Bearing Angle Measurements Research Articles

A bearing-angle approach for unknown target motion analysis based on visual measurements

Vision-based estimation of the motion of a moving target is usually formulated as a bearing-only estimation problem where the visual measurement is modeled as a bearing vector. Although the bearing-only approach has been studied for decades, a fundamental limitation of this approach is that it requires extra lateral motion of the observer to enhance the target’s observability. Unfortunately, the extra lateral motion conflicts with the desired motion of the observer in many tasks. It is well-known that, once a target has been detected in an image, a bounding box that surrounds the target can be obtained. Surprisingly, this common visual measurement especially its size information has not been well explored up to now. In this paper, we propose a new bearing-angle approach to estimate the motion of a target by modeling its image bounding box as bearing-angle measurements. Both theoretical analysis and experimental results show that this approach can significantly enhance the observability without relying on additional lateral motion of the observer. The benefit of the bearing-angle approach comes with no additional cost because a bounding box is a standard output of object detection algorithms. The approach simply exploits the information that has not been fully exploited in the past. No additional sensing devices or special detection algorithms are required.

Fast angles-only relative navigation using polynomial dynamics

A fast and efficient method for initial relative orbit determination from bearing-angle measurements is introduced. The range ambiguity problem for angles-only relative navigation is addressed by modeling nonlinear effects with a novel second-order mapping from relative orbit elements (ROE) to relative position coordinates. This model is used to form a system of polynomial constraint equations linking the line-of-sight measurements to the ROE. An efficient method for solving this system is developed around the insight that the ROE scale with the ratio of the inter-spacecraft separation to the orbit radius and are therefore small for most applications of interest. The method uses a truncated expansion of the quadratic formula to recursively eliminate unknowns, reduce the dimension of the system, and ultimately acquire an approximate solution. Strategies for improving robustness, efficiency, and accuracy are developed and the method is applied to general second-order systems as well as to a broad range of intial relative orbit determination scenarios. Modifications to the constraint equations and a solution algorithm are introduced to address the challenge of bias in the bearing-angle measurements.

Light-Emitting Diode-Based Optical Localization of a Robot in Continuous Motion Using Dynamic Prediction

Abstract For mobile robots, localization is essential for navigation and spatial correlation of its collected data. However, localization in Global Positioning System-denied environments such as underwater has been challenging. Light-emitting diode (LED)-based optical localization has been proposed in the literature, where the bearing angles extracted from the line-of-sight of the robot viewed from a pair of base nodes (also known as beacon nodes) are used to triangulate the position of the robot. The state-of-the-art in this approach uses a stop-and-go motion for the robot in order to ensure an accurate position measurement, which severely limits the mobility of the robot. This work presents an LED-based optical localization scheme for a mobile robot undergoing continuous motion, despite the two angles in each measurement cycle being captured at different locations of the robot. In particular, the bearing angle measurements are captured by the robot one at a time and are properly correlated with respect to the base nodes by utilizing the velocity prediction from Kalman filtering. The proposed system is evaluated in simulation and experiments, with its performance compared to the traditional state-of-the-art approach where the two angle measurements in each cycle are used directly to compute the position of the robot. In particular, the experimental results show that the average position and velocity estimation errors are reduced by 55% and 38%, respectively, when comparing the proposed method to the state-of-the-art.

Observer path planning for maximum information

This paper is concerned with finding an optimal path for an observer, or sensor, moving at a constant speed, which is to estimate the position of a stationary target, using only bearing angle measurements. The generated path is optimal in the sense that, along the path, information, and thus the efficiency of a potential estimator employed, is maximized. In other words, an observer path is deemed optimal if it maximizes information so that the location of the target is estimated with smallest uncertainty, in some sense. We formulate this problem as an optimal control problem maximizing the determinant of the Fisher information matrix, which is one of the possible measures of information. We derive analytical results for optimality using the Maximum Principle. We carry out numerical experiments and discuss the multiple (locally) optimal solutions obtained. We verify graphically that the necessary conditions of optimality are verified by the numerical solutions. Finally we provide a comprehensive list of possible extensions for future work.

Bias-Compensated Diffusion Pseudolinear Kalman Filter Algorithm for Censored Bearings-Only Target Tracking

This letter proposes a novel bias-compensated diffusion pseudolinear Kalman filter algorithm for censored bearings-only target tracking. The proposed algorithm considers two biases caused by the censored bearing angle measurements and the correlation between the measurement vector and the pseudolinear noise. First, the inverse Mills ratio is used to rebuild the uncensored measurements, which can efficiently compensate the bias arising from the censored measurements. Then, we present a bias analysis for the censored diffusion pseudolinear Kalman filter to develop a bias compensation method, leading to the BC-DPLKF-C algorithm. Simulation results show the improved performance of the proposed Kalman filter compared with existing algorithms.

Distributed Source Localization of Multi-Agent Systems With Bearing Angle Measurements

This note deals with the distributed source localization problem by considering a group of unicycle-type agents. Without the need of GPS and compass, we develop a distributed source localization scheme based on bearing angle measurements about neighbors. It is shown that if the sensing and communication graph is connected and the relative motion of every pair of neighboring agents satisfies a persistent excitation condition, then every agent is able to estimate the relative coordinate of the source asymptotically.

A New Target Tracking Algorithm for Synchronous Radar Network under Blanket Jamming

In order to improve the tracking accuracy of the synchronous radar network under blanket jamming with less computation, a new target tracking algorithm based on the optimal linearization is proposed. Firstly, the optimal linearization algorithm for the measurement equation is analyzed. Then the optimal estimation of the position is derived in 2D space according to the bearing angle measurements, and then the estimation is expanded to 3D space in accordance with the pitch angle measurements. Finally, the tracking algorithm for the moving target is presented and simulation testing is conducted. The simulation results show the tracking algorithm without iteration proposed by this paper can make it possible for the radar network under blanket jamming to track the target precisely.

Bearings-Only Tracking in the Plane

It is known that the conditional probability density function for the general filtering problem can be represented as a path integral. This representation is the basis of a new finite dimensional recursive filter which is applied to bearings only tracking. The filter computes an approximation to the density for the target position conditional on the measurements. The approximation is accurate provided only the most recent measurements are used. Two different models for the target motion are considered. In the first the model is a known motion subject to a perturbation by an Ornstein--Uhlenbeck process. In the second the acceleration of the target is a Brownian motion. Numerical experiments show that for the first model the bearing angle measurements add little or no range information, but for the second model they do add significant range information, especially if the noise level in the model is high.

Bearing angle measurements in RF systems having normally distributed arrival angle with unknown variance

Bearing angle measurements in RF systems having normally distributed arrival angle with unknown variance