Bearing-Only Tracking and Circumnavigation of a Fast Time-Varied Velocity Target Utilising an LSTM

TL;DR

The paper addresses bearing-only tracking and circumnavigation of targets whose velocity varies over time by introducing an LSTM-based estimator that predicts the relative target pose $d$ and velocity from bearing data, coupled with a circumnavigation controller that maintains a fixed radius $d^{*}$. The estimation and control pipeline trains the LSTM via an on-policy, iterative procedure to prevent destabilizing feedback, using windows of past observations to forecast $\hat{d}$ and $\hat{v}_T$ at each step. Empirical results across constant-velocity, circular, and nonholonomic target trajectories show substantially lower control and estimation errors compared to prior methods, with demonstrated robustness to input noise and the ability to track fast-moving targets. The work advances bearing-only tracking by leveraging sequence learning to model time-varying dynamics and provides a practical, fixed-radius circumnavigation strategy suitable for real-world mobile agents, with potential extensions to multi-agent and non-circumnavigation scenarios.

Abstract

Bearing-only tracking, localisation, and circumnavigation is a problem in which a single or a group of agents attempts to track a target while circumnavigating it at a fixed distance using only bearing measurements. While previous studies have addressed scenarios involving stationary targets or those moving with an unknown constant velocity, the challenge of accurately tracking a target moving with a time-varying velocity remains open. This paper presents an approach utilising a Long Short-Term Memory (LSTM) based estimator for predicting the target's position and velocity. We also introduce a corresponding control strategy. When evaluated against previously proposed estimation and circumnavigation approaches, our approach demonstrates significantly lower control and estimation errors across various time-varying velocity scenarios. Additionally, we illustrate the effectiveness of the proposed method in tracking targets with a double integrator nonholonomic system dynamics that mimic real-world systems.

Figures (12)

• Figure 1: Geometric representation of an agent circumnavigating a moving target.
• Figure 2: Target estimation model architecture. Here, $c$ denotes the cell state, which maintains long-term memory, while $h$ represents the hidden state, passed between each step in the LSTM layer.
• Figure 3: Result of the constant velocity simulation where $v = 9$ m/s. The agent markers indicate the final position of each respective system.
• Figure 4: Comparison of each agent's control and estimation error across fifteen simulations each using a constant velocity for $1000$ timesteps. For each trial, only the values from the last $5$ seconds were averaged, allowing the initial $15$ seconds for each system to settle.
• Figure 5: Result of the circle tracjetory simulation where $\omega = 0.4$ rad/s . The agent markers indicate the final position of each respective system.