Target Localization Problem Research Articles

Range-based cooperative underwater target localization

The paper addresses the problem of range-based cooperative underwater target localization. In its simplest form, target localization aims to estimate the position of a stationary or mobile target by using range measurements between the target and a vehicle, called a tracker, undergoing a trajectory that can be measured on-line. In this context, the tracker must execute sufficiently exciting maneuvers so as to maximize the range-based information available for target localization. The paper extends this set-up to the case where the tracker works in cooperation with another vehicle, called companion, that can also measure ranges to the target and shares this info with the tracker. The latter may have access to the position of the companion or, in some cases, only to the range between the two vehicles. We consider three different operating scenarios where the motion of the tracker is chosen so as to increase the accuracy with which the position of the target can be estimated. The scenarios reflect the situations where the motion of the companion vehicle satisfies one of three conditions: i) the motion is not defined a priori and can also be optimized, ii) the motion is fixed a priori and is known to the tracker (scenario in which the tracker benefits from the extra information acquired by the companion vehicle, which tracks a desired trajectory in the context of a separate, independent mission), and iii) the motion is not known a priori and must be learned in the course of the mission. By adopting an estimation-theoretical settings, optimal trajectories are computed by maximizing the determinant of an appropriately defined Fisher information matrix (FIM), subjected to vehicle maneuvering constraints and inter-vehicle collision avoidance. Simulation results illustrate the methodology adopted for cooperative target localization.

Guest editorial: special issue on Consensus‐based Applications in Networked Systems

Guest editorial: special issue on Consensus‐based Applications in Networked Systems

3-D Target Localization in Wireless Sensor Networks Using RSS and AoA Measurements

This paper addresses target localization problems in both noncooperative and cooperative 3-D wireless sensor networks (WSNs), for both cases of known and unknown sensor transmit power, i.e., $P_{T}$ . We employ a hybrid system that fuses distance and angle measurements, extracted from the received signal strength and angle-of-arrival information, respectively. Based on range and angle measurement models, we derive a novel nonconvex estimator based on the least squares criterion. The derived nonconvex estimator tightly approximates the maximum-likelihood estimator for small noise. We then show that the developed estimator can be transformed into a generalized trust region subproblem framework, by following the squared range approach, for noncooperative WSNs. For cooperative WSNs, we show that the estimator can be transformed into a convex problem by applying appropriate semidefinite programming relaxation techniques. Moreover, we show that the generalization of the proposed estimators for known $P_{T}$ is straightforward to the case where $P_{T}$ is not known. Our simulation results show that the new estimators have excellent performance and are robust to not knowing $P_{T}$ . The new estimators for noncooperative localization significantly outperform the existing estimators, and our estimators for cooperative localization show exceptional performance in all considered settings.

Asymptotically Efficient Target Localization From Bistatic Range Measurements in Distributed MIMO Radars

In this letter, the problem of target localization from bistatic range (BR) measurements in distributed multiple-input multiple-output radar systems is investigated. By introducing nuisance parameters, a pseudolinear set of BR equations is established. Then, a closed-form localization algorithm is developed, based on this pseudolinear set of equations and multistage weighted least squares estimation. This solution is shown analytically to attain the Cramer–Rao lower bound under the small Gaussian noise assumption. Simulations are included to support the theoretical studies. Unlike the existing studies where the variance of BR measurements is assumed to be independent of the corresponding transmitter-to-target and target-to-receiver distances, we consider the more realistic distance-dependent noise model. The positioning accuracy of the proposed algorithm is shown to outperform the existing closed-form methods under this distance-dependent noise model.

