不完全量测下基于信息一致性的分布式容积卡尔曼滤波算法

doi:10.3969/j.issn.1000-1093.2021.11.013

摘要/Abstract

摘要： 针对不完全量测条件下分布式火控系统中的非线性目标跟踪问题，为提高跟踪系统的估计精度并保证各探测单元估计结果的一致性，提出一种基于信息一致性的分布式容积卡尔曼滤波(ICDCKF)算法。针对非线性系统，给出不完全量测下的改进容积卡尔曼滤波。考虑到各探测单元间局部估计信息的相关性，该算法首次将协方差交叉方法应用于非线性一致性滤波算法，提高互协方差未知情形下分布式融合的估计精度。特别地，为确保算法的可行性，给出不完全量测情形下，ICDCKF算法估计结果收敛的条件，并从理论上严格证明在该条件下ICDCKF算法可以保证估计方差的有界性。ICDCKF算法应用于一类光电跟踪网络，与现有CKFI算法、CKF_CI算法、KCF_ Me算法对比分析表明：ICDCKF算法在保证各探测单元估计结果一致性的同时，大幅度提高了跟踪系统的估计精度。

关键词: 分布式估计, 不完全量测, 信息一致性, 协方差交叉, 容积卡尔曼滤波

Abstract: For nonlinear target tracking of distributed fire control systems with intermittent observations，an information consensus-based distributed cubature Kalman filter (ICDCKF) algorithm is presented to improve the estimation accuracy of tracking system and ensure the consistency of estimated results of each sensor node. The modified cubature Kalman filter with intermittent observations is presented for nonlinear systems. Considering the correlation between local estimation information of sensor nodes，the covariance intersection method is firstly utilized in the nonlinear consensus filtering algorithm，and the estimation accuracy is improved under the condition of unknown cross-covariances. Specially，the condition for guaranteeing the convergence of estimated results of ICDCKF slgorithm with intermittent observations is derived for the feasibility. In this condition，the boundedness of the estimation covariance is proved strictly in theory. The proposed ICDCKF algorithm is applied to an electo-optical sensor network. The results show that the proposed ICDCKF algorithm can greatly improve the estimation accuracy of tracking system with the consensus estimation compared with CKFI, CKF_CI and KCF_Me algorithms.

Key words: distributedestimation, intermittentobservation, informationconsensus, covarianceintersection, cubatureKalmanfilter

中图分类号:

TP202⁺.4

王宁，李银伢，戚国庆，盛安冬. 不完全量测下基于信息一致性的分布式容积卡尔曼滤波算法[J]. 兵工学报, 2021, 42(11): 2396-2408.

WANG Ning， LI Yinya， QI Guoqing， SHENG Andong. Information Consensus-based Distributed Cubature Kalman Filtering Algorithm with Intermittent Observations[J]. Acta Armamentarii, 2021, 42(11): 2396-2408.

