Bearings-only Target Localization Research Articles

Trajectory Optimization to Enhance Observability for Bearing-Only Target Localization and Sensor Bias Calibration.

This study addresses the challenge of bearing-only target localization with sensor bias contamination. To enhance the system's observability, inspired by plant phototropism, we propose a control barrier function (CBF)-based method for UAV motion planning. The rank criterion provides only qualitative observability results. We employ the condition number for a quantitative analysis, identifying key influencing factors. After that, a multi-objective, nonlinear optimization problem for UAV trajectory planning is formulated and solved using the proposed Nonlinear Constrained Multi-Objective Gray Wolf Optimization Algorithm (NCMOGWOA). Simulations validate our approach, showing a threefold reduction in the condition number, significantly enhancing observability. The algorithm outperforms others in terms of localization accuracy and convergence, achieving the lowest Generational Distance (GD) (7.3442) and Inverted Generational Distance (IGD) (8.4577) metrics. Additionally, we explore the effects of the CBF attenuation rates and initial flight path angles.

GHOST target suppression for distributed multi-array localization using temporal and spatial correlations

We propose a ghost target suppression method for distributed multi-array localization. Triangulation, included in bearings-only target localization method for the well-separated array, is highly dependent on bearing measurements. Its performance is degraded by ghost targets from the ambiguity of bearing measurements. The proposed method is based on the assumption that received signals from the same target have similar frequency components within short-term time and at different locations. We utilize the consistency of acoustic signals in Frequency-Azimuth plots by measuring the frequency component similarities of the target signal over time at a single array (temporal information) and across different arrays (spatial information). The ghost target suppression is evaluated using in situ data from Swellex-96 S5 Event and results reveal the target track along time with much less ghost targets. [Work supported by Korea Research Institute for defense Technology planning and advancement(KRIT)—Grant funded by the Korea government(DAPA(Defense Acquisition Program Administration))(No. KRIT-CT-23-026, Integrated Underwater Surveillance Research Center for Adapting Future Technologies, 2024).]

Sampled Value Optimization Based Bearing-only Localization

This paper proposes a sampled value optimization based estimator (SVOE) for bearing-only target localization (BTL). When the variances of the bearing noise are unknown, multiple measurements are made at the same sensor location. Then the sampled moments are calculated and used to establish a cost function. When the cost is minimized, the optimal is proven to be consistent and has the covariance proportional to the Cramer-Rao lower bound. The simulation results demonstrate the superior performance of the SVOE method over other methods.

Robust Bearing-Only Localization Using Total Least Absolute Residuals Optimization

Robust techniques critically improve bearing-only target localization when the relevant measurements are being corrupted by impulsive noise. Resistance to isolated gross errors refers to the conventional least absolute residual (LAR) method, and its estimate can be determined by linear programming when pseudolinear equations are set. The LAR approach, however, cannot reduce the bias attributed to the correlation between system matrices and noise vectors. In the present study, perturbations are introduced into the elements of the system matrix and the data vector simultaneously, and the total optimization problem is formulated based on least absolute deviations. Subsequently, an equivalent form of total least absolute residuals (TLAR) is obtained, and an algorithm is developed to calculate the robust estimate by dual ascent algorithms. Moreover, the performance of the proposed method is verified through the numerical simulations by using two types of localization geometries, i.e., random and linear. As revealed from the results, the TLAR algorithm is capable of exhibiting significantly higher localization accuracy as compared with the LAR method.

One-Bit Recursive Least-Squares Algorithm With Application to Distributed Target Localization

Adaptation and learning over low-cost wireless networks, meanwhile keeping an acceptable performance, are well motivated. This paper focuses on online parameter estimation over binary networks, which consist of noisy low-resolution sensors, each only giving coarsely one-bit quantized output observations and transmitting them to a fusion center. We develop a class of recursive least-squares (RLS) algorithms based on an expectation–maximization framework, which realizes adaptive parameter estimation from one-bit observations of the noisy output stream. The developed algorithms are, respectively, derived with and without prior knowledge of the noise variances, and their performances are theoretically and experimentally evaluated. Moreover, it is shown that, although the information contained in the one-bit observations is very limited, the proposed algorithms are comparable to the classical RLS algorithm using the original (nonquantized) observations. In addition, as a practical application, the proposed algorithm combined with array signal processing techniques is applied to bearing-only target localization over wireless sensor array networks, and its effectiveness is verified through simulation experiments.

