测量数据延迟下的不完全量测滤波研究
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摘要
随着科技的发展,目标跟踪系统越来越多地采用多传感器网络来对目标进行探测和跟踪。对于网络,尤其是无线网络,广泛地存在数据延迟和丢包现象,反映到滤波系统中就表现为测量数据的延迟和丢失,造成探测概率小于1,也就是不完全量测的情况。此时,滤波系统要进行相应的变化,使其能够尽可能准确地对目标状态进行滤波而不至于发散。以往的不完全量测滤波的研究往往着重讨论测量数据发生丢失的情况,而没有对测量数据发生延迟的情况加以足够的重视,而这正是本论文的研究重点,即测量数据延迟下的不完全量测滤波研究。
首先,建立一种考虑了测量数据发生延迟和随机性丢失的数学模型。针对探测概率是否已知,测量通道为单通道还是多通道,先分别对测量数据的随机性丢失和延迟的不同情况进行建模,然后得到同时考虑了测量数据延迟和丢失的数学模型,为随后的滤波理论和方法研究奠定了基础。
紧接着,研究了测量数据发生随机性丢失下的滤波理论和方法。利用已建立的模型和Kalman滤波原理,针对探测概率是否已知两种情况给出不同的滤波方法,并分别对其进行了仿真实验和分析,说明了各自的优缺点和适用环境。
之后,研究了测量数据发生延迟下的滤波理论和方法。在单测量通道的测量数据发生延迟时,利用新息修正方法处理延迟的测量数据。此方法存在滤波增益在延迟时段内不匹配的问题,本文克服了该问题并得到了改进后的新息修正方法。在多测量通道其中一个通道的测量数据发生固定延迟时,利用重排新息方法处理延迟的测量数据,提高滤波性能。随后的仿真实验和分析也给出了这些方法各自的滤波性能和优缺点。
最后,结合以上的研究成果讨论了测量数据延迟下的不完全量测滤波理论和方法。在多测量通道下,针对测量数据同时发生延迟和随机性丢失的情况,推导了相应的滤波方程,并用仿真实验和分析说明了其滤波性能和优缺点。
Nowadays, more and more target tracking systems begin to adopt multi-sensor network to detect and track the targets. In the network, especially the wireless one, delay or dropouts of the data packets exist widely, which in turn make the whole filtering system face the challenge of partial observations. Under this circumstance, the filter should be modified to guarantee the convergence of the system and inhibit the disturbance of measurements uncertainty. Previous researches mainly discuss one typical phenomenon of the measurement uncertainty-missing measurements and its influence on the filtering system. However, this paper concerns another typical phenomenon of the measurement uncertainty-delayed measurements and differentiates it with the missing ones. Also, the modification of the filter to adapt the delayed measurements is proposed.
First, this paper has constructed different mathematic models for missing and delayed measurements in the filtering system under different conditions of measurements uncertainty, such as different number of measurement channels, whether knowing the detection probability or not. This is the precondition for designing the suitable filters.
Then, the paper discusses the filtering theory and method when there exist randomly distributed missing measurements. Two different filtering methods are proposed based on whether konwing the detection probability or not. The numerical examples in the end of this part test those methods.
Next, the filtering theory and method considering the existence of measurement delay are discussed. Those methods are different due to the fact that the target tracking system has single measurement channel or multiple ones. In the case of single measurement channel, the innovation fix method is proposed to utilize the delayed measurements, while the innovation re-organization method is applied when the system owns multiple measurement channels. Numerical examples and the relating analysis also follow.
Finally, considering both the missing and delayed measurements, the paper combines the filtering theories and methods discussed above and solves the filter design problems. The filtering equations are deduced under the system with multiple measurement channels. In the end, the numerical experiments have proved the effectiveness of the method.
首先,建立一种考虑了测量数据发生延迟和随机性丢失的数学模型。针对探测概率是否已知,测量通道为单通道还是多通道,先分别对测量数据的随机性丢失和延迟的不同情况进行建模,然后得到同时考虑了测量数据延迟和丢失的数学模型,为随后的滤波理论和方法研究奠定了基础。
紧接着,研究了测量数据发生随机性丢失下的滤波理论和方法。利用已建立的模型和Kalman滤波原理,针对探测概率是否已知两种情况给出不同的滤波方法,并分别对其进行了仿真实验和分析,说明了各自的优缺点和适用环境。
之后,研究了测量数据发生延迟下的滤波理论和方法。在单测量通道的测量数据发生延迟时,利用新息修正方法处理延迟的测量数据。此方法存在滤波增益在延迟时段内不匹配的问题,本文克服了该问题并得到了改进后的新息修正方法。在多测量通道其中一个通道的测量数据发生固定延迟时,利用重排新息方法处理延迟的测量数据,提高滤波性能。随后的仿真实验和分析也给出了这些方法各自的滤波性能和优缺点。
最后,结合以上的研究成果讨论了测量数据延迟下的不完全量测滤波理论和方法。在多测量通道下,针对测量数据同时发生延迟和随机性丢失的情况,推导了相应的滤波方程,并用仿真实验和分析说明了其滤波性能和优缺点。
Nowadays, more and more target tracking systems begin to adopt multi-sensor network to detect and track the targets. In the network, especially the wireless one, delay or dropouts of the data packets exist widely, which in turn make the whole filtering system face the challenge of partial observations. Under this circumstance, the filter should be modified to guarantee the convergence of the system and inhibit the disturbance of measurements uncertainty. Previous researches mainly discuss one typical phenomenon of the measurement uncertainty-missing measurements and its influence on the filtering system. However, this paper concerns another typical phenomenon of the measurement uncertainty-delayed measurements and differentiates it with the missing ones. Also, the modification of the filter to adapt the delayed measurements is proposed.
