This work presents the design of a frequency modulated continuous wave (FMCW) multiple-input multiple-output radar system with collocated antennas. A key part of this article is the modification and application of the iterative adaptive algorithm (IAA) for digital beamforming to an FMCW radar system. The implemented system operates in the 2.4 GHz Industry, Scientific and Medical band with 100 MHz of bandwidth and consists of a transmit (TX) site with four antennas and a receive (RX) site with four antennas. The angular resolution is greatly improved from 15° with the common delay-and-sum beamforming to only 5° with IAA beamforming, which was verified by the results from a radar simulator and by a field test with the implemented hardware. The challenge of synchronisation and maintaining phase coherence in systems with remote TX and RX sites is also addressed by proposing a low-frequency clock and trigger distribution system. This approach allows for cost-efficient systems which can be distributed over longer distances.

Attitude estimation from vector observations is widely employed in aerospace applications for accurate integrated navigation using solutions to Wahba's problem. Wahba's solutions are practical but may corrupt facing critical cases in the presence of almost collinear reference vector measurements, which is inevitable in robotic applications with redundant sensor arrays or platforms with celestial vision sensors in similar directions. Different from existing algorithms, this study presents a novel sequential multiplicative quaternion attitude estimation method from various vector sensor outputs. The unique linear constitution of the algorithm leads to its specific name of Recursive Linear Quaternion Estimator (RLQE). The algorithm's architecture is designed to use each single pair of vector observation linearly so that the vector observations can be arbitrarily chosen and fused. The closed-form covariance of the RLQE is derived that builds up the existence of a highly reliable RLQE Kalman filter. Simulations and experiments are carried out to give the performances of the authors’ algorithm and representative ones. Compared with other works, the proposed RLQE maintains good precision, better consistency and lower variance bounds. Moreover, the attitude estimation performance with critical cases is especially much better than conventional Wahba's solution on its continuity, accuracy and variance.

This study proposes a modified terrain referenced navigation (TRN) algorithm considering slant range measurement. The TRN estimates a vehicle's position by comparing the measured terrain information with digital elevation map data. A conventional TRN assumes that a vertical range is measured by a radar altimeter and the measurement error exists only in the vertical direction. Recently, many researches have focused on applying the slant range sensor data, such as light detection and ranging or interferometric radar altimeter data to improve the TRN performance. In such cases, not only the vertical error but also the horizontal error components are generated by slant range measurement errors and the effect of these error components increases significantly as the flight altitude and the slant range measurement errors increase. Therefore, a proper TRN algorithm should be considered to estimate the vehicle position in a stable and accurate manner. In this study, a modified extended Kalman filter [EKF]-based TRN algorithm (ETRN) considering the slant range measurement and the corresponding measurement variance is proposed. The proposed algorithm converts the ETRN measuring the slant range to the conventional ETRN measuring the vertical range. Also, the proposed algorithm provides robust and accurate TRN results by accounting for the vertical and horizontal error components generated by the slant range errors.

The strong non-linear relationship between the range rate and the target state can be introduced using the range rate to track a target. A linear measurement equation can be constructed based on the geometrical relationship between the range rate and the velocity components. Then, the linear Kalman filtering (KF) algorithm can be used. To improve the performance of the converted measurement method, a novel multiplicative unbiased converted measurement KF algorithm with range rate (UCMKF-R) is developed. To eliminate the conversion bias, one-step prediction estimation is used to replace the position measurement to calculate the converted measurement error covariance in the UCMKF-R algorithm, which removes the correlation between the converted measurement error covariance and the measurement noise. Thus, a Decorrelated UCMKF-R (DUCMKF-R) is proposed. The experimental results show that the measurement conversion of the DUCMKF-R algorithm is unbiased, consistent and has an estimation bias that is close to zero. The proposed UCMKF-R and DUCMKF-R algorithms are compared with the state-of-the-art approaches, namely, the Sequential Extended KF algorithm, the Sequential Unscented KF algorithm, and the Converted Measurement KF with Range Rate algorithm. The experimental results show that the proposed algorithms have good performance.

In this study, the authors extend the high-degree cubature Kalman filter to operate with continuous-time non-linear stochastic systems with discrete measurements. For this purpose, they utilise two known approximations to solve the stochastic differential equation used in the modelling of continuous-time dynamics. The first approach is grounded in an ordinary differential equations solver. The second approach is based on the Itô–Taylor expansion of order 1.5. In addition, the errors presented in each approach were classified. Finally, the proposed filters were compared with the continuous–discrete cubature Kalman filter in a challenging radar-tracking experiment. The results of the experiment show an improvement in the accuracy of the proposed method, and more importantly, a better performance of the filters based on the Itô–Taylor expansion.