A Novel Subspace Approach for Bearing-Only Target Localization

A new subspace method is proposed to solve the bearing-only target localization (BOTL) problem. Instead of linearizing the nonlinear bearing equations to form least-squares optimization, we construct a scalar product matrix by making full use of all bearing and intersensor bearing geometric information. After exploiting the dimension and eigenstructure of the scalar product matrix, we devise a subspace algorithm for BOTL with its weights computed from a prior location estimate. Simulation results show that the proposed algorithm achieves a mean square error performance close to the Cramer–Rao lower bound, even at high noise levels. Field experiments demonstrate the superiority of the proposed algorithm.

The Bearing-Only Target localization via the Single UAV: Asymptotically Unbiased Closed-Form Solution and Path Planning

The target localization based on the unmanned aerial vehicle (UAV) is becoming more and more popular due to its flexible mobility. In this paper, the bearing-only localization with respect to the single UAV in the three-dimensional (3D) scenario is studied by the angle of arrival (AOA). In the current researches, the bias of the closed-form solution caused by the coefficient errors of the pseudo-linear equations constructed by the AOA is not effectively eliminated. In order to reduce the bias, an asymptotically unbiased localization algorithm is proposed, which eliminates the bias by constructing the constrained weighted least-squares. Since the term that causes the bias is constrained to a constant, which no longer affects the closed-form solution of the pseudo-linear equations, the closed-form solution is unbiased. After that, the position errors of the UAV are considered in path planning, which improves localization accuracy by taking account of both AOA errors and position errors of the UAV rather than just AOA errors.

A distributed subband valley fusion (DSVF) method for low frequency broadband target localization.

A distributed subband valley fusion method is proposed in this paper for target localization for a multi-array fusion system. Instead of employing two-step processing like the traditional bearings-only target localization (BOTL) methods, the target location estimate is directly obtained from the intersection of the estimated bearing line of each array, which is automatically produced after applying a subband valley energy detection process to the reciprocal of the steered response power over predefined grid points. Bearing information at all frequencies and ranges are used to generate the bearing line and the intersection structure, leading to higher localization accuracy in comparison with the BOTL methods. In multiple-target situations, the data association problem is solved by distinguishing true targets from the ghost ones from the power and the number of bearing lines at the corresponding intersection grid point. The method is subsequently tested by the SWellEx-96 shallow water experiment data set. Simulation and experimental results demonstrate the localization accuracy of the proposed method.

Observer Path Design for Bearings-Only Localization with State Constraints

In bearings-only target localization, observer path have an important effect on the accuracy of target localization. Based on the analysis of Fisher information matrix, an optimal approach to designing observer path is proposed. Observer path derived from the step-by-step optimal algorithm only depends on observer's initial states and state constraints. The optimal path resulted with step-by-step algorithm is demonstrated by computer simulation. Compared with traditional methods, our algorithm is not limited to the number of observations as well as terminating conditions.

Weighted Constrained Total Least Squares for Bearing-Only Target Localization

Paper has been removed due to suspected plagiarism.

Bearings-only target localization for unmanned underwater vehicles

This paper reports on target localization for autonomous underwater vehicles (AUVs) with acoustic bearing sensors where the bearing sensor provides detection and beamforming capabilities and reports target bearings with the associated measurement uncertainties. Estimating the state of a moving target using a bearing sensor on a moving platform is a difficult problem due to both the nonlinear nature of the measurement equations with respect to the unknown target parameters but also the observability conditions for the unknown parameters which require the observer to maneuver. This paper will report on a maximum likelihood (ML) method using Levenberg–Marquardt (LM) optimization for estimating the target state parameters. A known issue with ML solutions to this problem is that the algorithm may have difficulty reaching the global minimum unless the initial solution guess is close to the true solution. This paper will report on a genetic algorithm approach to making the initial solution guess. The performance of this approach, obtained from Matlab simulation, is presented. The implementation of the algorithms in the MOOS architecture is described using a very fast Lapack implementation for the LM parameter estimation to support the goal of optimal AUV maneuvering to improve the target state estimate.

Location Discovery Based on Fuzzy Geometry in Passive Sensor Networks

Location discovery with uncertainty using passive sensor networks in the nation's power grid is known to be challenging, due to the massive scale and inherent complexity. For bearings-only target localization in passive sensor networks, the approach of fuzzy geometry is introduced to investigate the fuzzy measurability for a moving target inR2space. The fuzzy analytical bias expressions and the geometrical constraints are derived for bearings-only target localization. The interplay between fuzzy geometry of target localization and the fuzzy estimation bias for the case of fuzzy linear observer trajectory is analyzed in detail in sensor networks, which can realize the 3-dimensional localization including fuzzy estimate position and velocity of the target by measuring the fuzzy azimuth angles at intervals of fixed time. Simulation results show that the resulting estimate position outperforms the traditional least squares approach for localization with uncertainty.