First, this paper has constructed different mathematic models for missing and delayed measurements in the filtering system under different conditions of measurements uncertainty, such as different number of measurement channels, whether knowing the detection probability or not. This is the precondition for designing the suitable filters.
Then, the paper discusses the filtering theory and method when there exist randomly distributed missing measurements. Two different filtering methods are proposed based on whether konwing the detection probability or not. The numerical examples in the end of this part test those methods.
Next, the filtering theory and method considering the existence of measurement delay are discussed. Those methods are different due to the fact that the target tracking system has single measurement channel or multiple ones. In the case of single measurement channel, the innovation fix method is proposed to utilize the delayed measurements, while the innovation re-organization method is applied when the system owns multiple measurement channels. Numerical examples and the relating analysis also follow.
Finally, considering both the missing and delayed measurements, the paper combines the filtering theories and methods discussed above and solves the filter design problems. The filtering equations are deduced under the system with multiple measurement channels. In the end, the numerical experiments have proved the effectiveness of the method.
引文
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[13]S. F. Chen, I. K. Fong. Robust Filtering for 2-D State-Delayed Systems With NFT Uncertainties [J]. IEEE Transactions on Signal Processing,2006,54(1):274-285
[14]T. C. Aysal, K. E. Barner. Meridian Filtering for Robust Signal Processing [J]. IEEE Transactions on Signal Processing,2007,55(8):3949-3962
[15]H. Xiao, Z. D. Wang, D. H. Zhou. LMI-Based Robust Filtering:A Survey [C]. Chinese Control Conference,2008,1:165-169
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[30]H. L. Dong, Z. D. Wang. H∞ Filering for Systems With Repeated Scalar Nonlinearities Under Unreliable Communication Links [J]. Signal Processing,2009,89(2):1567-1575
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[36]A. Farina, L. Timmoneri, S. Immediata, B. Ristic. CRLB with Pd< 1 fused tracks [C]. International Conference on Information Fusion,2005,1:191-196
[37]Y. Zhou, J. X. Li, D. L. Wang. Cramer-Rao Lower Bounds for Target Tracking in Sensor Networks With Quantized Rang-Only Measurements [J]. IEEE Signal Processing Letters,2010,17(2):157-160
[38]M. Lei, J. Barend, Y. Qi. Online Estimation of the Approximate Posterior Cramer-Rao Lower Bound for Discrete-Time Nolinear Filtering [J]. IEEE Transactions on Aerospace and Electronics Systems,2011,47(1):37-57
[39]M. Lei, C. Baehr, P. D. Moral. Fisher Information Matrix-Based Nonlinear System Conversion for State Estimation [C].8th IEEE Internationl Conference on Control and Automation,2010,1:837-841
[40]Z. G. Xu, A. D. Sheng, Y. Y. Li. Cramer-Rao Lower Bounds for Bearing-Only Maneuvering Target Tracking With Incomplete Measurements [C]. Control and Decision Conference,2009,1:2201-2206
[41]H. L. Li, X. L. Li, M. Anderson. A Class of Adaptive Algorithms Based on Entropy Estimation Achieving CRLB for Linear Non-Guassian Filtering [J]. IEEE Transactions on Signal Processing,2011,99:1-6
[42]B. Sinopoli, L. Schena. Kalman Filtering With Intermittent Observations [J]. IEEE Transactions on Automatic Control,2004,49(9):1753-1764
[43]高玺璟.多通道不完全量下的估计算法研究[D].南京理工大学硕士论文,2010
[44]S. H. Liu, A. Goldsmth. Kalman Filtering With Partial Observation Losses [C]. IEEE Conference on Decision and Control,2004,4:4180-4186