An optimal tone detector based on the Neyman–Pearson criterion is proposed for the optical fibre vector hydrophone (OFVH). The detector takes account of the difference between noise levels on the acoustic pressure channel and the three particle acceleration channels of an OFVH. Explicit expressions for the impulse responses of pre-filters that are central to the proposed detector are given. Analyses show that the proposed detector is equivalent to the minimum variance distortionless response beamformer for the OFVH. In the case of identical noise on all particle acceleration channels, the signal-to-noise ratio (SNR) gain of the detector is dB ( is the noise power ratio of OFVH channels at the tone frequency), whereas the SNR gain also depends on target direction and is bounded by and dB when noise on all particle acceleration channels are different. Results from both simulations and lake experiment data show that the proposed detector outperforms tone detectors that use (i) the acoustic pressure signal, (ii) the particle acceleration signals and (iii) equally the combination of acoustic pressure signal and particle acceleration signals.

A coherent scheme of federated architecture for the ultra-tight integration of global navigation satellite system (GNSS) and MEMS (micro-electro-mechanical system) inertial measurement unit (IMU) is presented. Inside the receiver baseband, both the controls for code numerically controlled oscillator (NCO) and carrier NCO are designed. They are each composed of two parts, one part is derived from the navigation solutions of outer loop, and the other part is given on the basis of the channel pre-filter outputs from inner loop. Each tacking channel has two filters of cascaded structure, one is the traditional pre-filter which is used to achieve GNSS signal tracking errors, and the second one is an extractor which is constructed to extract navigation solution derivation errors from the designed NCO controls and the signal tracking errors. For the ultra-tight integration navigation filter, the receiver clock residual error model after compensating the receiver clock drift is derived in detail. Finally, semi-physical simulation environment of the proposed ultra-tight integration scheme is built and closed-loop experiment under high dynamics scenario is put forward. The simulation results show that the proposed integration scheme can stably and robustly track the GNSS signals, and can achieve accurate navigation solutions even in harsh cases.

The recent proliferation of distributed sensor networks makes the multitrack fusion under unknown correlation highly significant. There have been two major approaches developed to date for the multitrack fusion under unknown correlation: an approach based on maximum mutual information and another based on the minimum overestimate of covariance intersection. Unfortunately, the former is applicable only to two tracks while the latter becomes ineffective for multiple tracks with excessive overestimation. This paper presents solutions for fusing an arbitrary number of tracks under unknown correlation. First, a maximum bound of cross-covariance between two tracks of unknown correlation is computed analytically, such that the computed maximum bound is used for fusion with the fused track less conservative than the one provided by covariance intersection method. For more than two tracks, the above two-track method can be sequentially applied for fusion. However, the sequential fusion results in a sequence-dependent and suboptimal solution. Therefore, this paper presents several alternative solutions that provide a better trade-off between optimality and consistency in fusion. Simulation results are provided to demonstrate the effectiveness of the proposed method.

In this study, the authors consider the radar sequence generation problem, where the sequence is required to possess the spectral nulling and low-correlation levels in crowded electromagnetic environments. The design problem of the sequence with the desired spectrum and correlation properties is formulated as the minimisation of the difference between the true ones and the desired ones, respectively. Then a spectral fitting method is proposed to solve it, by applying the time-frequency transformation. The proposed method is based solely on fast Fourier transform operations, thus it is computationally efficient. An extension to sequence sets design is also presented. Numerical simulations indicate that, compared with the state-of-the-art algorithms, the proposed method can achieve better or identical results with greatly reduced running time.

Warhead and decoy classification is one of the most important and difficult technical problems in ballistic missile defence. The conventional methods extract features from the measured data and employ some classification algorithms. However, it is hard to extract all the information embedded in the raw data, and there might be contradictory features lowering the classification ability. A one-dimensional convolutional neural network structure named RCSnet was proposed to classify the warhead and decoy targets of the same shape in midcourse, which directly utilises the radar cross-section (RCS) time series. It was compared with 5 conventional classification algorithms which used 26 selected features on simulation dataset, and it outperformed them in both classification performance and predicting speed. Different training algorithms and networks of the RCSnet structure with different filter numbers were explored for better utilising the RCSnet.

