Nowadays, high-accuracy satellite-based positioning and navigation solutions are obtained using carrier-phase observations together with a differential correction scheme. A slip of only a few carrier-phase cycles can, however, bias observations causing a reduction in position accuracy. Therefore, reliable detection and handling of cycle slips (CSs) is essential for achieving high-accuracy positioning performance. Generally, it is harder to resolve CS in single-frequency observations, but the area deserves attention as differential positioning using low-cost single-frequency receivers is expected to be the key for many emerging mass-market applications. This study reviews and compares CS detection and correction techniques for single-frequency GNSS receivers with respect to their application for low-cost real-time kinematic (RTK) positioning. No prior performance comparison of CS detection and correction techniques exists; thereby, the authors have proposed four parameters to assess performance quality of CS resolution scheme for RTK positioning. Subsequently, an up-to-date list of existing techniques, classified according to the CS detection strategy, is reviewed with respect to measurement model, CS correction approach and test results. The techniques are also analysed for performance quality and it is observed that they do not conform to all parameters. Finally, conclusions are drawn and future research directions are proposed at the end.

Terrain-aided navigation (TAN) is a promising technique to determine the location of underwater vehicle by matching terrain measurement against a known map. The particle filter (PF) is a natural choice for TAN because of its ability to handle non-linear, multimodal problems. However, the terrain measurements are vulnerable to outliers, which will cause the PF to degrade or even diverge. Modification of the Gaussian likelihood function by using robust cost functions is a way to reduce the effect of outliers on an estimate. The authors propose to use the Huber function to modify the measurement model used to set importance weights in a PF. They verify their method in simulations of multi-beam sonar in a real underwater digital map. The results demonstrate that the proposed method is more robust to outliers than the standard PF (SPF).

The study presents a direction-finding method that is not limited to the main lobe zones of antenna patterns. The technique allows for the angular sector of interest to be divided by few channels, pursuing low size, weight, costs, and computational power in radar detection. Experiments done on a building rooftop have shown that, with a minimum of 150 processed pulses, the distributions of estimates of direction of arrival are well behaved, with a relationship between standard deviation and signal-to-noise ratio. As a result, information is provided that may soften the deinterleaving of radar pulses.

A task scheduling algorithm based on value optimisation is proposed under comprehensive priority for anti-missile phased array radar. The model of threat degree is established for ballistic missile targets. The task comprehensive priority is obtained utilising a two-dimensional priority table which synthesises the target threat degree and the task deadline. Then, based on the comprehensive priority, each task gets a dynamic value function, instead of a fixed value as usual. In this way, the task value is enlarged when it is executed close to the desired execution time. A value optimisation model for task scheduling is constructed, and the genetic algorithm is utilised to solve this scheduling model. Thereby tasks can be executed as close as possible to the desired time, and the principle of scheduling timeliness can be better achieved. The performance of the proposed algorithm (PA) is compared with traditional scheduling algorithms by simulation experiments, as well as the impact that parameters of task value function have on scheduling performance is analysed. Simulation results show that compared to the traditional algorithms, the PA reduces the average time shift ratio and improves the value achieving ratio.

This study presents a Rao-Blackwellised particle filter (RBPF)-based encoder/inertial navigation system (INS)/global navigation satellite system (GNSS) integration method for improving the navigation performance of an autonomous land vehicle (ALV) with wheel slipping. In contrast to traditional integration methods, the proposed integration method introduces an overall wheel slip consideration for the ALV, which greatly improves the accuracy of the velocity estimation, especially when the inertial sensor is low cost. Additionally, the proposed integrated system uses double-difference pseudorange measurements instead of single point positioning results provided by low-cost GNSS receivers, which greatly improves the accuracy of the position estimation. To verify the navigation performance of the proposed integrated system, comparisons between the states estimated by the proposed system, the EKF-based integrated system and the joint wheel-slip and motion-estimation system are provided. The results of the experiment show that the proposed integrated system has the highest accuracy in both the position estimation and the velocity estimation among the three compared systems, and can improve the navigation performance during GNSS signals outages.

