基于最小二乘类的空间配准算法研究
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摘要
时空配准包括时间配准和空间配准两个方面,是传感器组网系统进行信息融合前的重要环节,对组网系统的探测性能有着至关重要的影响。目前大多数学者的研究都偏向于空间配准,这是因为空间配准所涉及的范围更为广泛,更为复杂,而且急待需要解决的工程问题更多。本文将立足于空间配准,对现有部分较为成熟算法的进行分析,提出自己的改进意见和算法,论文的主要研究工作和取得的成果如下:
(1)结合实际应用背景,将已有的一些空间配准算法移植到单平台级纯方位传感器组网系统,并利用最小二乘、总体最小二乘的理论基础,深入分析了随机误差和系统误差对系统误差估计模型的影响,得到了量测方程的系数矩阵中存在误差且误差存在统计相关性的结论。再根据这一结论,提出了结构总体最小二乘空间配准算法,仿真表明该算法能有效的提高系统误差估计的精度。
(2)将最小二乘类算法推广到多平台多传感器组网系统。通过引入地心地固坐标变换,解决了地球曲率所造成的误差影响,并以工程上常用广义最小二乘算法为背景建立配准模型。但分析发现所建立的配准模型并不精准,为此论文对广义最小二乘空间配准算法所建立的配准模型进行了改进。由于改进后的模型不能再利用广义最小二乘算法进行求解,本文结合最小二乘类算法理论,在改进的系统误差估计模型的基础上,提出了约束总体最小二乘空间配准算法。
(3)在配准模型不完全可观测的情况下,现有研究成果都无法完整地指出系统可观测度和系统误差估计精度之间的定量关系。虽然如此,却能通过其它间接方式改善系统可观测度,提高系统误差估计精度。论文利用系数矩阵条件数的倒数作为可测度指标,对原始量测数据进行筛选,从而优化滑窗内的数据,达到改善结构总体最小二乘空间配准性能的目的。
最后,对全文进行了总结和展望。
Time-space registration includes time registration and space registration. It is an important part of information fusion in the sensor network system and plays a important role in the system’s detection performance. Most scholars’researches tend to space registration with its complexity and universality. This paper based on space registration analyses some existing algorithms which is relatively mature and proposes own improved views and algorithms. Then, show the paper’s main researches and achievements:
(1) Combined with practical applications, this paper transplants some existing space registration into the single-platform sensor network system. By the basic theories of least squares, total least squares, it analyses the influent of the random error and system error in systematic error estimation model. Then the conclusion that there are statistical correlation errors in the coefficient matrix of measurement equation is given. According to this conclusion, the structured total least squares space registration algorithm is proposed. The simulation shows that the algorithm can effectively improve the accuracy of system error estimation.
(2) Least squares type algorithm will be extended to multi-platform and multi-sensor network system. By bringing in the Earth-centered Earth-fixed coordinate transformation, the error caused by earth curvature can be removed. And the registration model is created in accordance with generalized least square which is commonly used in engineering. But we find that the established registration model is not accurate, so this paper amends this model. After this operation, we find the improved model isn’t fit for generalized least squares. With using the basic theory of least squares type algorithm, this paper proposes the constrained total squares space registration algorithm based on the improved model.
(3) If the registration model is not fully observed, the existing research results can’t perfectly describe the quantitative relationship between observability and systematic error estimation accuracy. Even so, the system’s observability can be improved by other indirect means. Meanwhile, it also raises the systematic error estimation precision. This paper uses the inverse of the coefficient matrix condition number as the observability index. Then filter the original measurement data can be filtered through the observability index to optimize the data in the sliding window. If you do so, the performance of the structured total least squares space registration can be improved.
Finally, the whole dissertation is summarized and outlooked.