[45]B. Sinopoli, Y. Mo. Characterization of The Critical Value for Kalman Filtering With Intermittent Observations [C]. IEEE Conference on Decision and Control,2008,1: 2692-2697
[46]Y. Boers, H. Driessen. Modified Riccati Equation and Its Applications to Target Tracking [C]. IEEE Proceedings on Radar, Sonar and Navigation,2006,153(1):7-12
[47]X.Lu, H. S. Zhang. Kalman Filtering for Multiple Time-Delay Systems [J]. Automatica, 2005,41:1455-1461
[48]G. L. Wei, H. S. Shu. H∞ Filering on Nonlinear Stochastic System With Delay [J]. Choas, Solitons and Fractals,2007,33:663-670
[49]G. L. Wei, Z. D. Wang. Robust Filtering for Stochastic Genetic Regulatory Networks With Time-Varying Delay [J]. Mathematical Bioscience,2009,200:73-80
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[2]许志刚,陈黎,穆育强,盛安冬.不完全测量下Cramer-Rao下界与数据丢失位置的关系[J].自动化学报,2009,35(8)：1080-1086
[3]陈黎,许志刚,盛安冬.不完全测量下光电跟踪系统估计误差分析[J].南京理工大学学报,2009,33(5)：672-676
[4]陈黎,许志刚,盛安冬.不完全测量下一类非线性光电跟踪系统滤波器设计[J].航空学报,2009,30(9)：1745-1753
[5]许志刚,盛安冬,郭治.基于不完全测量下离散线性滤波的修正Riccati方程[J].控制理论与应用,2009,26(6)：673-677
[6]周凤岐,卢晓东.最优估计理论[M].北京：高等教育出版社,2009
[7]R. E. Kalman. A New Approach to Linear Filtering [J]. Journal of Basic Engineering, 1960,81(2):35-45
[8]付梦印,邓志红,闫莉萍. Kalman滤波理论及其在导航系统中的应用[M].北京：科学出版社,2010
[9]J. Joseph, J. Laviola. A Comparition of Unscented and Extended Kalman Filtering for Estimating Quaternion Motion [C]. American Control Conference,2003,3(13): 2435-2440
[10]B. Alacam, B. Yazici, X. Intes. Extended Kalman Filtering for the Modeling and Analysis of ICG Pharmacokinetics in CancerousTumors Using NIR Optical Methods [J]. IEEE Transactions on Biomedical Engineering,2006,53(10):1861-1871
[11]D. J. Jwo, S. H. Wang. Adaptive Fuzzy Strong Tracking Extended Kalman Filtering for GPS Navigation [J]. IEEE Sensors Journal,2007,7(5):778-789
[12]H. D. Tuan, P. Apkarian, T. Q. Nguyen. Robust Mixed H2/H∞ Filtering of 2-D Systems [J]. IEEE Transactions on Signal Processing,2002,50(7):1759-1771
[13]S. F. Chen, I. K. Fong. Robust Filtering for 2-D State-Delayed Systems With NFT Uncertainties [J]. IEEE Transactions on Signal Processing,2006,54(1):274-285
[14]T. C. Aysal, K. E. Barner. Meridian Filtering for Robust Signal Processing [J]. IEEE Transactions on Signal Processing,2007,55(8):3949-3962
[15]H. Xiao, Z. D. Wang, D. H. Zhou. LMI-Based Robust Filtering:A Survey [C]. Chinese Control Conference,2008,1:165-169
[16]N. E. Nahi. Opimal Recursive Estimation With Uncertain Observation [J]. IEEE Transactions on Information Theory,1969,15(4):457-462
[17]M. T. Hadidi, S.C. Aidala. Linear Recursive State Estimators Under Uncertain Observations [J]. IEEE Transactions on Automatic Control,1979,24(6):944-948
[18]W. NaNacara, E. Yaz. Rercursive Estimator for Linear and Nonlinear System With Uncertain Observations [J]. Signal Process,1997,62(2):215-288
[19]M. Mariton. Jump Linear System [M]. New York:Marcel Dekker,1990
[20]S. Smith, P. Seiler. Estimation with Lossy Measurements:Jump Estimators for Jump System [J]. IEEE Transactions on Automatic Control,2003,48(12):2163-2171
[21]J. Nilsson, B. Bernhardsson. Stochastic Analysis and Control of Real-Time Systems With Random Delays [J]. Automatica,1998,34(1):57-64
[22]M. Micheli, M. Jordan. Random Sampling of A Continous-Time Stochastic Dynamical System [C]. International Symposium on Mathematical Theory of Networks and Systems,2002
[23]G L. Wei, Z. D. Wang, H. S. Shu. Robust Filtering with Stochastic Nonlinearities and Multiple Missing Mearements [J]. Automatica,2009,45(2):836-841
[24]T. Fortmann, Y. Bar-Shalom, M. Scheffe. Detection Thresholds for Tracking in Clutter-A Connection Between Estimation and Signal Process [J]. IEEE Transactions on on Automatic Control,1985,30(3):221-228