Multi-sensor cooperative scheduling has been the main mean to gather intelligence information due to the complexity of the battlefield environment and variability of targets. This study presents a non-myopic scheduling method of mobile sensors for manoeuvring target tracking. Within the partially observable Markov decision process framework, the sensor scheduling model is formulated since the target state cannot be observed directly, and the cost function is given based on the posterior Carmér-Rao lower bound. The multi-step scheduling cost is predicted with a certain number of particles generated by the unscented sampling method, which can reduce the computation complexity. For multi-target tracking cases, a target threat degree function is presented to assess the target threat. The scheduling problem is transformed into a decision tree optimisation problem by discretising the manoeuvring direction, and an improved decision tree searching algorithm is proposed to solve the sensor scheduling scheme quickly based on the branch-and-bound technique.

Advanced Receiver Autonomous Integrity Monitoring (ARAIM) with two or more constellations will be widely used in the aircraft to safeguard the safety of the flight crew and passengers. The ARAIM based on tight integration of Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS) attracts widespread attention for its ability to meet the integrity requirement of Category-I (CAT-I) approach. However, more available satellites lead to higher satellite fault probability. So a fault exclusion (FE) method is necessary to continue providing positioning services and integrity performance after the faults are detected. In this study, an FE method for GNSS/INS ARAIM is presented to identify the failing satellite and to provide real-time integrity performance after exclusion. The proposed subset-identifying method takes into account the prior probabilities of satellite faults, which is able to greatly improve the accuracy of finding the failing satellite. The simulation results show that the proposed after-exclusion integrity estimating method is able to provide integrity performance meeting the requirements of CAT-I. Therefore, the proposed method is able to improve the continuity and availability performance of the navigation system for civil aviation.

The authors address the performance analysis of the least squares (LS) Prony method for estimating the natural frequencies of radar target in the study. Based on the perturbation theory and the Taylor series expansion, the authors get explicit expressions of the mean square error (MSE) of the LS solution, the MSE of the z-plane natural frequencies and the MSE of the s-plane natural frequencies. The validity of the derived expressions is demonstrated by comparing the analytic results with simulation results. For further validation of the results, simulation results of the GPOF method have been used for comparison.

In modern radars, the problem of estimating elevation angle at low grazing angles is typically solved using super-resolution techniques. These techniques often require one to provide an estimate of the number of waveforms impinging the array, which one can accomplish using model selection techniques. In this study, the authors investigate the performance of an alternative approach, based on the Bayesian-like model averaging. The Bayesian approach exploits the fact that the parameters of the model related to multipath signals are nuisance ones, which allows one to avoid the estimation of the number of waveforms and improves estimation performance. The method is introduced for the classical conditional maximum-likelihood estimator and extended to its, recently proposed, robustified version. The authors find, however, that the robustified estimator includes its own soft-decision mechanism and benefits from the averaging only for low levels of model uncertainty.

This study deals with the problem of heterogeneous sensor fusion based on Copula theory and importance sampling. The proposed fusion algorithm is grounded on Copula statistical modelling and Bayesian probabilistic theory. The distinctive advantage of this Copula-based methodology is that it formulates the internal dependency between the local sensors' data, which is usually unknown but essential for accurate track fusion. To this end, a joint distribution of the local sensors' observations is constructed based on Copula functions, and the corresponding fusion rule is derived with a specific correlation term. In addition, a Monte–Carlo importance sampling technique is adopted to improve the computational efficiency by drawing less random samples from the local estimates to be fused. After that, a procedure of Kernel density estimation is applied to learn a Gaussian approximation of the fused density. In the end, extensive Monte–Carlo simulations are conducted to evaluate the proposed sensor fusion method in a distributed target-tracking scenario.

