Low-complexity three-dimensional AOA-cross geometric center localization methods via multi-UAV network

The angle of arrival (AOA) is widely used to locate a wireless signal emitter in unmanned aerial vehicle (UAV) localization. Compared with received signal strength (RSS) and time of arrival (TOA), AOA has higher accuracy and is not sensitive to the time synchronization of the distributed sensors. However, there are few works focusing on three-dimensional (3-D) scenarios. Furthermore, although the maximum likelihood estimator (MLE) has a relatively high performance, its computational complexity is ultra-high. Therefore, it is hard to employ it in practical applications. This paper proposed two center of inscribed sphere-based methods for 3-D AOA positioning via multiple UAVs. The first method could estimate the source position and angle measurement noise at the same time by seeking the center of an inscribed sphere, called the CIS. Firstly, every sensor measures two angles, the azimuth angle and the elevation angle. Based on that, two planes are constructed. Then, the estimated values of the source position and the angle noise are achieved by seeking the center and radius of the corresponding inscribed sphere. Deleting the estimation of the radius, the second algorithm, called MSD-LS, is born. It is not able to estimate angle noise but has lower computational complexity. Theoretical analysis and simulation results show that proposed methods could approach the Cramér–Rao lower bound (CRLB) and have lower complexity than the MLE

Range-only Target Localisation using Geometrically Constrained Optimisation

The problem of optimal range-only localisation of a single target is of considerable interest in two-dimensional search radar networking. For coping with this problem, a range-only target localisation method using synchronous measurements from radars is presented in the real ellipsoidal earth model. In the relevant radar localisation scenario, geometric relationships between the target and three radars were formed. A set of localisation equations was derived on range error in such a scenario. Using these equations, the localisation task has been formulated as a nonlinear weighted least squares problem that can be performed using the Levenberg- Marquardt (LM) algorithm to provide the optimal estimate of the target’s position. To avoid the double value solutions and to accelerate the convergence speed for the LM algorithm, the initial value was approximately given according to observations from two radars. In addition, the relative validity has been defined to evaluate the performance of the proposed method. The performance of the proposed approach is evaluated using two simulation experiments and a real-test experiment, and it has been found to possess higher localisation accuracy than the other conventional method.Defence Science Journal, Vol. 65, No. 1, January 2015, pp.70-76, DOI:http://dx.doi.org/10.14429/dsj.65.547

3-D Hybrid Localization with RSS/AoA in Wireless Sensor Networks: Centralized Approach

This dissertation addresses one of the most important issues present in Wireless Sensor Networks (WSNs), which is the sensor’s localization problem in non-cooperative and cooperative 3-D WSNs, for both cases of known and unknown source transmit power PT . The localization of sensor nodes in a network is essential data. There exists a large number of applications for WSNs and the fact that sensors are robust, low cost and do not require maintenance, makes these types of networks an optimal asset to study or manage harsh and remote environments. The main objective of these networks is to collect different types of data such as temperature, humidity, or any other data type, depending on the intended application. The knowledge of the sensors’ locations is a key feature for many applications; knowing where the data originates from, allows to take particular type of actions that are suitable for each case. To face this localization problem a hybrid system fusing distance and angle measurements is employed. The measurements are assumed to be collected through received signal strength indicator and from antennas, extracting the received signal strength (RSS) and angle of arrival (AoA) information. For non-cooperativeWSN, it resorts to these measurements models and, following the least squares (LS) criteria, a non-convex estimator is developed. Next, it is shown that by following the square range (SR) approach, the estimator can be transformed into a general trust region subproblem (GTRS) framework. For cooperative WSN it resorts also to the measurement models mentioned above and it is shown that the estimator can be converted into a convex problem using semidefinite programming (SDP) relaxation techniques.It is also shown that the proposed estimators have a straightforward generalization from the known PT case to the unknown PT case. This generalization is done by making use of the maximum likelihood (ML) estimator to compute the value of the PT . The results obtained from simulations demonstrate a good estimation accuracy, thus validating the exceptional performance of the considered approaches for this hybrid localization system

