequentially optimises the interpulse frequency, the FH order and the intrapulse-polyphase code to achieve the optimal extended-range correlation sidelobes. Simulation results validate the performance of the optimised waveform and the feasibility of the involved design method.

To deal with the track coalescence problem of the joint probabilistic data association (JPDA) filter, a novel approach based on the Kullback–Leibler divergence (KLD) is developed in this study. In JPDA, the posterior probability density function (PDF) is approximated by a single Gaussian PDF at each time step. The authors propose a novel method of optimising the posterior PDF to obtain a single Gaussian PDF that minimises the KLD from the posterior PDF. However, the KLD is intractable because the posterior PDF is a Gaussian mixture model. Hence, an approximation of the KLD is introduced as the cost function to simplify the problem. The cost function is a linear combination of multiple objective functions which are not conflicting. Therefore, the minimisation of the cost function is easier to operate, because all objective functions can be optimised simultaneously. In addition, an iterative method is adopted for minimising the cost function. In the iteration process, the tracking accuracy is improved with the monotonic decrease of the cost function. Theoretical analysis and example show the feasibility of the proposed approach. Simulation results demonstrate the advantages of the new approach over others when tracking closely spaced targets with contaminated sensor measurements.

A new single-epoch single-frequency algorithm based on partial least-squares ambiguity decorrelation adjustment (Par Lambda) that employs baseline constraints is developed for BeiDou Navigation Satellite System (BDS) called Improved Par Lambda, based on the characteristics of building deformation monitoring. The floating solution of double-difference ambiguities is obtained by means of double-difference observations and least-squares method. The double-difference observation equations with baseline length constraint are composed of the equations of BDS single-frequency pseudo-range observations and carrier phase observations and the baseline length constraint equation. The least-squares principle is used to compute floating solution of double-difference ambiguities and the corresponding cofactor matrix. Based on the precision of double-difference ambiguities, the ambiguities will be divided into different levels (2, 1, 1,…, 1) and then be fixed based on the Lambda method progressively. The 1, 5 and 10 s short baseline data of BDS single-epoch single-frequency based on B1 band carrier phase were computed through this method. The results showed that, for BDS single-epoch single-frequency, the success rate and the search efficiency of fixing ambiguities of Improved Par Lambda were all better than the traditional methods and the success rate was more than 98%.

To identify potential man-made objects, traditional synthetic aperture radar (SAR) imaging techniques are used to consider the dependence in either frequency or azimuth domain. However, these existing methods may result in inaccurate scattering estimation without utilising the inherent polarimetric diversity property. To improve the imaging performance, a polarimetric object-level SAR imaging algorithm is proposed. In the scheme, the polarimetric SAR imaging with canonical scattering characterisation is transferred into a simultaneous sparse approximation (SSA) problem by virtual of incorporating sparse representation and canonical shape feature model. Then the SSA problem is solved via an efficient -norm () regularisation algorithm. The main advantages of the proposed method are twofold: (i) considering the dispersive, anisotropic and polarimetric scattering characteristics of scatterers allows for more accurate estimation of physically relevant scattering geometry information of scattering centres in comparison with the method ignoring polarisation dependence; and (ii) by exploiting joint sparsity of the multiple polarisation measurements, it can effectively enhance the recovery accuracy in the consistency of the canonical scatterers’ number and locations in different channels. Experimental results are provided to verify the effectiveness of the proposed method.

In this study, a spectrum sharing technique is investigated for enhanced detection of moving targets. This approach, the spectrum sensing-multi-objective optimisation technique, passively monitors the electromagnetic environment for radio frequency (RF) emissions radiated by RF systems. This technique then identifies a continuous frequency sub-band that simultaneously maximises radar performance and reduces the radars spectral footprint. The goal of the investigation presented in this study is to quantify performance improvement of a notional radar model in the presence of RF emissions measured at 2.42 GHz (by a real-time spectrum analyser). In addition to an improved signal-to-interference plus noise ratio, the proposed radar model increases range resolution performance as the target approaches the radar.

Active radar is vulnerable to illegal eavesdroppers due to its high-gain beam-scanning signals. To reduce active radar visibility and enhance its low probability of intercept (LPI) capability, this study proposes a cognitive LPI transmit beamforming scheme using frequency diverse array (FDA) and multiple-input multiple-output (MIMO) hybrid array antenna. The achievement of LPI is due to the unique range-angle-dependent transmitting beampattern of FDA-MIMO radar, which minimises the beam power at the target location to reduce its visibility and simultaneously maximise the power at the radar receiver without degrading the radar detection performance. Furthermore, the FDA-MIMO radar operates in a cognitive way: the receiver estimates the target range and the direction of arrival with a two-dimensional multiple signal classification algorithm, and feedbacks their estimates to the transmitter to update the FDA-MIMO transmit beamforming. As the transmit beamforming optimisation is non-convex problem, the authors propose three methods, namely linear combination, non-linear combination and closed form solution. All the proposed methods are verified by simulation results.

The authors investigate the problem of two-dimensional (2D) direction of arrival (DOA) estimation of multiple signals for coprime planar arrays (CPAs) in this study and they propose a computationally efficient 1D partial spectral search approach based on multiple signal classification (MUSIC) algorithm. The conventional 2D MUSIC algorithm for CPAs has a great DOA estimation performance, but suffers from a tremendously expensive computational complexity due to the 2D spectral search. To this end, the proposed approach first decreases the dimension of the spectrum function to one dimension and then utilises the linear relationship between the true and ambiguous DOA estimates to form a 1D partial spectral search over a small sector. Finally, the true DOA estimates can be achieved based on the coprime property. The proposed approach can have an impressively good DOA estimation performance, but with a low computational cost. Simulation results validate the effectiveness and superiority of the proposed approach.

In this study, a human–vehicle classification using a feature-based support vector machine (SVM) in a 77-GHz automotive frequency modulated continuous wave (FMCW) radar system is proposed. As a classification criterion, the authors use a newly defined parameter called root radar cross section which reflects the reflection characteristics of targets. Based on this parameter, three distinctive signal features are extracted from frequency-domain received FMCW radar signals, and they become classification standards used for the SVM. Finally, through measurement results on the test field, the classification performance of the authors’ proposed method is verified, and the average classification accuracy from a four-fold cross data validation is found to be higher than 90%. In addition, the authors’ proposed classification method is applied to distinguish a pedestrian, a vehicle, and a cyclist in a more practical situation, and it also shows good classification performance.

The registration of inverse synthetic aperture radar (ISAR) images is a key process in interferometric ISAR (InISAR) imaging. According to published literature, there are mainly two solutions for ISAR image registration, one is correlation coefficient based method and the other is parameter estimation of target angular motion. Though some simulation results are effective, defects of these two methods still need to be studied and solved. Different from precedent methods, the authors try new approach for ISAR image registration in this study and better results are obtained. The authors’ new approach is based on joint translational motion compensation, which consists of two steps namely joint range alignment and joint phase autofocus. The first step realises registration along range direction and the second one realises registration along cross-range direction. The new method achieves ISAR image registration along with the translational motion compensation, thus no extra computation is needed. In addition to high computational efficiency, the new method is more precise compared with precedent methods and works well even under strong noise. Simulation results show the advantages of the proposed method in computing efficiency, precision, robustness and practicability.