An adaptive robust Kalman filter algorithm is derived to account for both process noise and measurement noise uncertainty. The adaptive algorithm estimates process noise covariance based on the recursive minimisation of the difference between residual covariance matrix given by the filter and that calculated from time-averaging of the residual sequence generated by the filter at each time step. A recursive algorithm is proposed based on both Massachusetts Institute of Technology (MIT) rule and typical non-linear extended Kalman filter equations for minimising the difference. The measurement update using a robust technique to minimise a criterion function originated from Huber filter. The proposed adaptive robust Kalman filter has been successfully implemented in relative navigation using global position system for spacecraft formation flying in low earth orbit, with real-orbit perturbations and non-Gaussian random measurement errors. The numerical simulation results indicate that the proposed adaptive robust filter can provide better relative navigation performance in terms of accuracy and robustness as compared with previous filter algorithms.

In this study, a new approach is proposed for accurate target identification, required by the phased array radar systems that are employed in through-the-wall imaging applications. In radar imaging, the effects of the multipath propagation are materialised in fake impressions of the true target, known as ghost images. The developed algorithm removes these ambiguities related to the existence of a target by cancelling, in the final radar image, the ghost images by means of improving the global signal-to-spurious-ratio (SSR) and the target-to-ghost-ratio (TGR) that characterise the real target signature. The development of the approach is based on beamforming and on coherent signal processing upon the returned signal and clutters, for a phased array monostatic radar system. The performances of the algorithm are measured in terms of both the global SSR gain and the TGR and they are verified through simulations and measurements in scenarios that quantify the robustness of the approach. The obtained numerical results concerning the global SSR gain and the TGR certify that the proposed method improves the target localisation and removes the ghost images for radars that operate in rich scattering environments. In the end, the limitations of the approach are also presented.

This study is concerned with an L _∞ filtering problem for non-linear systems with persistent bounded disturbances and intermittent measurements. The non-linear plant is represented by the Takagi–Sugeno (T–S) fuzzy model that is employed to approximate the non-linear dynamic systems. The system measurements may be unavailable at any sample time and the probability of the occurrence of missing data is assumed to be known. In this study, to design the L _∞ fuzzy filter with the estimation error, the estimation error because of persistent bounded disturbance is minimised by some linear matrix inequalities and the filter error system is stochastically stable in the mean square. A stochastic variable satisfying the Bernoulli random binary distribution is utilised to model the phenomenon of the missing data. Finally, the results indicate that the proposed method attenuates the peak of estimation error and preserves a guaranteed L _∞-gain performance.

Compressive sensing theory suggests that accurate reconstruction of a signal can be achieved using its highly undersampled measurements, provided that the signal is sparse in an a priori known dictionary. For the range imaging problem in wideband radar, this dictionary is typically taken to be a DFT basis. However, since practical target scatterers do not lie exactly in the frequency lattice of the discrete Fourier transform (DFT) basis, there is always mismatch between the assumed DFT basis and the actual dictionary for sparsity. To address this, the authors consider the radar echo sparsifying dictionary as refinable and develop a compressive imaging approach using dynamic dictionaries. The approach treats the frequency gridding points as adjustable parameters of the sparsifying Fourier dictionary and achieves dynamical dictionary refinement via iterative optimisation of these parameters. To achieve joint image formation and dictionary refinement, the approach utilises the variational expectation-maximisation algorithm to iteratively perform a two-step process, that is, estimating sparse backscattering coefficients given a dictionary and then updating the dictionary to better fit the data sparsity model. The experimental results based on both synthetic and anechoic chamber data demonstrate that the approach improves the precision in range estimation and suppresses spurious spikes in the constructed profiles.

This article studies the problem of joint detection and tracking of a target using multi-static Doppler-only measurements. The assumption is that in the surveillance volume of interest a single transmitter of known frequency is active with multiple spatially distributed receivers collecting and reporting Doppler-shift frequencies to the data fusion centre. The measurements are not only affected by additive noise but also contaminated by false detections and missed detections. The study develops for this application of a multi-sensor Bernoulli particle filter with information gain-driven receiver selection. The simulation results indicate robust performance of the proposed Bernoulli particle filter.

Target tracking through particle filter (PF) for time-varying presence of a target is compared for thresholded and non-thresholded measurements, where in both cases a track produces more than one measurement. To that end, thresholded split measurements PF along with non-thresholded measurements, sequential importance resampling PF (SIR PF) and auxiliary variable PF (AV PF) are extended to cope with time-varying target presence. Simulations show superiorities in working through non-thresholded measurements. Furthermore, they surprisingly demonstrate that non-thresholded measurements SIR PF leads to less root-mean-square position estimation error than non-thresholded measurements AV PF in case of uncertain target presence and unclear measurements origin besides dynamic model mismatching.