(1)结合实际应用背景,将已有的一些空间配准算法移植到单平台级纯方位传感器组网系统,并利用最小二乘、总体最小二乘的理论基础,深入分析了随机误差和系统误差对系统误差估计模型的影响,得到了量测方程的系数矩阵中存在误差且误差存在统计相关性的结论。再根据这一结论,提出了结构总体最小二乘空间配准算法,仿真表明该算法能有效的提高系统误差估计的精度。
(2)将最小二乘类算法推广到多平台多传感器组网系统。通过引入地心地固坐标变换,解决了地球曲率所造成的误差影响,并以工程上常用广义最小二乘算法为背景建立配准模型。但分析发现所建立的配准模型并不精准,为此论文对广义最小二乘空间配准算法所建立的配准模型进行了改进。由于改进后的模型不能再利用广义最小二乘算法进行求解,本文结合最小二乘类算法理论,在改进的系统误差估计模型的基础上,提出了约束总体最小二乘空间配准算法。
(3)在配准模型不完全可观测的情况下,现有研究成果都无法完整地指出系统可观测度和系统误差估计精度之间的定量关系。虽然如此,却能通过其它间接方式改善系统可观测度,提高系统误差估计精度。论文利用系数矩阵条件数的倒数作为可测度指标,对原始量测数据进行筛选,从而优化滑窗内的数据,达到改善结构总体最小二乘空间配准性能的目的。
最后,对全文进行了总结和展望。
Time-space registration includes time registration and space registration. It is an important part of information fusion in the sensor network system and plays a important role in the system’s detection performance. Most scholars’researches tend to space registration with its complexity and universality. This paper based on space registration analyses some existing algorithms which is relatively mature and proposes own improved views and algorithms. Then, show the paper’s main researches and achievements:
(1) Combined with practical applications, this paper transplants some existing space registration into the single-platform sensor network system. By the basic theories of least squares, total least squares, it analyses the influent of the random error and system error in systematic error estimation model. Then the conclusion that there are statistical correlation errors in the coefficient matrix of measurement equation is given. According to this conclusion, the structured total least squares space registration algorithm is proposed. The simulation shows that the algorithm can effectively improve the accuracy of system error estimation.
(2) Least squares type algorithm will be extended to multi-platform and multi-sensor network system. By bringing in the Earth-centered Earth-fixed coordinate transformation, the error caused by earth curvature can be removed. And the registration model is created in accordance with generalized least square which is commonly used in engineering. But we find that the established registration model is not accurate, so this paper amends this model. After this operation, we find the improved model isn’t fit for generalized least squares. With using the basic theory of least squares type algorithm, this paper proposes the constrained total squares space registration algorithm based on the improved model.
(3) If the registration model is not fully observed, the existing research results can’t perfectly describe the quantitative relationship between observability and systematic error estimation accuracy. Even so, the system’s observability can be improved by other indirect means. Meanwhile, it also raises the systematic error estimation precision. This paper uses the inverse of the coefficient matrix condition number as the observability index. Then filter the original measurement data can be filtered through the observability index to optimize the data in the sliding window. If you do so, the performance of the structured total least squares space registration can be improved.
Finally, the whole dissertation is summarized and outlooked.
引文
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[3]王德纯,丁家会,程望东等.精密跟踪测量雷达技术[M].北京:电子工业出版社, 2006: 89-131.
[4] W. D. Blair, T. R. Rice. A Synchronous Data Fusion for Target Tracking with a Multitasking Radar and Option Sensor[J]. Acquisition Tracking and Pointing, SPIE, 1991, 1482: 234-245.
[5]周锐,申功勋等.多传感器融合目标跟踪[J].航空学报, 1998, 19(5): 536-540.
[6]王宝树,李芳社.基于数据融合技术的多目标跟踪算法研究[J].西安电子科技大学学报, 1998, 25(3): 269-272.
[7]李林,黄柯,何芳.集中式多传感器融合系统中的时间配准研究[J].传感技术学报, 2007, 20(11): 2445-2449.
[8]刘利生.外测数据事后处理[M].北京:国防工业出版社, 2000: 190-191.
[9]梁凯,潘泉,宋国明等.基于曲线拟合的多传感器时间对准方法研究[J].火力与指挥控制, 2006, 31(12): 51-53.
[10]朱永杰、李忠锐.雷达数据实时时间配准算法研究[J].火控雷达技术, 2010, 39(2): 53-56.
[11]江红,张炎华,赵忠华.多传感器信息融合的时间不确定性[J].上海交通大学学报, 2005, 39(3): 366-372.
[12] J. L. Poirot, G. V. Mcwilliams. Application of Linear Statistical Models to Radar Location Techniques[J], IEEE Transactions on Aerospace and Electronic Systems, 1974: 830-934.
[13] W. L. Fischer, C. E. Cameron, A. G. Cameron. Registration Errors in a Netted Air Surveillance System[R]. Boston, MIT Lincoln Laboratory, 1980: 83.
