This study presents a novel method for time–frequency (TF) signal analysis and chirp rate estimation dedicated for electromagnetic spectrum sensing, electronic warfare, electronic intelligence and/or passive bistatic radar purposes in which frequency modulated signals occur. The approach is based on the double-adaptive chirplet transform, providing optimal analysis window parameters, which is a crucial problem during TF processing. The presented methodology is based on a Gaussian window with two degrees of freedom, which results in a strong concentration of energy on the TF plane around the main component, even if the initial window parameters were mismatched. As an example of the method's usefulness, different types of real-life radar pulses were processed: firstly, two types of non-linear frequency-modulated waveforms were examined as a suitable illustration of the changeability of the analysis window parameters. Secondly, the linear frequency modulated signals were analysed in the presence of strong interference and multipath propagation. The waveforms were processed and compared, creating individual radar signatures, which may allow transmitter classification and signal reconstruction to be carried out in further processing. Moreover, the estimation limitations were compared to the Cramer-Rao lower bound, and an appendix organising mathematical fundamentals for the analysed methods is provided.

The authors deal with the problem of detecting point-like targets in the presence of diffuse multipath under the assumption of a partially homogeneous Gaussian disturbance by introducing an unknown scaling factor which represents the mismatch between the noise contribution of the cell under test and the training samples. Also, they model the target echo as a superposition of direct plus multipath components where multipath returns are thought of as scattered signals from a glistening surface. Hence, multipath echoes are represented as a Gaussian distributed random vector with an unknown covariance matrix. Then, the authors derive a constrained generalised likelihood ratio test under the assumption that the primary data covariance structure is similar to the covariance matrix obtained from training samples where the degree of similarity is up to both noise scaling factor and multipath contribution. Besides, they prove that the proposed detector ensures constant false alarm rate (CFAR) property with respect to the unknown parameters. Finally, they compared the devised algorithm with the commonly used CFAR estimators. The results show that the proposed detector copes well with diffuse multipath conditions under partially homogeneous environments.

For high-resolution scene mapping and object recognition, optical technologies such as cameras and LiDAR are the sensors of choice. However, for future vehicle autonomy and driver assistance in adverse weather conditions, improvements in automotive radar technology and the development of algorithms and machine learning for robust mapping and recognition are essential. In this study, the authors describe a methodology based on deep neural networks to recognise objects in 300 GHz radar images using the returned power data only, investigating robustness to changes in range, orientation and different receivers in a laboratory environment. As the training data is limited, they have also investigated the effects of transfer learning. As a necessary first step before road trials, they have also considered detection and classification in multiple object scenes.

Drifting of anchor nodes due to ocean currents and tides is a challenging issue in efficient localisation for underwater acoustic sensor networks. This study therefore proposes a correction method to compensate the error caused by drifting (and accurately localise the target) by introducing an extra floating anchor node. The floating anchor node is placed in the middle of the localisation area and its coordinates are known by GPS. The floating anchor node acts as a reference node and therefore is useful in compensating the localisation error. The detailed method consists of three stages: (i) estimate the floating anchor node's location with other anchor nodes; (ii) calculate the compensation parameter from both real-time and calculated coordinates of floating anchor node; and (iii) locate the target with anchor nodes first and then correct the result with compensation parameter calculated in stage (ii). Simulations and experiment results show that the proposed method produces a improvement in localisation accuracy. A remarkable improvement of 27% is demonstrated with the experimental data with the cost of only a single floating anchor node.

The decomposition of multi-component micro-Doppler signals overlapping in the time-frequency (T-F) domain is critical and challenging, especially in the case of irregular instantaneous Doppler frequency. The authors propose a novel time-based decomposition method called the short-time variational mode decomposition (STVMD) to analyse the irregular (FM) micro-Doppler signals, and present an optimal model combined with T-F transformation. Then, considering the STVMD may fail to extract the instantaneous frequency (IF) of overlapped components, an improved STVMD algorithm is put forward. Since the dependence of the STVMD algorithm on the initial value, they adopt the Kalman filtering to implement IF tracking and regrouping under the global constraint, further accelerating the convergence of the algorithm. Furthermore, due to the mode aliasing at the intersection point, they adopt a degenerate STVMD model to decompose the signals with known centre frequencies, which can be viewed as a Wiener filter. With the two steps, the improved STVMD algorithm can effectively solve the decomposition of T-F overlapping irregular FM micro-Doppler signals. Compared with the peak ridge technique and the ridge path regrouping and intrinsic chirp component decomposition (RPRG + ICCD), the proposed method shows the effectiveness and adaptability even for irregular FM signals with large T-F spectrum amplitude fluctuation in the low signal-to-noise ratio environment.