A direct coning mitigation algorithm based on the detection of a sinusoidal component in the gyro measurements is proposed. The coning error, which is one of dominant error sources affecting the accuracy of attitude computation in the inertial navigation system (INS), is induced by the sinusoidal motion such as a manoeuvre of vehicle or the vibration of a dithering of ring laser gyro. However, many researchers have developed coning error mitigation algorithms based on the higher-order polynomial model and its correction terms are extracted from the gyro output without faithful consideration of the periodicity of motion. Hence, the authors first detect and estimate the sinusoidal components from gyro measurements, and then find the higher-order correction terms from the estimated sinusoidal parameters. The authors also show that this algorithm can be applied to the mitigation of sculling error because of its duality to the coning motion. Simulation results show that the direct compensation algorithm works effectively for the navigation of vehicles with continuous and steady oscillations. Also, the rate table test with HG1700 inertial measurement unit (IMU) is conducted to show the effectiveness of proposed algorithm on real INS signal.

In this study, a single snapshot imaging method of the moving targets in multiple-input multiple-output (MIMO) radar with sparse antenna array is proposed. First, a configuration of sparse antenna array is presented and then, on the basis of this, an imaging method based on compressed sensing theory is put forward. With this method, the image of a moving target can be achieved via single snapshot imaging processing. It not only can avoid motion compensation processing as required by conventional inverse synthetic aperture radar imaging, but also can dramatically reduce the number of the antenna elements, which is a quite large number in the typical configuration of MIMO radar system with linear antenna array. Finally, the effectiveness of this method is validated by the simulation results.

In this study, the authors present a multiband time-of-arrival (TOA) positioning model and validate the performance in a practical dynamic spectrum access scenario according to results obtained from an ultra-high-frequency (UHF) spectrum occupancy measurement campaign. The statistical analysis of the measured data shows a distinguishable difference between the unoccupied and occupied portion of the UHF band. The bandwidth availability for the UHF band is shown to follow a Gaussian distribution according to the measurement results. The positioning model is verified using the non-linear least squares, linear least squares and two-step maximum-likelihood location estimation algorithms. The root-mean-square error (RMSE) performance evaluation of the proposed model revealed the advantage of utilising five discrete bands to perform TOA estimation, especially in poor signal-to-noise ratio (SNR) conditions ranging from − 10 to 0 dB. At a fixed SNR of 0 dB, an average RMSE improvement of 74 and 82% was observed for a double- and triple-band system when compared with a conventional single-band TOA system. This particular positioning technique can enable improved location estimation in a dynamic spectrum access environment.

In this study, a general signal-processing architecture is proposed for next generation radar (NGR). When the NGR works in MIMO mode, we derive the closed-form Cramer–Rao bound of the estimation of coherent-processing parameters, which include the time-delay differences and phase synchronisation errors among different apertures. When the NGR turns to work in fully coherent mode, assuming the time-delay differences are ideally compensated, the authors present the closed-form signal-to-noise ratio (SNR) gain and analyse the SNR gain loss of the NGR because of inaccurate phase synchronisation errors.

The motion compensation (MOCO) plays a significant role to accommodate the motion errors caused by atmosphere turbulence and/or aircraft maneuvers in airborne synthetic aperture radar configurations. In broadside or small squint cases, the well-focused image can be obtained by the typical two-step MOCO to have the quadratic motion errors compensated. However, with the increasing of squint angle, not only the high-order motion errors, but also the azimuth-variant errors must be taken into account. In this study, a modified non-linear chirp scaling (MNLCS) algorithm is proposed to handle this problem in highly-squinted case. The key is to use the method of series reversion to cover the high-order motion errors, the MNLCS to precondition the data to process the azimuth-variant components and a series expansion to obtain an accurate form of the signal spectrum. The skewed spectrum in highly-squinted case is reduced through the use of a linear range cell migration correction. The simulated results have shown the MNLCS algorithm can handle data with more complicated geometries than the previous algorithm.

The micro-motion characteristics of radar target are useful features for target recognition. Extended targets (as opposed to point target) have various scattering centres, such as the familiar point, localised and distributed scattering centres, as well as the rarely discussed but often encountered migratory scattering centres. The migratory scattering phenomenon of smooth surface is particularly concerned in this study. The motion information recoded in radar signals are actually that of migratory scattering centres rather than the real motions of the rigid target. Therefore the misleading motion information will bring unpredictable error to the radar application of target discrimination or recognition. To tackle this problem, the influence of migratory scattering phenomena of extended targets on micro-motion characteristics contained in radar signal is analysed in detail. Some meaningful conclusions are reached. The backscattered signals of extended targets are computed by the well-validated full-wave numerical method, hybrid finite element-boundary integral-multilevel fast multipole algorithm. The numerical results agree well with the analytical conclusions given in this study.