For the multiple receiver synthetic aperture sonar, traditional fast imaging algorithms are limited by the approximation of the point target reference spectrum (PTRS). To solve this problem, a novel imaging algorithm based on a new PTRS is proposed in this study. With the presented method, the matched filtering function in the azimuth dimension must be first derived. Then, the range–azimuth coupling phase is obtained by using the difference between the PTRS and the matched filtering function in the azimuth dimension. To perform the decoupling between the range dimension and the azimuth dimension, the bulk range cell migration correction (RCMC) and the differential RCMC based on the range-dependent sub-block processing method are used. Compared to traditional methods, the new method avoids the complicated series expansion. Furthermore, it can handle the general case with the explicit point of the stationary phase. Processing results of the simulated data and the real data indicate that the high-performance results can be got by using the presented method. Moreover, it further shows that the presented method is very suitable for the wide-swath imagery.

Extracting valuable and discriminative features is one of the crucial issues for target recognition in synthetic aperture radar (SAR) images. In this study, a feature extraction method based on robust locality discriminant projection (RLDP) is presented for SAR target recognition. To characterise the local structural information of SAR images, the manifold learning technique called the supervised locality preserving projection is introduced to learn a linear projection, with which the SAR image can be cast into an implicit feature space. Then, the authors extend t-distributed stochastic neighbour embedding to a parametric framework for optimising the linear projection. In the resulting feature space, the intrinsic neighbour relation with a certain class can be preserved. In addition, the separation between different classes can be enhanced. Unlike most local manifold learning methods, the proposed method is robust to changes of the neighbour parameter. To further analyse the non-linear structure, a useful variant of RLDP named kernel RLDP (KRLDP) is proposed. KRLDP exploits RLDP in an implicit reproducing kernel Hilbert space, where the kernel-based non-linear projection is learned to capture the non-linear structural information. Extensive experiments on moving and stationary target automatic recognition databases demonstrate the effectiveness of the proposed methods.

Information geometry-based matrix constant false alarm rate (CFAR) detector is an efficient solution to target detection, especially for the K-distributed clutter environment with respect to a small bunch of pulses. The main reason for the matrix CFAR detector to achieve better detection performance is covariance matrix captures the correlations between the data. However, most existing matrix CFAR detectors suffer from heavy computational complexity, which leads to a limitation in practical detection scenarios. Motivated by this, the authors utilise the eigenvalues of the covariance matrix to capture the correlation and propose an eigenvalue-based detection method with lower computational complexity. Based on the Neyman–Pearson criterion, they first analyse the likelihood ratio test (LRT) in the eigenvalue domain and derive the relationship between the LRT test statistic and the maximum eigenvalue. To meet the practical requirement, they further design a totally blind scheme: the maximum eigenvalue-based matrix CFAR detector. By employing the group invariant theory, they show that the proposed detector presents the CFAR property. In addition, the theoretical performance analysis is also provided. Simulation results based on the numerical experiment and real sea clutter data verify that the proposed method with a low computational complexity can achieve a better detection performance.

A method is proposed for removing falsely matched points after sparse matching in synthetic aperture radar (SAR) images. This method uses epipolar geometry as well as random sample consensus (RANSAC) to automatically remove false matches (outliers) among all points. The method randomly selects at least four points among all matched points. Then, using a bilinear equation, a generic relation is established between the pixel coordinates of a reference point in the master image and the parameters of the corresponding epipolar line in the slave image. Therefore, it is possible to calculate the epipolar line for all points using the bilinear function and then evaluate the accuracy of the matched points. Moreover, the proposed method is compared with the method that uses the RANSAC with an affine function, which is a common method for removing outliers. Here, the output of the scale-invariant feature transform algorithm is used to conduct the experiments. Furthermore, the SAR image pairs from southern Iran are utilised to evaluate the performance of the method. Experiments are conducted on TerraSAR-X images, and the results demonstrate that the proposed method has high reliability for removing false matches.

Geometry-free linear combination of dual-frequency signal code and carrier phase observations have been used for multiple purpose such as to remove ionosphere-delays, improve the success rate in integer ambiguity resolution and accuracy in position solution. Out of three civil signals in GPS L1/L2C/L5 and Galileo E1/E5/E6, a user has many ways to form geometry-free linear combinations to solve integer ambiguity in carrier phase observations. In precise carrier phase positioning, probability of fixing integer ambiguities using code-carrier and carrier-carrier difference models rely on the ionosphere bias and code phase observation noise. When three frequency signals are available, the code phase observation noise can be reduced using ionosphere delay matched linear combination of carrier phase observations. Furthermore, the low noise smoothed code phase observations can be used to form a code-carrier difference model to fix ionosphere-free integer ambiguity. In this study, analyzed the propagation of observation noise and ionosphere bias in a geometry-free linear combination of GPS L1/L2/L5 code and carrier phase observations, i.e. ionosphere-free, wide-lane, extra wide-lane, medium-lane, and narrow-lane. Further, the feasibility and success-rate of using smoothed code phase observations in a wide-lane integer ambiguity solution is analyzed in precise positioning applications. Experimental validation is provided.