Jet engine modulation (JEM) are micro-Doppler features obtained from the radar data of aircraft, including jet aircraft and helicopters, and generally viewed as unique phenomenon suitable for identifying aerial targets. The authors demonstrate however, that JEM are not unique, and that the rotating wheel spokes on the wheels of ground vehicles produce a modulation similar to the rotating rotor blades of jet engines and helicopter rotor blades. They also develop a mathematical model to analyse the radar signal scattering mechanism of wheel spokes, and also employ a Ku-band Doppler radar system to collect radar echoes from a wheeled vehicle and a helicopter. Both the theoretical and experimental results verify the existence of rotor blade modulation (RBM) phenomena from helicopters and wheel spoke modulation (WSM) phenomena from vehicles. Both RBM and WSM are similar to JEM features. This fact indicates that JEM is a necessary but insufficient condition for the identification of aerial targets, and additional recognition features inherent in surface surveillance radar are needed to distinguish the JEM spectra arising from aerial targets and ground vehicles.

In radar, the minimisation of redundancies within the sensing array can lead to significant hardware computational savings. Arrays with a coprime-pair configuration enjoy increased degrees of freedom and can detect more sources than sensors. To achieve this, a virtual array (VA) consisting of the full complement of lags is usually constructed and subspace-based algorithms are then employed to obtain the direction-of-arrival (DOA) or frequency estimates. However, the application of the subspace techniques to the VA incurs a significant computational cost and requires spatial smoothing. The authors propose and analyse the application of the fast iterative interpolated beamformer (FIIB) to the coprime DOA estimation problem. The FIIB enjoys a computational complexity of the same order as the fast Fourier transform and does not require spatial smoothing. They consider two implementations that construct the VA differently with the first selecting a single estimate for each lag and the other employing averaged values of the lag estimates. They present a comprehensive study of the estimation performance as a function of signal-to-noise ratio, number of snapshots and source separation. The results clearly show that the FIIB delivers high-fidelity frequency estimates that consistently outperform the high-resolution subspace-based methods.

The efficacy of any moving target tracking technique depends on the understanding the background, or clutter, and the parameters that describe the detection properties of the objects. The nature of these quantities is statistical and not only are they unknown as a rule in practice, but they are also variable over both time and space. The study proposes a method for estimating the time-varying probability of detection of each tracked object individually, and the density of false alarms in the immediate vicinity of the current position of an object. The method is based on the generalised maximum likelihood approach, assuming tracking of a solitary target. The applicability and constraints of the proposed solution are illustrated by simulations.

The time needed to get the first position is one of the key parameters to assess the performance of a global position system (GPS) receiver. Here, the authors present an autonomous satellite orbit prediction algorithm to provide usable ephemeris before the broadcast ephemeris is completely collected. Experimental results show that, with the ephemeris prediction algorithm, the TTFF of the receiver saves ∼74% in cold start mode. Furthermore, the accuracy of the presented algorithm is improved by using an empirical SRP model with parameters depending on the angle between the Sun and the satellite's orbital plane. Simulation results show that, for GPS PRN 5, when the SRP model with constant parameters is used to extrapolate the orbit for 5 days, only 43% of the position error is within 10 m, but this percentage can reach to 87% using the SRP model presented here. In addition, some single point positioning experiments with simulated satellite signals and real satellite signals are conducted to analyse the positioning results of the receiver with ephemeris prediction. The experimental results verify the effectiveness of the proposed algorithm.

This article describes a numerically inexpensive composite model for the microwave Doppler spectrum of sea clutter. The model is based on the small perturbation method, includes the contribution of specular reflections and uses a linear description of the sea surface to provide an analytically tractable description of the Doppler spectrum. The analytical model is tested by comparison with direct simulation. The model results are found to be in reasonable agreement with measured data and with recently published results produced using the considerably more complex and numerically challenging second-order small-slope approximation.

In order to reduce the uncertainty of radar manoeuvring target tracking (RMTT) in cluttered background, a joint detection and tracking algorithm based on cognitive radar is proposed. First, a prism structure resolution cell of time-delay, Doppler and azimuth is designed. Then, an approximate expression of measurement error covariance including waveform and detection threshold parameters is given. Then, based on the idea of human brain perception-action cycle, a joint waveform and detection threshold adaptive tracking algorithm based on minimum information entropy criterion is proposed. Finally, a cognitive structure adaptive particle filter (CSAPF) algorithm, based on parallel structure of extended Kalman filter (EKF) and particle filter, are used with Probabilistic Data Association (PDA) algorithm for RMTT. During the process, CSAPF-PDA can always obtain the best tracking performance with the minimum number of particle samples, thus effectively taking into account the tracking accuracy and efficiency. The effectiveness of the proposed algorithm is verified by simulation experiments.