Coalition Formation for Bearings-Only Localization in Sensor Networks—A Cooperative Game Approach

In this paper, formation of optimal coalitions of nodes is investigated for data acquisition in bearings-only target localization such that the average sleep time allocated to the nodes is maximized. Targets are required to be localized with a prespecified accuracy where the localization accuracy metric is defined to be the determinant of the Bayesian Fisher information matrix (B-FIM). We utilize cooperative game theory as a tool to devise a distributed dynamic coalition formation algorithm in which nodes autonomously decide which coalition to join while maximizing their feasible sleep times. Nodes in the sleep mode do not record any measurements, hence, save energy in both sensing and transmitting the sensed data. It is proved that if each node operates according to this algorithm, the average sleep time for the entire network converges to its maximum feasible value. In numerical examples, we illustrate the tradeoff between localization accuracy and the average sleep time allocated to the nodes and demonstrate the superior performance of the proposed scheme via Monte Carlo simulations.

Relationship Between Geometric Translations and TLS Estimation Bias in Bearings-Only Target Localization

This paper analyzes the effects of local coordinate translations and rotations on the bias and mean-squared error performance of the total least squares (TLS) bearings-only target localization algorithm. The TLS estimator was originally proposed to alleviate the severe bias problems associated with the traditional pseudolinear estimator. An interesting property of the TLS estimator, which is not shared by the pseudolinear estimator, is that its bias is sensitive to where the origin of the local Cartesian coordinates is placed. The paper provides a formal proof of this observation, discusses its implication on bias minimization, and proposes a simple and effective method for TLS bias reduction. The findings of the paper are illustrated with comprehensive simulation examples.

A Fast Global Node Selection Algorithm for Bearings-only Target Localization

In the target tracking, the nodes aggregate their observations of the directions of arrival of the target. The network then uses an extended Kalman filter (EKF) to combine the measurements from multiple snapshots to track the target. In order to rapidly select the best subset of nodes to localize the target with the minimum mean square position error and low power consumption, this paper proposes a simple algorithm, which uses the location information of the target and the network. The lower bound of localization error is utilized according to the distances between the target and the selected active nodes. Furthermore, the direction likelihoods of the active nodes is predicted by way of the node/target bearing distributing relationships.

Bearings-only target localization using total least squares

A total least-squares (TLS) algorithm is developed for two-dimensional location estimation of a stationary target by using only passive bearing measurements of the target. This problem has been studied extensively for several decades and has applications in electronic warfare, surveillance, passive sonar, interference location and suppression, and so forth. The nonlinear nature of the estimation problem poses a number of challenges related to complexity, convergence and estimation bias. After a critical review of the least-squares (LS) algorithms, a TLS estimation algorithm is developed based on the method of orthogonal vectors with the advantage of simplicity and reduced bias in the presence of bearing noise and observer position errors. A constrained TLS (CTLS) algorithm is also developed to improve the estimation accuracy, especially in the case of large measurement errors. Numerical examples are provided to compare the performance of the TLS and CTLS algorithms with the LS target localization algorithms, viz. the maximum likelihood estimator, Stansfield estimator and the method of orthogonal vectors.

On the bias of linear least squares algorithms for passive target localization

The paper derives analytical bias expressions for the least squares bearings-only target localization algorithms. A detailed analysis of the interplay between the target localization geometry and the estimation bias is provided for the cases of elliptical and linear observer trajectories. It is observed that the estimation bias is proportional to the distance between the target and the centre of mass of the observer positions. The effect of the localization geometry parameters on the estimation bias is illustrated analytically and by way of numerical examples. The theoretical findings of the paper are backed up with simulation studies.

Optimization of observer trajectories for bearings-only target localization

The problem of bearings-only target localization is to estimate the location of a fixed target from a sequence of noisy bearing measurements. Although, in theory, this process is observable even without an observer maneuver, estimation performance (i.e., accuracy, stability and convergence rate) can be greatly enhanced by properly exploiting observer motion to increase observability. This work addresses the optimization of observer trajectories for bearings-only fixed-target localization. The approach presented herein is based on maximizing the determinant of the Fisher information matrix (FIM), subject to state constraints imposed on the observer trajectory (e.g., by the target defense system). Direct optimal control numerical schemes, including the recently introduced differential inclusion (DI) method, are used to solve the resulting optimal control problem. Computer simulations, utilizing the familiar Stansfield and maximum likelihood (ML) estimators, demonstrate the enhancement to target position estimability using the optimal observer trajectories.