Cooperative target localization using multiple UAVs with out-of-sequence measurements

PurposeThe time delay would occurs when the measurements of multiple unmanned aerial vehicles (UAVs) are transmitted to the date processing center during cooperative target localization. This problem is often named as the out-of-sequence measurement (OOSM) problem. This paper aims to present a nonlinear filtering based on solving the Fokker–Planck equation to address the issue of OOSM.Design/methodology/approachAccording to the arrival time of measurement, the proposed nonlinear filtering can be divided into two parts. The non-delay measurement would be fused in the first part, in which the Fokker–Planck equation is utilized to propagate the conditional probability density function in the forward form. The time delay measurement is fused in the second part, in which the Fokker–Planck is used in the backward form approximately. The Bayes formula is applied in both parts during the measurement update.FindingsUnder the Bayesian filtering framework, this nonlinear filtering is not only suitable for the Gaussian noise assumption but also for the non-Gaussian noise assumption. The nonlinear filtering is applied to the cooperative target localization problem. Simulation results show that the proposed filtering algorithm is superior to the previous Y algorithm.Practical implicationsIn this paper, the research shows that a better performance can be obtained by fusing multiple UAV measurements and treating time delay in measurement with the proposed algorithm.Originality/valueIn this paper, the OOSM problem is settled based on solving the Fokker–Planck equation. Generally, the Fokker–Planck equation can be used to predict the probability density forward in time. However, to associate the current state with the state related to OOSM, it would be used to propagate the probability density backward either.

Robust target localization in the absence of signal propagation models

This paper considers a problem of target or source localization based on the measurements from a mobile sensor or a network of sensors. The assumption is that the received signal strength is strictly monotonic with the distance between the target and the sensor. No explicit signal propagation model, neither the structure nor the mathematical description, is assumed or used in localization. The contribution of the paper is to show that this mere knowledge of monotonicity suffices in locating the unknown target in the absence of noise. Further in the presence of noise, robust localization algorithms are developed and analyzed by exploiting various forms of angular, temporal and spatial averages. The asymptotic convergence results have been established in the presence of noise and further the finite step performance results are developed.

A Closed-Form Solution for RSS/AoA Target Localization by Spherical Coordinates Conversion

This letter addresses the problem of target localization in a 3-D space, utilizing combined measurements of received signal strength and angle of arrival (AoA). By using the spherical coordinate conversion and available AoA observations to establish new relationships between the measurements and the unknown target location, we derive a simple closed-form solution method. We then show that the proposed method has straightforward adaptation to the case where the target’s transmit power is also not known. Simulation results validate the outstanding performance of the proposed method.

Distributed algorithm for target localization in wireless sensor networks using RSS and AoA measurements

This paper addresses target localization problem in a cooperative 3-D wireless sensor network (WSN). We employ a hybrid system that fuses distance and angle measurements, extracted from the received signal strength (RSS) and angle-of-arrival (AoA) information, respectively. Based on range measurement model and simple geometry, we derive a novel non-convex estimator based on the least squares (LS) criterion. The derived non-convex estimator tightly approximates the maximum likelihood (ML) one for small noise levels. We show that the developed non-convex estimator is suitable for distributed implementation, and that it can be transformed into a convex one by applying a second-order cone programming (SOCP) relaxation technique. We also show that the developed non-convex estimator can be transformed into a generalized trust region sub-problem (GTRS) framework, by following the squared range (SR) approach. The proposed SOCP algorithm for known transmit powers is then generalized to the case where the transmit powers are different and not known. Furthermore, we provide a detailed analysis of the computational complexity of the proposed algorithms. Our simulation results show that the new estimators have excellent performance in terms of the estimation accuracy and convergence, and they confirm the effectiveness of combining two radio measurements.

Moving Target Localization in Multistatic Sonar by Differential Delays and Doppler Shifts

A moving target creates the Doppler effect on the transmitted signal, which can be exploited to improve the target localization accuracy in multistatic sonar that normally utilizes differential delay time measurements only. In this letter, we first examine the contribution of Doppler measurements via the Cr $\acute{\text{a}}$ mer–Rao lower bound (CRLB) study, and then develop an algebraic closed-form solution for the moving target localization problem. The proposed algorithm is shown in both theory and simulation to be able to reach the CRLB performance under Gaussian noise, when the measurement error is small.

