Observability-Enhanced Target Motion Estimation via Bearing-Box: Theory and MAV Applications

TL;DR

This paper presents bearing-box, a monocular-vision–based motion estimator that leverages 3D bounding-box detections to jointly estimate target motion and size, removing the need for isotropic-shape assumptions and lateral observer maneuvers. It introduces a pseudo-linear Kalman-filter framework that uses normalized depth from 3D detections, along with an extension to MAV targets that exploits attitude–acceleration coupling to further relax observability requirements. Theoretical observability analyses demonstrate that the target state is recoverable under practical conditions, and comprehensive experiments on common objects and MAVs validate superior performance over traditional bearing-only and 2D-box methods in diverse scenarios. The approach shows strong potential for real-time deployment in autonomous navigation, pursuit, and dynamic SLAM contexts, especially where targets are maneuverable and sensing is limited to monocular vision. Overall, bearing-box advances robust, scalable target-motion estimation in monocular settings by exploiting 3D detection information and MAV-specific dynamics, with demonstrated applicability to both ground and aerial targets.

Abstract

Monocular vision-based target motion estimation is a fundamental challenge in numerous applications. This work introduces a novel bearing-box approach that fully leverages modern 3D detection measurements that are widely available nowadays but have not been well explored for motion estimation so far. Unlike existing methods that rely on restrictive assumptions such as isotropic target shape and lateral motion, our bearing-box estimator can estimate both the target's motion and its physical size without these assumptions by exploiting the information buried in a 3D bounding box. When applied to multi-rotor micro aerial vehicles (MAVs), the estimator yields an interesting advantage: it further removes the need for higher-order motion assumptions by exploiting the unique coupling between MAV's acceleration and thrust. This is particularly significant, as higher-order motion assumptions are widely believed to be necessary in state-of-the-art bearing-based estimators. We support our claims with rigorous observability analyses and extensive experimental validation, demonstrating the estimator's superior performance in real-world scenarios.

Figures (11)

• Figure 1: The experiment of existing pose estimation algorithms illustrates that monocular-based methods cannot deal with objects with similar appearances but different sizes. The Gen6D method liu2022gen6d is trained on the medium cube and thus works ineffectively on the other two cubes.
• Figure 2: The projection of the 3D box on the unit image plane. $\mathbf{R}_o^c$, $\mathbf{q}_o^c$ and $\mathbf{q}_i^c$ can be obtained from the 3D detection algorithms.
• Figure 3: The framework of the proposed bearing-box motion estimator for both common objects and MAVs. The rotation $\textbf{R}_o^c$, normalized dimensions $l_i$, projected vectors $\mathbf{q}_i^c$ could be obtained from 3D detection algorithms. The thrust direction $\textbf{h}$ is additionally measured for target MAVs.
• Figure 4: An illustration of the relationship between the attitude and thrust of a quadcopter MAV. The bottom shows the dynamic model.
• Figure 5: The symmetry problem met by pose estimation algorithms. It will not influence our visual measurements $\bar{\mathbf{T}}_{oc}^w$ and $\mathbf{h}$.

Theorems & Definitions (11)

• Lemma 1: (Normalized depth estimation)
• proof
• Theorem 1: Observability condition for MAVs based on second-order model
• proof
• Corollary 1: Observability condition for common objects based on first-order model
• Theorem 2: Observability condition for MAVs in continuous-time case
• proof
• Corollary 2: Observability condition for common objects in continuous-time case
• Theorem 3: Observability condition for MAVs in discrete-time case
• proof