In this study, the authors take further insight into the sparse geometry which offers a larger array aperture than uniform linear array with the same number of physical sensors. A novel direction of arrivals (DOAs) estimation model with flexible sparse geometry, which possesses the potential to significantly improve the estimation performance especially when the placed space and the weight of carrier such as airborne radar are restricted, is proposed to offer a larger aperture compared with co-prime array. The proposed algorithm can estimate DOAs by solving phase ambiguity. To improve the capability of spectrum analysis in frequency domain, all phase discrete Fourier transform (DFT), which can effectively alleviate spectrum leakage compared with traditional DFT, is proposed to apply into DOAs estimation. Additionally, the performance on degrees of freedom can be considerably improved compared with the state of the art where all the targets can be distinguished by Doppler information of received echo signal. More importantly, the proposed algorithm can effectively deal with DOA-closely-spaced targets because the proposed algorithm does not require to estimate signal subspace with ill-conditioned steering matrices. Both the theoretical analysis and simulation results demonstrate that the proposed algorithm significantly improves DOAs estimation precision with less computation cost.

Human identification plays a vital role in daily lives. A majority of biometric technologies require the active cooperation of humans, while gait recognition does not. Compared with other identification technologies, radar-based technology can monitor the human body around the clock without being affected by light/weather, and is not easy to be forged while protecting privacy. Previous researches have revealed that gait signatures acquired using radar can be used for human identification, but there is almost no literature on the long-term stability of gait signatures. Due to the long-term interval observation, the human micro-Doppler will change according to the subject (such as slight differences in walking posture). In this study, a novel network is proposed to realise stable identification of humans by extracting long-term stable features. The micro-Doppler data is processed by a short-time Fourier transform and finally classified by the proposed neural network. Data acquisition was carried out within more than a month. The experimental results demonstrate that the recognition accuracy of the validation set can reach about 99%, and the recognition accuracy of the test set can reach 90% (improved 3% compared with the network without a recurrent neural network), showing the potential of the proposed method in long-term stable identification.

Combined sky-wave and surface-wave monostatic high-frequency (CSSM-HF) radar is a new type of mono-static high frequency (HF) radar that uses multiple combined propagation modes of skywave and surface wave to detect targets. However, the detection range of different propagation modes partially overlaps, which results in multiple mode echoes from one target. To track the target in the presence of multi-mode echoes, a new multi-mode target tracking algorithm is proposed in the study, which uses the detection range as a priori knowledge. In CSSM-HF radar, the possible propagation mode of the target echo is related to the position of the target itself. Therefore, the study uses the detection range simulation results as a priori knowledge to construct a propagation mode judgment module to effectively improve the calculation efficiency and performance of the tracking algorithm. The simulation results show that the proposed algorithm can effectively track the target in the presence of multi-mode echoes and the tracking performance of the target with lower abscissa speed is better. In addition, the mode judgment module directly affects the performance of the algorithm. The tracking performance will be reduced when the output of the mode judgment module has an error mode.

The derivation of tight estimation lower bounds is a key tool to design and assess the performance of new estimators. In this contribution, first, the authors derive a new compact Cramér–Rao bound (CRB) for the conditional signal model, where the deterministic parameter's vector includes a real positive amplitude and the signal phase. Then, the resulting CRB is particularised to the delay, Doppler, phase, and amplitude estimation for band-limited narrowband signals, which are found in a plethora of applications, making such CRB a key tool of broad interest. This new CRB expression is particularly easy to evaluate because it only depends on the signal samples, then being straightforward to evaluate independently of the particular baseband signal considered. They exploit this CRB to properly characterise the achievable performance of satellite-based navigation systems and the so-called real-time kinematics (RTK) solution. To the best of the authors’ knowledge, this is the first time these techniques are theoretically characterised from the baseband delay/phase estimation processing to position computation, in terms of the CRB and maximum-likelihood estimation.