Consensus estimation‐based target localization in underwater acoustic sensor networks

SummaryTarget localization, which aims to estimate the location of an unknown target, is one of the key issues in applications of underwater acoustic sensor networks (UASNs). However, the resource‐constrained property of an underwater environment such as noise makes target localization a challenging problem. This paper considers a consensus estimation‐based approach to the target localization problem in UASNs. To detect and acquire the position of the target, a hybrid architecture is applied to UASNs, where autonomous underwater vehicles provide self‐location and clock synchronization for sensor nodes. Built on this architecture, a trilateration method coupled with a regional optimal solution is provided to estimate the rough localization of a target. Furthermore, a consensus estimation‐based algorithm is designed for the regional optimal solution, such that localization accuracy is improved. In the presence of measurement and communication noises, localization error and asymptotic unbiasedness for the estimation algorithm are also investigated. Finally, simulation results show that the proposed localization approach can avoid the occurrence of no‐solution while improving the localization accuracy. In addition, the hybrid communication architecture can reduce the number of transmissions compared with egalitarian decentralized networks. Copyright © 2016 John Wiley & Sons, Ltd.

Distributed RSS-AoA Based Localization With Unknown Transmit Powers

This letter addresses the hybrid range/angle-based target localization problem in a cooperative 3-D wireless sensor network where no central processor is available. Due to battery exhaust over time, sensors’ transmit powers are assumed different and unknown. Range and angle measurements are drawn from the received signal strength and angle-of-arrival models, respectively. By exploiting the measurement models, we derive a novel local-estimator by which each target updates its own estimate, based on the least squares criterion. Second-order cone relaxation technique is then applied to approximately solve the attained problem due to its non-convex nature. Our simulation results show that the proposed algorithm efficiently solves the localization problem.

On the Definition and Existence of a Minimum Variance Unbiased Estimator for Target Localization

The problem of target localization with ideal, binary detectors is considered in one-dimensional space for both the censored and noncensored scenarios. In the censored setting, the problem is equivalent to estimating the center of a uniform distribution, and does not admit a minimum-variance unbiasedestimator (MVUE). However, it is proven that if the detection range is known and the sensor deployment region is large, both censored and noncensored cases will have an MVUE within the class of functions that are invariant to Euclidean motion. In addition, it is shown that when the detection range is unknown, for the censored case one can still form an MVUE whereas in the noncensored case, an MVUE does not exist. Numerical tests support the theoretical findings of this letter.

Integrated Motion Planning, Control, and Estimation for Range-Based Marine Vehicle Positioning and Target Localization

Abstract: The paper addresses the problems of range-based marine vehicle positioning and target localization. Vehicle positioning aims to estimate the positions of one or more vehicles from a sequence of range measurements to fixed or moving acoustic beacons with known locations. In this context, the vehicles must execute sufficiently exciting maneuvers so as to maximize the range-based information available for multiple vehicle positioning. Using an estimation theoretical setting, the vehicle trajectories are computed by maximizing the determinant of a suitably defined Fisher information matrix (FIM), subject to inter-vehicle collision avoidance and vehicle maneuvering constraints. A numerical solution is proposed for the general case. Analytical solutions are obtained in the case of one vehicle and one beacon, when the latter undergoes trajectories that are straight lines, pieces of arcs, or a combination thereof. The theoretical analysis is complemented with practical experiments that focus on the dual problem of underwater target localization. The objective is to estimate the position of a moving underwater target by using range measurements between the target and a vehicle, called a tracker, undergoing a trajectory that can be measured on-line. The experimental set-up includes a surface and an autonomous underwater vehicle of the MEDUSA*-class playing the roles of tracker and target, respectively. In the methodology adopted for system implementation the tracker runs three key algorithms simultaneously, over a sliding time window: i) tracker motion planning, ii) tracker motion control, and iii) target motion estimation based on range data acquired on-line.

On the existence of an MVU estimator for target localization with censored, noise-free binary detectors

The problem of target localization with censored, noise-free binary detectors is considered. In this setting only the detecting sensors report their locations to the fusion center. It is proven that if the radius of detection is unknown to the fusion center, a minimum variance unbiased (MVU) estimator does not exist. Also it is shown that when the radius is known the center of mass of the possible target region is the MVU estimator among estimators that are invariant under Euclidean motion. In addition, a sub-optimum estimator is introduced whose performance is close to the MVU estimator but is preferred computationally. Moreover, for the case when the radius of detection is unknown a sub-optimum estimator is proposed that performs close to the Clairvoyant estimator. Furthermore, minimal sufficient statistics have been provided, both when the detection radius is known and when it is not. Simulations confirmed that the derived MVU estimator outperforms several heuristic location estimators.

