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A Bearing-Angle Approach for Unknown Target Motion Analysis Based on Visual Measurements

Zian Ning, Yin Zhang, Jianan Li, Zhang Chen, Shiyu Zhao

TL;DR

This paper tackles vision-based target motion estimation with a moving monocular camera by introducing a bearing-angle approach that uses bounding-box derived measurements. It augments the target state with its unknown size $\ell$ and recasts bearing and angle measurements into a pseudo-linear form suitable for Kalman filtering, improving observability without needing lateral observer motion. Theoretical analysis shows that the observer’s higher-order motion (e.g., nonzero acceleration) is sufficient for full observability, unlike bearing-only methods, and practical results from Matlab, AirSim, and real-world experiments confirm superior performance in diverse scenarios. The work offers a practical, computation-efficient solution for autonomous pursuit and tracking using standard vision outputs (bounding boxes) while clarifying the limits when $\ell$ varies rapidly.

Abstract

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.

A Bearing-Angle Approach for Unknown Target Motion Analysis Based on Visual Measurements

TL;DR

This paper tackles vision-based target motion estimation with a moving monocular camera by introducing a bearing-angle approach that uses bounding-box derived measurements. It augments the target state with its unknown size and recasts bearing and angle measurements into a pseudo-linear form suitable for Kalman filtering, improving observability without needing lateral observer motion. Theoretical analysis shows that the observer’s higher-order motion (e.g., nonzero acceleration) is sufficient for full observability, unlike bearing-only methods, and practical results from Matlab, AirSim, and real-world experiments confirm superior performance in diverse scenarios. The work offers a practical, computation-efficient solution for autonomous pursuit and tracking using standard vision outputs (bounding boxes) while clarifying the limits when varies rapidly.

Abstract

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.
Paper Structure (34 sections, 2 theorems, 67 equations, 13 figures, 2 tables)

This paper contains 34 sections, 2 theorems, 67 equations, 13 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Algorithms for bearing-only target motion estimation
  4. Observability analysis of bearing-only target motion estimation
  5. Problem Formulation
  6. Bearing-Angle Target Motion Estimator
  7. States transition equation
  8. Dynamic modeling of target's physical size
  9. Nonlinear measurement equations
  10. Pseudo-linear measurement equations
  11. Bearing-angle estimation algorithm
  12. Observability Analysis by Kalman's Criterion
  13. The observability matrix
  14. Case 1: the observer's velocity is constant
  15. Case 2: the observer's velocity is time-varying
  16. ...and 19 more sections

Key Result

Theorem 1

The target's motion $p_T(t)$ can be uniquely determined by the observer's motion $p_o(t)$, the bearing $g(t)$, and the angle $\theta(t)$ if and only if which means that the order of the observer's motion must be greater than the target.

Figures (13)

  • Figure 1: An observer MAV observes a target MAV with a monocular camera. The bearing $g$ and angle $\theta$ can be obtained from the bounding box that surrounds the target in the image.
  • Figure 2: The size of the bounding box varies when the camera rotates. By contrast, the angle subtended by the target object is invariant to the camera's orientation change.
  • Figure 3: The architecture of the proposed approach. All the simulation and real-world experiments in this paper follow this architecture.
  • Figure 4: Numerical simulation results based on 100 Monte Carlo runs in three scenarios.
  • Figure 5: Numerical simulation results for time-varying $\ell$.
  • ...and 8 more figures

Theorems & Definitions (4)

  • Theorem 1: (Necessary and sufficient observability condition)
  • Proof 6.1
  • Theorem 2: (Number of discrete observations)
  • Proof 6.2