Encrypted global navigation satellite system signals (GNSS) can be tracked using codeless techniques that do not require the knowledge of the spreading code used for signal generation. These techniques can also be applied to binary offset carrier (BOC) modulated signals whose unknown code sequence can be removed through squaring. In this study, an alternative codeless approach based on the cross-correlation principle is considered. Cross-correlation codeless processing is commonly used for tracking signal components on different frequencies, such as the global positioning system (GPS) L1 and L2 P(Y) signals, and it is adapted here to BOC modulations broadcast on a single frequency. A cross-correlation codeless framework is proposed where the BOC signal is split into two data streams that are cross-multiplied to remove the unknown code sequence. Two architectures, open-loop and closed-loop processing, are proposed and analysed. The codeless cross-correlation function is introduced and open-loop processing is used to reconstruct it from the received samples. Closed-loop processing based on cross-correlation phase lock loop (PLL) and delay lock loop (DLL) are used to estimate the signal parameters. The proposed cross-correlation framework is thoroughly analysed theoretically, through simulations and using real data. The analysis shows the effectiveness of the cross-correlation framework.

The Radon–Fourier transform (RFT) can effectively overcome the coupling between the range cell migration effect and Doppler modulation by jointly searching along range and velocity dimension for the moving target, which depends on envelope alignment and additional Doppler phase compensation. However, as to the conventional RFT method, it needs to wait until the whole coherent processing interval (CPI) is over before performing RFT integration, which is not flexible. Also, all echo data in the CPI takes the same weight. In this study, the weight of echo data has been generalised by the straightforward idea that new data should occupy more weight, while old echo data should take less. Thus, a novel method, named exponentially weighted recursive RFT (RRFT) has been proposed to realise RFT integration recursively. The computations can be started before all the data has been collected. The signal-to-noise ratio level of the echo signal is being improved during the iteration. The equivalent total coherent integration time and velocity resolution have been presented. The theoretical analysis shows that the computational complexity is of the same order as that of RFT. Finally, some numerical results are provided to validate the proposed method.

Ionospheric clutter is detrimental to target detection in high-frequency surface-wave radar (HFSWR). Adaptive beamforming (ABF) has been adopted to suppress the ionospheric clutter in recent years. Unfortunately, the performance of ABF degrades due to the heterogeneity of the ionospheric clutter. In this study, a new approach is proposed to suppress the ionospheric clutter. A novel heterogeneous ionospheric clutter model based on the mixture of mutually independent ionospheric clutter sources is established. The blind source separation (BSS) approach is used to separate the clutter sources first. Then the separated components are exploited to estimate the spatial covariance matrix (SCM) of the cell under test. The SCM estimation based on BSS is more accurate than the classical sample matrix inversion method under the heterogeneous ionospheric clutter. Therefore, the ABF performance improves due to the better SCM estimation. The simulation and real data results demonstrated the effectiveness of the new BSS-based ABF method in HFSWR. The signal-to-clutter-plus-noise ratio of the new method improved compared with the traditional ABF based on the SMI method. The new method can help to detect targets under the heterogeneous ionospheric clutter. It may also be a promising methodology in other ABF applications.

Networked radar systems can be used to improve target tracking performance. In the asynchronous radar network (ARN) system, the radars may work at different sampling rates, bringing difficulties in resource allocation. In this study, the authors propose a joint power and bandwidth allocation (JPBA) strategy to track a target by ARN in clutter. First, they build an asynchronous resource allocation model, in which a periodic allocation strategy is suggested. Second, they derive the Bayesian Cramér–Rao lower bound by incorporating the information reduction factor as a performance metric for the JPBA strategy. Third, the asynchronous power and bandwidth allocation optimisation problem are formulated by minimising the tracking root-mean-square error with given power and bandwidth budgets, which is non-convex but monotonic. Finally, by introducing the branch-reduce-and-bound algorithm, a global solution to the optimisation problem is obtained. Numerical results verify the validity of the proposed JPBA strategy for target tracking by ARN.

