In many applications, it may be desired to decompose a non-stationary signal into its individual components. If spectral components of the non-stationary signal do not overlap in the frequency domain then Fourier transform can be used to decompose the non-stationary signal. Fourier transform fails to decompose the non-stationary signal if its spectral components overlap in the frequency domain. In this study, the authors propose Fourier-Bessel transform and the time–frequency analysis in conjunction with the fractional Fourier transform (FB-TF) method for the separation of multi-component non-stationary signal whose components overlap in both time and/or frequency domains. The efficiency of the proposed method is compared with one of the traditional decomposition methods like EMD. The proposed approach is applied to both simulated and experimental radar data. Results demonstrate the effectiveness of the proposed method for non-stationary signal separation and for detecting manoeuvring target in heavy sea-clutter environments. The improvement factor and clutter attenuation are calculated and used to compare the performance of the EMD and the FB-TF methods in suppressing the sea-clutter and enhancing target detection. The proposed method can be used as a potential tool for detecting and enhancing the low observable manoeuvring air targets in the sea-clutter environment.

For synthetic aperture radar (SAR) systems, antenna array which is distributed in flight direction could increase the equivalent sample frequency in azimuth by a factor of the number of elements of antenna array. With a reconstruction algorithm, the aliased Doppler spectrum could be recovered. However, the degradation of conventional algorithms for reconstructing the Doppler spectrum with special pulse repetition frequency (PRF) shows poor robustness and the out-of-band energy which is caused by the side lobes of the antenna pattern deteriorates the azimuth ambiguity to signal ratio of a multichannel SAR. In this study, an improved reconstruction algorithm based on antenna pattern is proposed by generating an ambiguity matrix, which resembles the covariance matrix and could be used to reconstruct in-band signal and minimise the azimuth ambiguity energy. Aiming at increasing the robustness of the algorithm, the method of diagonal loading is introduced to the approach. Even in the scenario of special PRF, which is close to the singular point, the signal could be successfully reconstructed with the improved approach. Simulation results validate the proposed method.

Indoor positioning methods based on wireless local area network (WLAN) signal measurements have gained popularity because of high localisation accuracy. These methods use radio-maps obtained from wireless signal measurement surveys on location grids. Measurement sets from various WLAN access points are called fingerprints and they can be used to identify locations where the measurements are collected. WLAN positioning methods face unexpected changes in signal patterns because of attenuation changes or transient faults in WLAN cards or access points that often make signal strength readings unavailable. This study studies the effect of faulty measurements on the performance of popular state-of-the-art WLAN indoor positioning methods. Additionally, an integrity monitoring preprocessing algorithm is provided that demonstrates a possibility of faulty measurements mitigation for conventional methods such as K-nearest-neighbour. This is achieved by detecting and excluding faulty measurements prior to classification. Performance figures are provided for both simulated and empirical environments.

The authors propose a novel compressive sensing (CS)-based Dechirp-Keystone algorithm (DKA) for synthetic aperture radar (SAR) moving target imaging, which is called the CS-DKA. The DKA can focus on moving targets in range-Doppler domain efficiently through only keystone transform (KT), complex multiplication and Fourier transform (FT)/inverse Fourier transform (IFT) operations. It has been shown that the non-interpolation implementation of KT can be expressed by an orthonormal basis, and it is known that the complex multiplication and FT/IFT are linear and invertible; therefore, the Dechirp-Keystone operator (DKO) is also linear and invertible. In the proposed algorithm, the authors take the inverse of DKO (IDKO) rather than the exact SAR echo model to construct the representation basis in the CS frame owing to its high implementation efficiency. After that, a random transmitting/receiving scheme is considered, to implement the down-sampling operation, and then reconstruct the moving target image by solving a regularisation problem. Both simulated and real SAR data are processed to show that the CS-DKA with down-sampled data can focus the target as well as the conventional DKA does with full data, and at the same time can achieve much lower sidelobes.

A target of interest measured by a high range resolution radar may be modelled by multiple dominant points of reflections referred to as dominant scatterers. In this study a non-linear state space setting is used to model the states and measurements of a target moving in two dimensions. A resample-move particle filter (PF) with simulated annealing is successfully used to jointly infer the locations of the dominant scatterers and the motion parameters of the target. The location estimates of scatterers using the PF method are compared with those obtained using standard range-Doppler inverse synthetic aperture radar (ISAR) imaging when using the same radar returns for both cases. The PF infers the location of scatterers more accurately than ISAR processing, and the processing can be performed online as opposed to ISAR processing, which requires batching. It is relatively straightforward to extend the method to perform localisation and tracking of scatterers in three dimensions, whereas such an extension is challenging in ISAR processing. However, several challenges need be addressed to make this algorithm suitable for practical implementation and these challenges are discussed. This method may be used to obtain very accurate estimates of target state, which may in turn be used for accurate ISAR motion compensation.

Only target kinematic information is used in most conventional tracking systems, such as a radar or a sonar. Target attitude angles, which provide information about future trajectory curvature before radar measurement, can be used to improve tracking accuracy. The aim of this study is to track three-dimensional (3D) target with attitude angles (yaw and pitch) and radar measurement. Target velocity variations in each coordinate under attitude angles are derived after motion analysis under yaw and pitch angles separately. Then tracking models, the state vector of which includes attitude angles, are presented for target tracking. Targeting at non-zero mean characteristics of attitude measurement, and based on analysing Gaussian sum filter (GSF) and cubature Kalman filter (CKF), a Gaussian sum CKF (GSCKF) is presented to improve the filtering ability of non-linear non-Gaussian systems. Meanwhile, tracking models with different attitude components are established according to the changing law during target motion, and manoeuvering attitude angles are estimated through model switch. A comparison of performance with and without the use of attitude angles shows the benefits of attitude angle-aided 3D target tracking. Simulation results of GSFs with different sub-filters demonstrate that the performance of the presented GSCKF has improved over conventional GSFs.