Robust MIMO radar target localization via nonconvex optimization

This paper addresses the problem of robust target localization in distributed multiple-input multiple-output (MIMO) radar using possibly outlier range measurements. To achieve robustness against outliers, we construct an objective function for MIMO target localization via the maximum correntropy criterion. To deal with such a nonconvex and nonlinear function, we apply a half-quadratic optimization technique to determine the target position and auxiliary variables alternately. Especially, we derive a semidefinite relaxation formulation for the aforementioned position determination step. The robust performance of the developed approach is demonstrated by comparing with several conventional localization methods via computer simulation.

Multiple feature points representation in target localization of wireless visual sensor networks

This paper discusses the target localization problem in wireless visual sensor networks. Additive noises and measurement errors will affect the accuracy of target localization when the visual nodes are equipped with low-resolution cameras. In the goal of improving the accuracy of target localization without prior knowledge of the target, each node extracts multiple feature points from images to represent the target at the sensor node level. A statistical method is presented to match the most correlated feature point pair for merging the position information of different sensor nodes at the base station. Besides, in the case that more than one target exists in the field of interest, a scheme for locating multiple targets is provided. Simulation results show that, our proposed method has desirable performance in improving the accuracy of locating single target or multiple targets. Results also show that the proposed method has a better trade-off between camera node usage and localization accuracy.

Survey on Mobile Target Localization in Wireless Sensor Networks

As a novel technology of information acquisition and processing, Wireless Sensor Network (WSN) has been widely used for complex large-scale localization tasks. With global distribution and sensing ability, wireless sensor network can provide valid optimal localization for mobile targets. According to the key problems of mobile target localization under wireless sensor network, this paper depicted current research status in both of line-of-sight and non-line-of-sight environments. Typical and representative algorithms are sorted and their ideas are evaluated. Finally, we discussed and anticipated the future research direction.

Parameter Estimation and Cramer-Rao Bound in Wideband Bistatic MIMO Radar System

The problem of target localization and parameter estimation in wideband bistatic Multiple-Input Multiple-Output (MIMO) radar system is considered. In this paper, we use a novel approach to estimate Doppler stretch and time delay in fractional Fourier transform (FRFT) domain. We also develop two sub-array models to accurately estimate the direction-of-departure (DOD) and the direction-of-arrival (DOA). Furthermore, the Cramér-Rao bound for target parameter estimation is derived and computed in closed form. Parameter estimation performances are evaluated and studied theoretically and via simulations

Detection of Pedestrians in Motion with Rotation and Scale Variation

In this paper, a new framework for tracking non-rigid objects is introduced. By spatially masking the target with an isotropic kernel, a spatially smooth similarity function can be defined, and the target localization problem is then reduced to a search in the basin of attraction of this function. The smoothness of the similarity function allows for the application of a gradient optimization method by adopting a background weighted histogram. The proposed approach is effective for detecting objects in complex background and occlusion. Experimental results using various test videos containing objects in motion with rotation and scale changes show us superb detection accuracy over the conventional method.

An Explicit Solution for Target Localization in Noncoherent Distributed MIMO Radar Systems

This work focuses on the moving target localization problem in the noncoherent multiple-input multiple-output radar system with widely separated antennas. We assume that the time delay and Doppler shift between each transmit/receive element pair have already been measured by a preprocessing algorithm. Utilizing these measurements, an explicit method for jointly estimating the target position and velocity is proposed. It first divides the measurements into several groups based on the different transmitter elements or receive elements, and then employs two best linear unbiased estimators successively for each group to independently produce an estimate of target position and velocity. Finally, these results from different groups are combined to form a composite estimate. Simulation results show that the estimated accuracy of the proposed method achieves the Cramer-Rao lower bound at sufficiently small noise conditions.