针对机动目标难以精确跟踪的问题，提出了一种可在线学习的循环Kalman神经网络跟踪算法。考虑到状态转移矩阵、量测噪声和过程噪声矩阵在机动目标跟踪中难以实时、离线估计，且在实际应用中对应数据集获取成本高，因此使用在线学习的神经网络对其进行实时估计。由于Kalman滤波算法本身是一种循环结构，将简单的全连接层网络与其嵌合，全连接层网络实时输出状态转移矩阵、量测和过程噪声矩阵估计，构成一种广义的循环Kalman神经网络，根据网络最终输出的位置估计进行端到端的在线学习，并且通过理论推导证明了其在线学习的可行性。将提出的循环Kalman神经网络同3种经典机动目标算法进行了仿真对比，结果表明：循环Kalman神经网络跟踪需要很少的先验信息，在最优区域内较之其他3种算法具有最高的跟踪精度和鲁棒性，并且具有效率高、训练成本低以及可扩展性强的特点。
To overcome the problem of difficulty in accurate tracking of maneuvering targets, a recurrent Kalman neural network tracking algorithm that can be learned online is proposed. Considering that the state transition matrix, measurement noise and process noise matrix are difficult to estimate in real time and offline in maneuvering target tracking, and the cost for acquisition of corresponding data set is high in practical applications, the neural network of online learning is used to estimate them in real time. Since the Kalman filter algorithm itself is a cyclic structure, a simple fully connected layer network is integrated with it. The fully connected layer network outputs the state transition matrix, and measurement and process noise matrix estimation in real time, forming a generalized cyclic Kalman neural network. The end-to-end online learning is carried out according to the position estimation finally output by the network, and the feasibility of the online learning is proved through theoretical deduction. The simulation results show that the proposed recurrent Kalman neural network needs very little prior information, and has the highest tracking accuracy and robustness in the optimal region in comparison with three classical algorithms, demonstrating the characteristics of high efficiency, low training cost and strong scalability.
[1] 王林茜, 胡晓曦, 韩勋, 等. 单目标跟踪技术发展研究[J]. 空间电子技术, 2019, 16(1):1-10. WANG L Q, HU X X, HAN X, et al. Research on the development of single target tracking technology[J]. Space Electronic Technology, 2019, 16(1):1-10(in Chinese).
[2] 何友, 修建娟, 关欣, 等. 雷达数据处理及应用[M]. 3版.北京:电子工业出版社, 2013. HE Y, XIU J J, GUAN X, et al. Radar data processing with applications(Third Edition)[M]. 3rd ed.Beijing:Publishing House of Electronics Industry, 2013(in Chinese).
[3] BAR-SHALOM Y, BIRMIWAL K. Variable dimension filter for maneuvering target tracking[J]. IEEE Transactions on Aerospace and Electronic Systems, 1982, AES-18(5):621-629.
[4] RONG LI X, JILKOV V P. Survey of maneuvering target tracking. Part I. Dynamic models[J]. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39(4):1333-1364.
[5] SINGER R A. Estimating optimal tracking filter performance for manned maneuvering targets[J]. IEEE Transactions on Aerospace and Electronic Systems, 1970, 6(4):473-483.
[6] 周宏仁. 机动目标"当前"统计模型与自适应跟踪算法[J]. 航空学报, 1983, 4(1):73-86. ZHOU H R. A "current" statistical model and adaptive tracking algorithm for maneuvering targets[J]. Acta Aeronautica et Astronautica Sinica, 1983, 4(1):73-86(in Chinese).
[7] RONG LI X, JILKOV V P. Survey of maneuvering target tracking. Part V. Multiple-model methods[J]. IEEE Transactions on Aerospace & Electronic Systems, 2005, 41(4):1255-1321.
[8] 赵崇文. 人工神经网络综述[J]. 山西电子技术, 2020(3):94-96. ZHAO C W. A survey on artificial neural networks[J]. Shanxi Electronic Technology, 2020(3):94-96(in Chinese).
[9] VARGAS R, MOSAVI A, RUIZ R. Deep learning:A review[J/OL]. Advances in Intelligent Systems and Computing, (2020-12-5)[2021-1-2]. https://eprints.qut.edu.au/statistics/eprint/127354/.
[10] DENG L C, LI D, LI R F. Improved IMM algorithm based onRNNs[J]. Journal of Physics:Conference Series, 2020, 1518(1):012055.
[11] ZHANG X R, HE F H, ZHENG T Y. An LSTM-based trajectory estimation algorithm for non-cooperative maneuvering flight vehicles[C]//2019 Chinese Control Conference (CCC). Piscataway:IEEE Press, 2019:8821-8826.
[12] LIU J X, WANG Z L, XU M. DeepMTT:A deep learning maneuvering target-tracking algorithm based on bidirectional LSTM network[J]. Information Fusion, 2020, 53:289-304.
[13] LIU H J, XIA L W, WANG C L. Maneuvering target tracking using simultaneous optimization and feedback learning algorithm based on Elman neural network[J]. Sensors, 2019, 19(7):1596.
[14] ZAREMBA W, SUTSKEVER I, VINYALS O. Recurrent neural network regularization[DB/OL]. arXiv preprint:1409.2329, 2014.
[15] MILAN A, REZATOFIGHI S H, DICK A, et al. Online multi-target tracking using recurrent neural networks[DB/OL]. arXiv preprint:1604.03635, 2016.
[16] LIM B, ZOHREN S, ROBERTS S. Recurrent neural filters:learning independent Bayesian filtering steps for time series prediction[C]//2020 International Joint Conference on Neural Networks (IJCNN). Piscataway:IEEE Press, 2020:1-8.
[17] GUPTA A, JOHNSON J, LI F F, et al. Social GAN:Socially acceptable trajectories with generative adversarial networks[C]//2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition. Piscataway:IEEE Press, 2018:2255-2264.
[18] COSKUN H, ACHILLES F, DIPIETRO R, et al. Long short-term memory Kalman filters:Recurrent neural estimators for pose regularization[C]//2017 IEEE International Conference on Computer Vision. Piscataway:IEEE Press, 2017:5525-5533.
[19] WERBOS P J. Backpropagation through time:what it does and how to do it[J]. Proceedings of the IEEE, 1990, 78(10):1550-1560.
[20] PASCANU R, MIKOLOV T, BENGIO Y. On the difficulty of training Recurrent Neural Networks[DB/OL]. arXiv preprint:1211.5063, 2012.
[21] PASZKE A, GROSS S, MASSA F, et al. PyTorch:An imperative style, high-performance deep learning library[DB/OL]. arXiv preprint:1912.01703, 2019.
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