Scholarlink

<p>Ship-formation tracking with sea-surface radar is constrained by the scarcity of measured formation data, the difficulty of modeling inter-ship interactions, and the limited adaptability of standard Kalman filtering (KF). To address these issues, this paper proposes a Transformer-KF adaptive tracking algorithm for ship formations. First, a physically constrained ship-formation trajectory generation model is developed by integrating formation geometry, Nomoto-type single-ship maneuvering response, inter-ship distance maintenance, and environmental disturbances. The motion scale and formation stability of the generated trajectories are validated using the statistical ranges of Automatic Identification System (AIS) trajectories and a sensitivity analysis of interaction parameters. Second, a hybrid architecture consisting of a front-end baseline KF, Transformer-based dynamic-parameter prediction, and a back-end KF is designed. The front-end KF extracts filtered state estimates, innovation statistics, and formation-geometry features from noisy radar measurements. The Transformer learns historical motion features and spatial coupling among ships, and predicts state-prior corrections, acceleration priors, and process-noise variance parameters. The back-end KF performs measurement fusion and uncertainty updating. Simulation results show that, compared with KF, Transformer-KF reduces the root mean square error (RMSE) of posterior position, one-step prior position, velocity, acceleration, and inter-ship distance by approximately 15.1%, 18.8%, 33.9%, 44.0%, and 16.3%, respectively. Under complex scenarios including random missed detections, continuous measurement loss, short-term radar outage, measurement loss during strong maneuvers, non-Gaussian heavy-tailed noise, clutter false alarms, and clutter–measurement-loss coupling, Transformer-KF achieves lower tracking errors than all baseline methods. Ablation experiments and complexity analysis indicate that the back-end KF measurement update, formation-geometry features, and attention modeling all contribute positively to error reduction and recursive stability. Within the tested ranges of the number of targets, history-window length, and encoder depth, the algorithm maintains millisecond-level single-frame inference time.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Transformer-aided adaptive Kalman filtering for ship-formation tracking under degraded sea-surface radar measurements

  • 期刊论文

  • 发表日期：

    2026年7月17日

查看全文
  • Bingtai Han,
  • Wei Xiang,
  • Yanjun Li

摘要

Ship-formation tracking with sea-surface radar is constrained by the scarcity of measured formation data, the difficulty of modeling inter-ship interactions, and the limited adaptability of standard Kalman filtering (KF). To address these issues, this paper proposes a Transformer-KF adaptive tracking algorithm for ship formations. First, a physically constrained ship-formation trajectory generation model is developed by integrating formation geometry, Nomoto-type single-ship maneuvering response, inter-ship distance maintenance, and environmental disturbances. The motion scale and formation stability of the generated trajectories are validated using the statistical ranges of Automatic Identification System (AIS) trajectories and a sensitivity analysis of interaction parameters. Second, a hybrid architecture consisting of a front-end baseline KF, Transformer-based dynamic-parameter prediction, and a back-end KF is designed. The front-end KF extracts filtered state estimates, innovation statistics, and formation-geometry features from noisy radar measurements. The Transformer learns historical motion features and spatial coupling among ships, and predicts state-prior corrections, acceleration priors, and process-noise variance parameters. The back-end KF performs measurement fusion and uncertainty updating. Simulation results show that, compared with KF, Transformer-KF reduces the root mean square error (RMSE) of posterior position, one-step prior position, velocity, acceleration, and inter-ship distance by approximately 15.1%, 18.8%, 33.9%, 44.0%, and 16.3%, respectively. Under complex scenarios including random missed detections, continuous measurement loss, short-term radar outage, measurement loss during strong maneuvers, non-Gaussian heavy-tailed noise, clutter false alarms, and clutter–measurement-loss coupling, Transformer-KF achieves lower tracking errors than all baseline methods. Ablation experiments and complexity analysis indicate that the back-end KF measurement update, formation-geometry features, and attention modeling all contribute positively to error reduction and recursive stability. Within the tested ranges of the number of targets, history-window length, and encoder depth, the algorithm maintains millisecond-level single-frame inference time.