[14] R. E. Helmick, T. R. Rice. Removal of Alignment Errors in an Integrated System of Two 3D Sensors[J]. IEEE Transactions on Aerospace and Electronic Systems, 1993, 29(4): 1333-1343.
[15] J. Burke. The SAGE Real Quality Control Fraction and Its Interface with BUICⅡ/BUICⅢ[R]. Technical Report 308, MITRE Corporation, 1966.
[16]王波,王灿林,董云龙. RTQC误差配准算法性能分析[J].系统仿真学报, 2006, 18(11):3067-3081.
[17] H. Leung, M. Blanchette. A Least Square Fusion of Multiple Radar Data[C]. Proceedings of Radar 1994, Paris, 1994, 364-369.
[18] M. P. Dana. Registration: a Prerequisite for Multiple Sensor Tracking. In Multitarget-Multisensor Tracking: Advanced application[M]. Y. Bar-Shalom Ed Artech House, Norwood, MA, 1990.
[19] H. Leung, M. Blanchette, K. Gault. Comparison of Registration Error Correction Techniques for Air Surveillance Radar Network[C]. Signal Data Processing Small Targets, San Diego, USA, 1995, 498-508.
[20] Y. F.Zhou, L. Heung. An Exact Maximum Likelihood Registration Algorithm for Data Fusion[J]. IEEE Transactions on Signal Processing, 1997, 45(6): 1560-1572.
[21]王建卫.基于模拟退火算法的组网雷达系统误差校正[J].现代雷达, 2006, 28(8): 4-17.
[22] R. G. Mulholland, D. W. Stout. Stereographic Projection in the National Airspace System[J]. IEEE Transaction on Aerospace and Electronic Systems, 1982, 18(1): 48-57.
[23] Y. F. Zhou, L. Henry, B. Martin. Sensor Alignment with Earth-centered Earth-fixed Coordinate system[J]. IEEE Transaction on Aerospace and Electronic Systems, 1994, 30(3): 957-962.
[24]董云龙,何友,王国宏等.基于ECEF的广义最小二乘误差配准技术[J].航空学报, 2006, 27(3): 463-467.
[25] N. Nabba, H. Robert, Bishop. Solution to a Multisensor Tracking Problem with Sensor Registration Errors[J]. IEEE Transaction on Aerospace and Electronic Systems,1999, 35(1): 354-363.
[26] Y. F. Zhou. A Kalman Filter Based Registration Approach for Asynchronous Sensors in Multiple Sensor Fusion Applications[C]. IEEE International Conference on Acoustics, Speech and Signal Processing– Proceedings, Montreal, Canada, 2004, II293-II296.
[27] H. Karmiely, T. S. Hava. Sensor registration using neural network[J]. IEEE Transaction on Aerospace and Electronic Systems, 2000, 36(1): 85-100.
[28]潘平俊,冯新喜,孙鹏等. UKF和KF两级滤波雷达与红外配准算法[J].光电工程, 2008, 35(4): 28-34.
[29]刘煜,杨哲,韩崇昭.传感器定姿偏差的空间配准算法研究[J].现代雷达, 2009, 31(2): 29-35.
[30]连峰,韩崇昭,彭一峰.基于广义似然比的自适应在线配准算法[J].控制与决策, 2009, 24(1): 23-28.
[31] K. Pearson. On Lines and Planes of closest fit to points in space[J]. Plil Mag, 1901: 559-572.
[32] G. H. Golub, C. F. Van Loan. An Analysis of the Total Least Squares Problem[J]. SIAM J. Numer Anal, 1980, 17: 883-893.
[33] M. A. Rahman, K. B. Yu. Total Least Squares Approach for Frequency Estimation Using Prediction[J]. IEEE Trans Acoust Speech Signal Processing, 1987, 35: 1440-1450.
[34] B. D. Moor. Structured total least squares and L2 approximation problems[J]. Linear Algebra and Its Applications, 1993: 163-207.
[35] B. D. Moor. Total least squares for affinely structured matrices and the noisy realization problem[J]. IEEE Transactions on Signal Processing, 1994, 42(11): 3104-3113.
[36]张贤达.矩阵分析与应用[M].北京:清华大学出版社, 2004: 403-450.
[37]廖颖.一种基于“滑窗法”的自适应航迹起始方法[J].现代电子, 1996, 57(4): 34-41.
[38]薄万举.流动形变监测系统[M].北京:地震出版社, 2008: 123.
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