[25]O. Costa, S. Guerra. Stationary Filter for Linear Minimum Mean Square Error Estimator of Discrete-Time Markovian Jump Systems [J]. IEEE Transactions on on Automatic Control,2002,47(8):1351-1356
[26]Z. D. Wang, F. W. Yang. Robust Finite-Horizon Filtering for Stochastic Systems With Missing Measurement [J]. IEEE Transactions on Signal Processing,2005,12(6): 437-440
[27]Z. D. Wang, W. Daniel. Variance-Constrained Filtering for Uncertain Stochastic Systems With Missing Measurements [J]. IEEE Transactions on Automatic Control, 2003,48(7):1254-1258
[28]Z. D. Wang, W. Daniel. Variance-Constrained Control for Uncertain Stochastic Systems With Missing Measurements [J]. IEEE Transactions on Systems,2005,35(5):746-753
[29]Z. D. Wang, F. W. Yang. Robust H∞ Filering for Stochastic Time-Delay Systems With Missing Measurements [J]. IEEE Transactions on Signal Processing,2006,54(7): 2579-2587
[30]H. L. Dong, Z. D. Wang. H∞ Filering for Systems With Repeated Scalar Nonlinearities Under Unreliable Communication Links [J]. Signal Processing,2009,89(2):1567-1575
[31]H. L. Dong, Z. D. Wang. H∞ Fuzzy Control for Systems With Repeated Scalar Nonlinearities and Random Packets Losses [J]. IEEE Transactions on Fuzzy Systems, 2009,17(2):440-450
[32]Z. Bobrovsk, M. Zakai. A Lower Bound on The Estimation Error for Markov Processes [J]. IEEE Transactions on Automatic Control,1975,20(6):785-788
[33]P. Tichavsky, H. Muravchik, A. Nehorai. Posterior Cramer-Rao Bounds for Discrete-Time Nonlinear Filtering [J]. IEEE Transactions on Signal Processing,1998, 46(5):1374-1377
[34]A. Farina, B. Ristic, L. Timmon. Cramer-Rao Bound for Nonlinear Filtering With Pd< 1 and Its Application to Target Tracking [J]. IEEE Transactions on Signal Processing,2002,50(8):1916-1924
[35]M. Hernadez, B. Ristic, A. Farina. A Comparison of Two Cramer-Rao Bounds for Nonlinear Filtering With Pd<1 [J]. IEEE Transactions on Signal Processing,2004, 52(9):2361-2370
[36]A. Farina, L. Timmoneri, S. Immediata, B. Ristic. CRLB with Pd< 1 fused tracks [C]. International Conference on Information Fusion,2005,1:191-196
[37]Y. Zhou, J. X. Li, D. L. Wang. Cramer-Rao Lower Bounds for Target Tracking in Sensor Networks With Quantized Rang-Only Measurements [J]. IEEE Signal Processing Letters,2010,17(2):157-160
[38]M. Lei, J. Barend, Y. Qi. Online Estimation of the Approximate Posterior Cramer-Rao Lower Bound for Discrete-Time Nolinear Filtering [J]. IEEE Transactions on Aerospace and Electronics Systems,2011,47(1):37-57
[39]M. Lei, C. Baehr, P. D. Moral. Fisher Information Matrix-Based Nonlinear System Conversion for State Estimation [C].8th IEEE Internationl Conference on Control and Automation,2010,1:837-841
[40]Z. G. Xu, A. D. Sheng, Y. Y. Li. Cramer-Rao Lower Bounds for Bearing-Only Maneuvering Target Tracking With Incomplete Measurements [C]. Control and Decision Conference,2009,1:2201-2206
[41]H. L. Li, X. L. Li, M. Anderson. A Class of Adaptive Algorithms Based on Entropy Estimation Achieving CRLB for Linear Non-Guassian Filtering [J]. IEEE Transactions on Signal Processing,2011,99:1-6
[42]B. Sinopoli, L. Schena. Kalman Filtering With Intermittent Observations [J]. IEEE Transactions on Automatic Control,2004,49(9):1753-1764
[43]高玺璟.多通道不完全量下的估计算法研究[D].南京理工大学硕士论文,2010
[44]S. H. Liu, A. Goldsmth. Kalman Filtering With Partial Observation Losses [C]. IEEE Conference on Decision and Control,2004,4:4180-4186
[45]B. Sinopoli, Y. Mo. Characterization of The Critical Value for Kalman Filtering With Intermittent Observations [C]. IEEE Conference on Decision and Control,2008,1: 2692-2697
[46]Y. Boers, H. Driessen. Modified Riccati Equation and Its Applications to Target Tracking [C]. IEEE Proceedings on Radar, Sonar and Navigation,2006,153(1):7-12
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