参考文献

［1］薄煜明，郭治，钱龙军，等. 现代火控理论与应用基础［M］. 北京: 科学出版社，2012.
BO Y M，GUO Z，QIAN L J，et al. The theory of modern fire control system and its application basis［M］. Beijing: Science Press，2012. (in Chinese)
［2］王中许，张学彪，盛安冬. 基于分布式节点的火控体系研究［J］.兵工学报，2005，26(5):638-641.
WANG Z X，ZHANG X B，SHENG A D. Research on fire-control system based on distributed nodes［J］.Acta Armamentarii，2005,26(5): 638-641. (in Chinese)
［3］陈晨，陈杰，张娟，等.网络化防空火控系统体系结构研究［J］.兵工学报，2009，30(9):1253-1258.
CHEN C，CHEN J，ZHANG J，et al.Research on architecture of networked air defense fire control system［J］. Acta Armamentarii，2009，30(9):1253-1258.(in Chinese)
［4］ SUN S L，LIN H L，MA J，et al.Multi-sensor distributed fusion estimation with applications in networked systems: a review paper ［J］. Information Fusion，2017， 38:122-134.
［5］ SINOPOLI B，SCHENATO L，FRANSCESCHETTI L M，et al.Kalman filtering with intermittent observations［J］. IEEE Transactions on Automatic Control， 2004，49(9):1453-1464.
［6］陈黎，王中许. 不完全量测下光电跟踪系统中冗余测角信息的攫取研究［J］.兵工学报，2011，32(7):819-826.
CHEN L，WANG Z X. Research on data mining of redundant angle information in optic-electric tracking system with intermittent observations［J］.Acta Armamentarii，2011，32(7):819-826. (in Chinese)
［7］ BATTISTELLI G，CHISCI L. Kullback-Leibler average， consensus on probability densities， and distributed state estimation with gua- ranteed stability［J］.Automatica， 2014，50(3): 707-718.
［8］ LI W Y，WEI G L，HAN F，et al. Weighted average consensus-based unscented Kalman filtering［J］.IEEE Transactions on Cybernetics，2017，46(2):558-567.
［9］ WEI G L，LI W Y，DING D R，et al. Stability analysis of covariance intersection-based Kalman consensus filtering for time-varying
systems［J］.IEEE Transactions on Systems， Man and Cybernetics: Systems， 2020， 50(11): 4611-4622.
［10］ LI W L，JIA Y M，DU J P. Distributed Kalman consensus filter with intermittent observations ［J］. Journal of the Franklin Institute， 2015， 352(9): 3764-3781.
［11］ XU H X，BAI X Z，LIU P，et al. Hierarchical fusion estimation for WSNs with link failures based on Kalman-consensus filtering and covariance intersection ［C］∥Proceedings of 39th Chinese Control Conference，. Shenyang， China: IEEE， 2020: 5150-5154.
［12］陈烨，盛安冬，戚国庆，等.不完全量测下事件触发卡尔曼一致滤波及在光电探测网中的应用［J］.兵工学报，2018，39(4): 625-634.
CHEN Y，SHENG A D，QI G Q，et al. Event-triggered Kalman consensus filter with intermittent measurements and its application to the electro-optical sensor network ［J］. Acta Armamentarii， 2018， 39(4):625-634. (in Chinese)
［13］ SHI J，QI G Q，LI Y Y，et al. Stochastic convergence analysis of cubature Kalman filter with intermittent observations［J］.Journal of Systems Engineering and Electronics，2018，29(4):823-833.
［14］王小旭，潘泉，黄鹤，等.非线性系统确定采样型滤波算法综述［J］.控制与决策.2012，27(6):801-812.
WANG X X，PAN Q，HUANG H，et al. Overview of deterministic sampling filtering algorithms for nonlinear system ［J］. Control and Decision，2012，27(6):801-812. (in Chinese)
［15］ DAN S. Optimal state estimation: Kalman，H∞， and nonlinear approaches［M］. Hoboken，NJ，US: John Wiley & Sons，Inc.，2006.
［16］ XIAO L，BOYD S，LALL S.A scheme for robust distributed sensor fusion based on average consensus［C］∥ Proceedings of the 4th International Symposium on Information Processing in Sensor Networks. Boise，ID，US: IEEE，2005: 63-70.
［17］丁自然，刘瑜，曲建跃，等. 基于节点通信度的信息加权一致性滤波［J］.系统工程与电子技术，2020，42(10): 2181-2188.
DING Z R，LIU Y，QU J Y，et al. Information weighted consensus filter algorithm based on node communication degree［J］.Systems Engineering and Electronics，2020，42(10): 2181-2188. (in Chinese)
［18］ RAN C J，DENG Z L. Robust fusion Kalman estimators for networked mixed uncertain systems with random one-step measurement delays，missing measurements， multiplicative noises and uncertain noise variances［J］. Information Sciences，2020，534: 27-52.
［19］ JULIER S J，UHLMAN J K. Handbook of multisensor data fusion［M］. Boca Raton，FL，US: CRC Press， 2009.
［20］ XIONG K，ZHANG H Y，CHAN C W. Performance evaluation of UKF-based nonlinear filtering［J］. Automatica，2006，42(2): 261-270.
［21］ KLUGE S，REIF K，BROKATE M. Stochastic stability of the extended Kalman filter with intermittent observations ［J］. IEEE Transactions on Automatic Control，2010， 55(2):514-518.
［22］ BOUTAYEB M，AUBRY D. A strong tracking extended Kalman observer for nonlinear discrete-time systems ［J］. IEEE Transactions on Automatic Control，1999，44(8): 1550-1556.
［23］穆静，蔡远利. 迭代容积卡尔曼滤波算法及其应用［J］. 系统工程与电子技术，2011，33(7):1454-1457.
MU J，CAI Y L. Iterated cubature Kalman filter and its application ［J］. Systems Engineering and Electronics， 2011，33(7):1454-1457. (in Chinese)
［24］王帅，杨文，侍洪波. 带丢包一致性滤波算法研究［J］. 自动化学报，2010，36(12): 1689-1696.
WANG S，YANG W，SHI H B. Consensus-based filtering algorithm with packet-dropping［J］. Acta Automatica Sinica，2010，36(12): 1689-1696. (in Chinese)
［25］巫春玲，韩崇昭. 基于平方根求积卡尔曼滤波器的弹道目标跟踪［J］. 控制与决策，2010，25(5):721-724.
WU C L，HAN C Z. Tracking ballistic target based on square root quadrature Kalman filter［J］.Control and Decision，2010，25(5): 721-724. (in Chinese)

第42卷第11期2021 年11月
兵工学报ACTA ARMAMENTARII
Vol.42No.11Nov. 2021

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