The authors propose an algorithm to estimate the path followed by refracted signals from a source to a target, through a medium formed by uniform parallel layers with known different refractive indices, a common model used for ice radio-echo sounding. The analytical solution is a polynomial with a degree that exponentially depends on the number of layers, being computationally inefficient. For low incidence angles, the small-angle approximation can be used to avoid the polynomial. In their technique, they normalise the governing equations to obtain a framework where to find a narrow angular interval containing the solution, finally estimated interpolating the boundaries. The new approach improves the results regarding the small-angle approximation for a wider angular range at a slightly higher computational time. This method has been applied to focus airborne synthetic aperture radar images for deep ice sounding, reducing the calculation time and improving the detected response in wide beam and squinted geometries, used for high along-track resolution or the detection of sloping internal layers.

An adaptive extend Kalman filter（EKF） is designed to estimate the roll angle for trajectory correction projectile only using radial magnetometers. By analysing the characteristics of the radial magnetometer output signal and the complex angular motion of the high-spin projectiles, the measurement equation is established. Two important measures, namely noise parameter adaptation and increasing system observation, are taken to improve the performance of the designed EKF. The novelty of this study is the proposed adaptive EKF has no requirements on the magnetometer measurement accuracy. That is the magnetometers used need not undergo a complicated calibration process. In addition, orthogonal difference method is introduced to adjust noise parameters. Finally, a series of numerical simulations and flight tests are carried out to verify the performance of the proposed method. The results show the designed adaptive EKF can effectively estimate the roll angle for the trajectory correction projectile and could be extended to practical engineering applications.

Cognitive radars have the capability of adapting the transmitted waveform with the dynamic state of target and environment, to enhance the radar performance. In this study, a cost function is proposed for designing the waveform parameters in cognitive radars, along managing the radar time resources. The proposed cost function has the capability of adapting to any radar measurement vector. The purpose of the proposed cost function is to design the waveform parameters adaptively, so that a compromise between the different radar measurement errors is made. This compromise between the different radar measurement errors depends on the prior and posterior target state estimations. Both simulated target data and real target data are used for evaluating the proposed cost function. Also the performance of the proposed cost function is compared to the previously presented cost function. Simulation results indicate that by exploiting the proposed cost function, a great saving on time resources is achieved, while tracking error is kept stable. This time resource-saving lies within the range of 10% up to 50% depending on the target manoeuvre scenario. Also, in a non-time resource management case, an improvement in tracking error is achieved.

Underdetermined wideband direction of arrival (DOA) estimation based on the sparse array is studied here and a novel algorithm is developed to improve the estimation performance of off-grid targets in the framework of sparse Bayesian learning. First, the narrowband off-grid model is extended to a wideband case and the sparse Bayesian model containing off-grid biases is deduced. Then, a sequential solution is proposed to obtain the estimation, where the fast sparse Bayesian learning strategy is employed to improve the computational efficiency. The estimation accuracy is improved significantly through off-grid compensation and the computational complexity is reduced remarkably. Simulation results verify the effectiveness of the proposed method.

With the multi-function need for airborne space-time adaptive processing (STAP) radar, range synthesis is usually necessary for the follow-up function of target recognition. Utilising the excellent performance on orthogonality and bandwidth synthesis of the frequency division multiple access (FDMA) waveform and the longer accumulation time of multiple-input multiple-output (MIMO) radar, a robust low-sidelobe target synthesis method for airborne FDMA–MIMO STAP radar is developed. The spectra characteristics of target and clutter are first analysed. Then, the keystone transform is employed to mitigate velocity migration. To avoid gain fluctuation induced by multiple independent adaptive weight vectors, the robust STAP beamformer is developed. Finally, to decouple the range–angle coupling relationship resulted from the FDMA waveform, angle compensation is added in the robust STAP beamformer. Numerical examples are given to demonstrate the effectiveness of the presented method.

The construction of the third generation of the Chinese BeiDou navigation satellite system (BDS), which provides global positioning, navigation, and timing (PNT) services, will be completed in 2020. As BDS satellites contain the geostationary orbit (GEO), inclined geosynchronous (IGSO), and medium earth orbit (MEO), orbital manoeuvres occur more frequently. Thus, orbit manoeuvre detection is important for continuous and reliable PNT services. A BDS orbit manoeuvre detection method based on the combination of global positioning system (GPS) and BDS observations is proposed in this study. The standard deviations of the observation residuals of the epoch-differenced velocity estimation of the single BDS system and combined GPS + BDS system were compared to determine the beginning and end of the orbit manoeuvre. The results show that the orbital manoeuvre leads to a position, velocity, and receiver clock error bias of approximately tens to hundreds of metres, several centimetres per second, and tens to hundreds of metres, respectively. Based on the proposed method, the start and end times can be detected in real time and the usable observation time can be extended by >157 min.