Multibeam radar (MBR) systems based on waveform diversity require a set of orthogonal waveforms in order to generate multiple channels in transmission and extract them efficiently at the receiver with digital signal processing. Linear frequency modulated (LFM) signals are extensively used in radar systems due to their pulse compression properties, Doppler tolerance, and ease of generation. Here, the authors investigate the level of isolation between MBR channels based on LFM chirps with rectangular and Gaussian amplitude envelopes. The orthogonal properties and the mathematical expressions of the isolation are derived as a function of the chirp design diversity, and specifically for diverse frequency slopes and frequency offsets. The analytical expressions are validated with a set of simulations as well as with experiments at C-band using a rotating target.

The time link calibration of Global Positioning System (GPS) based on carrier phase observation has been performed in the past few years. However, the calibration accuracy is expected to be improved. In this paper, an approach of time link calibration for reducing the uncertainty is proposed. The mechanism and procedure for time link calibration based on GPS are investigated in depth firstly. And then GPS data processing method and strategies in calibration are discussed, where the precise time transfer solution (PTTSol) software is also developed. The experiment of zero baseline time link is employed, of which the standard deviation (STD) value of clock difference reaches 0.03 ns. The root mean square (RMS) value of clock difference in long distance time link is 0.11 ns which compared with the international GPS service (IGS) value. At last, one calibration campaign was organized at the national time service center (NTSC) from modified Julian day (MJD) 57598 to MJD 57616. With a travel receiver forming three common clock difference (CCD) modes, the estimated uncertainty of the calibration value was 0.13 ns, which neglected uncertainty of 1 pulse per second (1 PPS) signal relative to the local time reference point.

Synthetic aperture radar (SAR) imaging with an independently moving transmitter and receiver introduces motion artefacts difficult to compensate for, especially between satellites in separate orbits that rendezvous over a target. A solution for polarisation-resolved bistatic frequency-modulated continuous-wave (FMCW) SAR with independently moving platforms is derived and demonstrated through simulation. This solution accounts for the polarisation of the source, susceptibility tensor of the target, and the velocity and acceleration of the transmitter and receiver. The accuracy of the solution is demonstrated by reconstructing simulated point ground targets with a pair of X-band SAR satellites of realistic parameters.

A new direction-of-arrival (DOA) estimation method for the sparse receiving array with gain/phase uncertainties is proposed. Because of the sparsity of the received signals, compressed sensing theory can be used to sample and recover receiving signals with less data. Owing to the existence of the gain/phase uncertainties, it would be difficult to estimate the DOA accurately when the sparse representation of the signals is not optimal. In order to reduce the influence of the gain/phase uncertainties on the sparse representation, the authors firstly transfer the array signal receiving model with the gain/phase uncertainties into an errors-in-variables (EIV) model, which treats the gain/phase uncertainties as an additive error matrix. Then a new DOA estimation method named simultaneous orthogonal matching pursuit-total least squares algorithm based on the EIV model is proposed. The DOAs will be obtained by estimating the sparse coefficients through iterations with the proposed method. Simulation results show that the sparse regularised total least squares algorithm is able to provide a more accurate DOA estimation with the gain/phase uncertainties than the existing calibration algorithms even with the sparse array.

An efficient bias mitigation algorithm based on time of flight is proposed for positioning the target location and reducing the non-line-of-sight (NLOS) error and clock jitter error in three-dimensional wireless cooperative localisation networks. Through linearising the range-based expressions and utilising novel three-step weighted linear least squares algorithm, an algebraic solution of target can be derived, in which the clock jitter error and NLOS error can be alleviated effectively. Meanwhile, the Cramer–Rao lower bound (CRLB) is derived for the standard of performance evaluation. The location accuracy of the proposed algorithm is analysed and compared with the conventional methods through simulation experiment. The simulation results indicate that the precision of the proposed algorithm can approach the CRLB, what is more, the proposed algorithm can provide obvious improvements in positioning accuracy compared to the state-of-the-art approaches.