用强化学习优化无源跟踪中的观测器机动，平衡精度与稳定性。
Reinforcement Learning Trained Observer Control for Bearings-Only Tracking
- 将跟踪问题建模为信念马尔可夫决策过程，用立方卡尔曼滤波表示状态
- 在5000次蒙特卡洛测试中，β=0.7时误差降低近十倍，精度媲美信息理论基线
- 适合需要高鲁棒性无源跟踪的无人系统，如无人机或潜艇自主追踪
本文提出一种基于深度强化学习的观测器控制策略，用于自主无源目标跟踪。将观测器机动问题建模为信念马尔可夫决策过程，信念状态由立方卡尔曼滤波（CKF）后验分布表示。设计奖励函数以兼顾两个冲突目标：最小化目标位置估计误差（欧氏距离）和保持CKF估计一致性（马氏距离）。奖励函数在帕累托前沿上通过加权因子$β∈[0,1]$进行几何插值。策略采用深度Q网络（DQN）训练，共50,000个训练周期。在5,000次蒙特卡洛实验中评估性能，并与两种基线对比：垂直于方位角启发式方法和D-最优费舍尔信息最大化准则。结果表明，当$β=0.7$时，DQN策略在准确性和鲁棒性间取得最佳平衡：平均跟踪精度达到信息理论基线水平，最差情况误差降低近十倍，归因于奖励函数中马氏项对滤波一致性的隐式正则化。
原文摘要 · Abstract (English)
This paper develops a deep reinforcement learning based observer control policy for autonomous bearings-only tracking of a moving target. The observer manoeuvre problem is formulated as a belief Markov decision process, where the belief state is represented by the posterior of a cubature Kalman filter (CKF). The reward function is designed to address two conflicting objectives: minimising the absolute target position estimation error (Euclidean distance) and maintaining CKF estimation consistency (Mahalanobis distance). The reward is formulated as a geometric interpolation between the two objectives on the Pareto front, parametrised by a weighting factor $β\in [0,1]$. The policy is implemented as a deep Q-network (DQN) trained over 50,000 episodes. Performance is evaluated over 5,000 Monte Carlo episodes and compared against two baselines: the perpendicular-to-bearing heuristic and the D-optimal Fisher information maximisation criterion. The results show that the DQN policy at $β= 0.7$ achieves the best trade-off between accuracy and robustness: it matches the information-theoretic baseline on mean tracking accuracy while reducing the worst-case error by nearly a factor of ten, owing to the implicit filter-consistency regularisation provided by the Mahalanobis term in the reward.
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