Sparsity-Cognizant Total Least-Squares for Perturbed Compressive Sampling

Solving linear regression problems based on the total least-squares (TLS) criterion has well-documented merits in various applications, where perturbations appear both in the data vector as well as in the regression matrix. However, existing TLS approaches do not account for sparsity possibly present in the unknown vector of regression coefficients. On the other hand, sparsity is the key attribute exploited by modern compressive sampling and variable selection approaches to linear regression, which include noise in the data, but do not account for perturbations in the regression matrix. The present paper fills this gap by formulating and solving TLS optimization problems under sparsity constraints. Near-optimum and reduced-complexity suboptimum sparse (S-) TLS algorithms are developed to address the perturbed compressive sampling (and the related dictionary learning) challenge, when there is a mismatch between the true and adopted bases over which the unknown vector is sparse. The novel S-TLS schemes also allow for perturbations in the regression matrix of the least-absolute selection and shrinkage selection operator (Lasso), and endow TLS approaches with ability to cope with sparse, under-determined "errors-in-variables" models. Interesting generalizations can further exploit prior knowledge on the perturbations to obtain novel weighted and structured S-TLS solvers. Analysis and simulations demonstrate the practical impact of S-TLS in calibrating the mismatch effects of contemporary grid-based approaches to cognitive radio sensing, and robust direction-of-arrival estimation using antenna arrays.Comment: 30 pages, 10 figures, submitted to IEEE Transactions on Signal Processin

3D Localisation of Target using Elevation Angle Algorithm with the use of Ground Radars

A new novel method based on elevation angle algorithm (EAA) is proposed in this paper, to obtain 3D position of target using range and azimuth measurements of two ground 2D radars. The EAA estimates optimal target elevation angle wrt contributing radar by solving a non-linear optimisation problem using Levenberg-Marquardt method in geo-centric frame such as earth-centred-earth-fixed. The target position in geodetic frame (WGS84) is then obtained using slant range, azimuth and estimated elevation angle. The proposed method is evaluated using simulated but realistic radar data and accuracy of estimated position is found to be comparable with true position (error within acceptable limit). The method is also evaluated with real data from actual ground 2D radars and estimated target position is found to be comparable with reference navigation data (GPS) on-board of target. For each radar, corresponding Extended Kalman filter (EKF) is used to handle noisy, asynchronous measurements and to provide estimated range and azimuth at common reference time for altitude estimation using proposed EAA method. In case of real data, the estimated altitude is found to be comparable GPS altitude with error less than 5 % of true altitude. From the study, it is found that EAA is suitable to estimate target position using measurements from only two contributing asynchronous 2D radars in real-time as compared to some other techniques such triangulation and Trilateration where at-least three radars are required to get the position of target. This method can be useful to utilise network of vintage long range 2D radars to determine target position and to fill the gap wherever/whenever target is out of detection range of 3D radars. In addition, EAA method is compared with commonly used methodology such range only localisation and results are presented

Exploiting Sparse Structures in Source Localization and Tracking

This thesis deals with the modeling of structured signals under different sparsity constraints. Many phenomena exhibit an inherent structure that may be exploited when setting up models, examples include audio waves, radar, sonar, and image objects. These structures allow us to model, identify, and classify the processes, enabling parameter estimation for, e.g., identification, localisation, and tracking.In this work, such structures are exploited, with the goal to achieve efficient localisation and tracking of a structured source signal. Specifically, two scenarios are considered. In papers A and B, the aim is to find a sparse subset of a structured signal such that the signal parameters and source locations maybe estimated in an optimal way. For the sparse subset selection, a combinatorial optimization problem is approximately solved by means of convex relaxation, with the results of allowing for different types of a priori information to be incorporated in the optimization. In paper C, a sparse subset of data is provided, and a generative model is used to find the location of an unknown number of jammers in a wireless network, with the jammers’ movement in the network being tracked as additional observations become available