The study presents an underwater acoustic signal processing approach for the identification of the material of an object using wideband chirp pulses. The echo from the target is formed by a number of processes that occur during reflection of the pulse from an object. The timing of these reflected components and geometry of their wave paths determine speed of sound in the wave propagating material. The calculated speed of sound is then used to identify the material. The novel method enables automated material identification without any training data. The object of the material identification is a two-layer metal spherical shell filled with liquid and placed in a fresh water tank. The presented approach identifies the shell and filler materials of the sphere. In this work, the sphere thickness is limited by 2% in relation to the radius. Results are evaluated for the sphere's radius in a range from 0.05 to 0.15 m. The approach yields 83.5% success rate for the shell material identification and 79.9% success rate for the filler material on the synthetic data. For the experimental data, 67.3 and 80% success rates were obtained for shell and filler material identification, respectively.

This study proposes a low-band scheme utilising the polarisation dominance of the target's resonance regions in the frequency domain to recognise a fighter-sized aircraft. The methodology implements a binary decision tree based on three polarisation power terms, namely Stokes variables, to determine the polarisation dominance of six directions, and subsequently, predict the canonical shape of the target substructures. The decision tree comprises three inequalities of the Stokes variables subject to an orthogonality threshold to reflect the dominant polarisation directions as a function of the target resonance region. The simulation data for two fighter-sized aircraft illustrate the feasibility of the method by comparing the differences (or similarity) in the target decision outcomes. The results indicate that resonance-scattering region lies within the frequency band of 9–200 MHz where thin-wedge scattering is prominent within the frequency band of 9–30 MHz, whereas the corner (dihedral) scattering becomes dominant within the band of 110–170 MHz, mainly when the radar illuminates the target sides aspect. The method was robust to the noise and target aspect change using the paradigms of the MIG29 and F16 aircraft models.

In this study, an algebraic closed-form method for jointly locating the target and refining the antenna positions in multiple-input–multiple-output radar systems is proposed. First, a set of linear equations is formed by non-linear transformation and nuisance parameters elimination, and then, an estimate of the target position is obtained by employing a weighted least-squares estimator. To jointly refine the target and antenna positions, the associated error terms are estimated in the sequence. The proposed method is shown analytically and confirmed by simulations to attain the Cramér–Rao lower bound performance under small-error conditions. Numerical simulations are given to support the theoretical developments.

Clutter filtering according to distinct Doppler echoes is a major measure to deal with the interference in radar signals caused by the rotating blades of nearby wind turbines. For the problem that the traditional simulation method of scattering point superposition model could not simulate the continuity of induced current on the blade's complex surface, the authors proposed a new simulation method of Doppler echoes based on scattered electric field calculation and expounded the basic principle and implementation steps of the method. First, they found the correspondence between the electric field's complex amplitude vector and the echo signal by deducing the equations of echo signal and scattering electric field; second, they used the quasi-static technique, the hybrid algorithm of physical optics and method of moment to achieve an accurate solution of the scattered electric field sequence; finally, the authors used the short-time Fourier transform to obtain the time–frequency domain data of blades Doppler echoes. The result was compared with data obtained from the scattering point superposition model and in-field experiments, and the accuracy of the proposed method was verified.

In this study, mutual information (MI)-based waveform design methods for the coexistence between orthogonal frequency division multiplexing (OFDM) radar system and communication system corrupted by Gaussian mixture interference are investigated for the first time. Firstly, the received signal is formulated as a Bayesian linear model. Subsequently, from a statistical perspective, the approximate differential entropy of received signal is derived, followed by three different approximate MIs and corresponding theoretic upper bounds. After that, two adaptive waveform design methods are proposed by maximising MI and minimising radar transmitted power, respectively. The numerical results show that exploiting the reflected communication signals helps to obtain higher MI value and reduce radar transmitted power. Besides, by maximising the MIs, the optimised radar waveforms remarkably outperform the fixed ones, which benefits the estimation performance.