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A Cooperative Bearing-Rate Approach for Observability-Enhanced Target Motion Estimation

Canlun Zheng, Hanqing Guo, Shiyu Zhao

TL;DR

This work tackles the limited observability and velocity lag in vision-based target motion estimation for multi-camera aerial tracking. It introduces STT-R, a cooperative estimator that fuses bearing and bearing-rate measurements within a distributed recursive least-squares framework to enhance observability and reduce velocity lag. The approach provides pseudo-linear measurement models for bearing and bearing-rate, asserts necessary and sufficient observability conditions under cooperation, and validates the method through simulations and indoor real-world experiments, showing superior velocity tracking while maintaining competitive position accuracy. The results demonstrate that incorporating bearing-rate information with cooperative fusion enables more responsive tracking of highly maneuverable targets in 3D environments.

Abstract

Vision-based target motion estimation is a fundamental problem in many robotic tasks. The existing methods have the limitation of low observability and, hence, face challenges in tracking highly maneuverable targets. Motivated by the aerial target pursuit task where a target may maneuver in 3D space, this paper studies how to further enhance observability by incorporating the \emph{bearing rate} information that has not been well explored in the literature. The main contribution of this paper is to propose a new cooperative estimator called STT-R (Spatial-Temporal Triangulation with bearing Rate), which is designed under the framework of distributed recursive least squares. This theoretical result is further verified by numerical simulation and real-world experiments. It is shown that the proposed STT-R algorithm can effectively generate more accurate estimations and effectively reduce the lag in velocity estimation, enabling tracking of more maneuverable targets.

A Cooperative Bearing-Rate Approach for Observability-Enhanced Target Motion Estimation

TL;DR

This work tackles the limited observability and velocity lag in vision-based target motion estimation for multi-camera aerial tracking. It introduces STT-R, a cooperative estimator that fuses bearing and bearing-rate measurements within a distributed recursive least-squares framework to enhance observability and reduce velocity lag. The approach provides pseudo-linear measurement models for bearing and bearing-rate, asserts necessary and sufficient observability conditions under cooperation, and validates the method through simulations and indoor real-world experiments, showing superior velocity tracking while maintaining competitive position accuracy. The results demonstrate that incorporating bearing-rate information with cooperative fusion enables more responsive tracking of highly maneuverable targets in 3D environments.

Abstract

Vision-based target motion estimation is a fundamental problem in many robotic tasks. The existing methods have the limitation of low observability and, hence, face challenges in tracking highly maneuverable targets. Motivated by the aerial target pursuit task where a target may maneuver in 3D space, this paper studies how to further enhance observability by incorporating the \emph{bearing rate} information that has not been well explored in the literature. The main contribution of this paper is to propose a new cooperative estimator called STT-R (Spatial-Temporal Triangulation with bearing Rate), which is designed under the framework of distributed recursive least squares. This theoretical result is further verified by numerical simulation and real-world experiments. It is shown that the proposed STT-R algorithm can effectively generate more accurate estimations and effectively reduce the lag in velocity estimation, enabling tracking of more maneuverable targets.

Paper Structure

This paper contains 17 sections, 2 theorems, 26 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Setup
  3. Problem Statement
  4. Bearing Measurement
  5. Bearing Rate Measurement
  6. System Architecture
  7. State and Measurement Equations
  8. State Equations
  9. Measurement Equations
  10. Cooperative Motion Estimator
  11. Objective Function
  12. STT-R Estimator
  13. Observability Analysis
  14. Simulation Verification
  15. Simulation Setup
  16. ...and 2 more sections

Key Result

Lemma 1

For any unit bearing vectors $\mathbf{g}_1, \mathbf{g}_2\in\mathbb{R}^3$, we have ${\rm rank}(\mathbf{P}_{\mathbf{g}_1}+\mathbf{P}_{\mathbf{g}_2})=3$ if and only if $\mathbf{g}_1$ is not parallel to $\mathbf{g}_2$.

Figures (4)

  • Figure 1: Two observers cooperatively estimate a target MAV state with target detection and optical flow detection.
  • Figure 2: System architecture of the proposed target estimation approach. The system includes three parts: detection, estimation, and communication.
  • Figure 3: The simulation results of CKF, CIKF, CMKF, STT, and STT-R in 8-shape motion and square-shape motion, respectively.
  • Figure 4: (a) is the target MAV (DJI Phantom 4). (b) are the two observation devices. Each observer device consists of a camera and an IMU sensor. (c) The target detection results (upper images) and the optical flow detection results (lower images). The color of each pixel in the optical flow detection results indicates the velocity of that pixel in the image frame. (d) shows the 3D Estimated trajectories in two scenarios. (e) shows the estimated positions and velocities in two scenarios, respectively.

Theorems & Definitions (3)

  • Lemma 1: zheng2023optimal
  • Theorem 1: Multi-observer observability condition
  • proof