In this study, a covariance differencing-based matrix decomposition algorithm is proposed for locating coherent sources under spatially coloured noise in bi-static multiple-input–multiple-output (MIMO) radar. The method contains three steps. First, the covariance differencing technique is employed to eliminate sensor noise, especially the spatially coloured noise. Second, a block Toeplitz or block Hankel matrix is constructed for decorrelation with the covariance differenced matrix. The forward-only, backward-only and combined forward-backward block Toeplitz/Hankel matrix constructions are defined, respectively. Third, unitary estimation of signal parameters by rotational invariance techniques (ESPRIT) algorithm is applied to estimate directions-of-departure (DODs) and directions-of-arrival (DOAs) of sources. The proposed algorithm offers several advantages. First, it is more robust and provides better estimation performance than other methods. Then, the coloured noise problem is overcome in a simple and effective way. Further, the computational load is comparatively low. Simulation results demonstrate the validity of the proposed algorithm.

In this study, the authors deal with the problem of detecting a signal in partially homogeneous environments, where both the test data and the training data share the same covariance matrix up to an unknown scaling factor. A generalised persymmetric parametric adaptive coherence estimator (GPer-PACE) detector is proposed, where the disturbance is modelled as a multichannel autoregressive process. To mitigate the effect of limited training samples, the subspatial aperture smoothing is performed in the design of the authors’ GPer-PACE detector. Moreover, the persymmetric structure information is exploited to further reduce the sample requirements. The performance of the GPer-PACE is assessed by numerical examples. The results show that the GPer-PACE outperforms other traditional detectors in sample-deficient scenarios.

This study presents a method of improving time measurements resolution in a direct sequence-code division multiple access receiver by using a fine code tracking loop based on fractional delay filtering of a despreading sequence. It briefly describes the structure of a generic digital code tracking loop and the proposed modification which allows to measure time difference of arrival values with the subsample resolution, together with suggestions to reduce computational complexity by storing the set of samples of fractionally-delayed signals in memory. The proposed solution was tested in a laboratory and in real environment in a radionavigation system built in Gdansk University of Technology.

The automatic identification system (AIS), a ship reporting system originally designed for collision avoidance, is becoming a cornerstone of maritime situational awareness. The recent increase of terrestrial networks and satellite constellations of receivers is providing global tracking data that enable a wide spectrum of applications beyond collision avoidance. Nevertheless, AIS suffers the lack of security measures that makes it prone to receiving positions that are unintentionally incorrect, jammed or deliberately falsified. In this study, the authors’ analyse a solution to the problem of AIS data verification that can be implemented within a generic networks of ground AIS base stations with no need for additional sensors or technologies. The proposed approach combines a classic radio-localisation method based on time difference of arrival with an extended Kalman filter designed to track vessels in geodetic coordinates. The approach is validated using anonymised real AIS data collected by multiple base stations that partly share coverage areas. The results show a deviation between the estimated origin of detected signals and the broadcast position data in the order of hundreds of metres, therefore demonstrating the operational potential of the methodology.

This study proposes a new multiple model estimation algorithm. Although the derivation of the proposed algorithm is different from the existing interacting multiple model (IMM), both algorithms are exactly the same if the dynamic system is linear. However, for non-linear systems, it appears that the proposed algorithm is different from the IMM algorithm. The proposed algorithm is applied to the tracking problem of re-entry vehicles that is known as highly non-linear system. The estimation performance of the proposed algorithm is compared with IMM by a series of simulation runs. The result shows that the proposed algorithm improves the estimation performance.

A non-linear filter is developed for continuous-time systems with observations/measurements carried out in discrete-time. The filter developed can approximate the a priori and a posteriori probability density function (pdf) with weighted Gaussian sums inside specific search regions. To make the approximations, first, Gaussians are placed with equal intervals inside the search regions and deterministic sample points are chosen within the search regions. The pdf values are then calculated at sample points using numerical solution of the Fokker–Planck equation for the a priori pdf and using Bayes’ rule for the a posteriori pdf. These values are used to find the weights of Gaussians using least-squares method. This process is similar to curve fitting with Gaussian radial basis functions. Inside the search regions, locations of the sample points and mean and covariance values of Gaussians are found by the help of a unscented Kalman filter (UKF). By adjusting the width of the search regions, all the parts, or the ones close to mean values of pdfs, can be approximated. The performance of the filter developed is analysed using a non-linear system with a single-state variable and two radar tracking applications. It is compared with particle filter, UKF and converted measurement Kalman filter for these cases.

In this paper, the received signal in a range cell is modelled as a multi-component linear frequency-modulated (LFM) signal after range compression and motion compensation, and a new method based on segment integration and Lv's transform (LVT) is introduced for parameter estimation of LFM signals over long observation interval. In this method, the LFM signals are firstly divided into segments and fast Fourier transform (FFT) is then applied within each signal segment. After that, the same frequency resolution bins of each segment are selected to construct new series and inter-segment LVT is implemented to obtain the parameter estimates. The criteria to choose the number of segments, output signal-to-noise ratio, computational complexity and memory cost are analysed in detail for this new approach. This method is fast and able to obtain the accurate parameter estimates by using the complex multiplications and FFT. Comparisons with other popular methods, LVT, maximum-likelihood estimation and fractional Fourier transform are performed. Experimental results demonstrate the proposed method is capable of obtaining the accurate parameter estimates with low computational burden and storage memory, making it suitable to be applied in memory-limited and real-time processing systems.