Based on the mean arrival time and temporal broadening of pulsed waves propagating through turbulent media, this study investigates the ionospheric effects induced by irregularity on medium-earth-orbit synthetic aperture radar (MEOSAR) range imaging quality. Considering radar signal two-way propagating through ionosphere irregularity, an analysis model for ionospheric effects induced by irregularities on MEOSAR range imaging quality is established based on the system characteristics of MEOSAR and ionospheric irregularity parameters. The mode extends the application of pulsed waves propagating through turbulent media to the field of synthetic aperture radar (SAR), and it can be used to analyse the effects on MEOSAR induced by both background ionosphere and ionospheric irregularity. The degradation of range image quality, including deterioration of resolution and shift in the image, due to the ionospheric irregularities is analysed. It is found that the effects induced by ionospheric irregularities will be very serious when the inner and outer scales of ionospheric irregularities are small or the fluctuation is strong. Furthermore, the degradation of resolution and the shift of image will become more and more serious with the increase of SAR orbit height. The results can help to evaluate ionospheric irregularity effects on range imaging for MEOSAR and provide a foundation for the design of MEOSAR.

Cognitive radars have the capability of using the prior environmental information to improve the radar performance. In this study, a cost function for fully adaptive waveform parameters design for cognitive tracking radars is proposed. These parameters include – but not limited to – pulse length, pulse repetition frequency, number of transmitted pulses, and target revisit rate. Thus, the proposed cost function is capable of reducing the tracking error, using adaptive waveform parameters, along the time resource management, with adaptive coherent processing interval and target revisit time. The purpose of the proposed cost function is balancing the different radar measurement errors (which depend on radar transmitted waveform in contrary directions), with respect to the target manoeuvre scenario, to reach the radar tolerable tracking error. Simulation results show that using the proposed waveform parameter design cost function, tracking error is reduced, and an optimised radar time resource usage is obtained.

This study proposes an intelligent tracking method based on the expectation maximisation approach. To obtain the consistent tracking performance, the observer should maintain contact with the target and continuously update its tracking data. Unfortunately, a significant problem arises from the uncertainty of the target motion. The reasons behind this uncertainty include losses, time-varying noises, external inputs, and others. Above all, a sharp manoeuvre by the arbitrary acceleration input mainly degrades the tracking performance. A variety of techniques were needed and studied to enhance performance levels. This study focuses on acceleration as the cause of the uncertainty and a consistent approximation of the acceleration, leading to highly efficient tracking performance. The EM makes it possible to separate the noise term from the acceleration inputs and the noise components. Finally, a manoeuvring submarine with three-dimensional coordinates is provided as an example to show the effectiveness of the proposed algorithm.

High-frequency surface wave radar (HFSWR) is an effective method for detecting and monitoring the targets on the ocean surface and above. To improve the detection performance of HFSWR, a new detector is proposed by applying weighted distance iteration (WDI) processing to the joint domain localised (JDL) matrix constant false alarm rate (CFAR) detector. Based on information geometry theory and Riemannian manifold, the proposed detector uses multi-dimensional information (azimuth, Doppler velocity and range information) of the signal to effectively find the target that has drowned in sea clutter and uses WDI-processing technique to suppress the clutter. The experimental results are given to show the superiority of the proposed detector. Compared with cell average CFAR detector and JDL matrix CFAR detector, the proposed detector improves the detection performance effectively.

Gait-based human identification aims to identify individuals by their walking style. In this study, the authors investigate the use of micro-Doppler (m-D) signatures retrieved from a frequency-modulated continuous-wave radar sensor to identify individuals based on their natural gait characteristics. The gait dataset of 20 persons has been collected in an indoor environment where each subject was allowed to walk naturally and freely, which is absolutely more realistic and challenging than most existing works based on limited walking behaviour. Then, they perform identification using a transfer learned ResNet-50, which was fine-tuned on the gait m-D dataset based on the deep transfer learning technique. Through experiments, they first determined the optimal observation window length of m-D samples, and with this input, they achieved an average identification accuracy of 96.7% on the test set for 20 subjects, which highly outperforms the state-of-the-art methods. The presented work provides prospects in developing a solution to automatically identify persons based on gait characteristics using a simple and cost-efficient radar device.