Distributed Triangulation Filter for Target Motion Estimation via Bearing-Only Measurements

This paper introduces the novel consensus-based distributed spatial-temporal coordinated triangulation filter (CD-STCTF), a unified framework designed to overcome the fundamental challenge of achieving reliable and high-precision motion estimation of non-cooperative targets using bearing-only measurements in multi-agent systems. First, our approach centers on the spatial-temporal coordinated triangulation (STCT) model, which optimally integrates historical and spatial bearing information to transform the nonlinear problem into a robust, pseudo-linear state estimation problem. Second, this powerful geometric linearization is embedded within a consensus-on-information-matrix distributed architecture, ensuring robust operation and network consistency across multi-agent systems with sparse communication topologies. Third, a key technical feature is the incorporation of a dynamic measurement noise covariance matrix, which correctly models the distance-dependent uncertainty in angular measurements. Furthermore, we prove the global bounded stability of the CD-STCTF dynamic error. Simulation and real-world experimental results against existing distributed algorithms and the centralized Kalman filter (CKF) benchmark demonstrate that the CD-STCTF achieves superior estimation accuracy, faster convergence rates, and enhanced robustness and is comparable to the CKF, establishing its efficacy for high-performance cooperative bearing-only target motion estimation. Note to Practitioners - This paper addresses the challenge of estimating the motion of uncooperative targets (e.g., unauthorized drones or malicious vehicles) using only visual bearing measurements from a network of autonomous agents like drones or mobile robots. In practice, relying solely on the direction to a target is cost-effective and suitable for small platforms but introduces severe nonlinearities that cripple traditional filtering methods. Our proposed CD-STCTF framework is designed for real-world deployment, enabling a team of agents to accurately track a target's position and velocity by intelligently fusing their historical and current bearing observations with those of their neighbors through a local communication network. A key practical feature is its distributed nature without requiring a powerful central computer. The algorithm dynamically adapts to the relative distance between agents and the target, which is critical as bearing measurement noise inherently increases with distance. This work can be directly applied to surveillance, counter-UAV systems, and collaborative search missions in GPS-denied environments such as indoors or in dense urban areas, where our method provides a scalable and effective solution using passive, vision-based sensors.