捷联成像导引头视线角速率估计方法研究
摘要
随着捷联惯性技术以及成像技术的快速发展,捷联成像导引头成为现代导弹导引头的发展趋势。然而,与采用常平架式导引头的传统导弹相比,捷联导引头的视线角速率不能直接提取,大的视野范围也导致了大的测量噪声,针对这两个缺点,本文研究了捷联成像导引头的视线角速率的提取方法。
文章首先对常用坐标系进行了定义。针对捷联成像导引系统,引入了体视线坐标系的定义,推导了坐标系之间的转换关系矩阵,并进一步推导了视线角速率解耦公式。
其次研究了经典弹目拦截方法。分别用追踪导引法和比例导引法进行了弹目拦截仿真,获得了视线角速率数据、体视线角速率数据以及相关的坐标系转换矩阵。
然后对测量量中存在的野值进行了分析。通过对Kalman滤波方程中的“新息”进行修正,得到了抗野值Kalman滤波算法。仿真表明,基于“新息”修正的抗野值Kalman滤波算法,对孤立型野值和斑点型野值都可以有效地剔除。
最后对背景噪声进行了分析,建立了Gaussian-Laplace噪声模型,并进一步建立了实现视线角速率提取的状态方程以及观测方程,得到了捷联成像导引系统的数学模型。由于传统的扩展Kalman(EKF)滤波方法不能完全适应复杂的非线性方程及非高斯噪声,进一步研究了利用粒子滤波(PF)以及无迹Kalman(UKF)滤波方法的视线角速率估计方法。
仿真研究表明,采用UKF方法对捷联成像导引系统视线角速率进行估计,既保证了系统对实时性的要求,又达到了较高的精度。
With the development of strapdown inertial technology and imaging technology, strapdown imaging seeker has turn into the developing trend of modern missile seeker. However, compared with the traditional seeker using inertial platform, the line of sight(LOS) rate of strapdown seeker can not directly be measured. In addition, more measurement noise is induced due to the wide sighting field. In view of the aforementioned problems, this paper studies the LOS rate estimation method of strapdown imaging seeker.
Firstly, coordinates are defined and body LOS coordinate is introduced. Then the transformation matrices among the coordinates and LOS rate decoupling expressions are deduced.
Secondly, classical tracking method of missile and target are studied. Tracking simulations, using pursuit guidance law and proportion guidance law, are accomplished in order to get LOS rate, body LOS rate and correlative coordinate transformation matrix.
Thirdly, the outliers existing in measurements are analyzed. Through amending“innovation”in the equations of Kalman filter, outlier-eliminating Kalman filtering algorithm is achieved. Simulation results show that outlier-eliminating Kalman filtering algorithm , which based on“innovation”amending, can effectively eliminate both the isolated outliers and patch-type outliers.
Finally, through analyzing background noise, Gaussian-Laplace noise model is established. Then state equations and measurement equations are established in order to distill the LOS rate. As traditional extended Kalman filter(EKF) can adapt to neither complicated nonlinear equations nor nonGaussian noise, LOS rate estimation using particle filter(PF) and unscented Kalman filter(UKF) are studied.
Simulation results show that LOS rate estimation, using UKF method for strapdown imaging guidance system, can meet both real-time and precision requirements.
文章首先对常用坐标系进行了定义。针对捷联成像导引系统,引入了体视线坐标系的定义,推导了坐标系之间的转换关系矩阵,并进一步推导了视线角速率解耦公式。
其次研究了经典弹目拦截方法。分别用追踪导引法和比例导引法进行了弹目拦截仿真,获得了视线角速率数据、体视线角速率数据以及相关的坐标系转换矩阵。
然后对测量量中存在的野值进行了分析。通过对Kalman滤波方程中的“新息”进行修正,得到了抗野值Kalman滤波算法。仿真表明,基于“新息”修正的抗野值Kalman滤波算法,对孤立型野值和斑点型野值都可以有效地剔除。
最后对背景噪声进行了分析,建立了Gaussian-Laplace噪声模型,并进一步建立了实现视线角速率提取的状态方程以及观测方程,得到了捷联成像导引系统的数学模型。由于传统的扩展Kalman(EKF)滤波方法不能完全适应复杂的非线性方程及非高斯噪声,进一步研究了利用粒子滤波(PF)以及无迹Kalman(UKF)滤波方法的视线角速率估计方法。
仿真研究表明,采用UKF方法对捷联成像导引系统视线角速率进行估计,既保证了系统对实时性的要求,又达到了较高的精度。
With the development of strapdown inertial technology and imaging technology, strapdown imaging seeker has turn into the developing trend of modern missile seeker. However, compared with the traditional seeker using inertial platform, the line of sight(LOS) rate of strapdown seeker can not directly be measured. In addition, more measurement noise is induced due to the wide sighting field. In view of the aforementioned problems, this paper studies the LOS rate estimation method of strapdown imaging seeker.
Firstly, coordinates are defined and body LOS coordinate is introduced. Then the transformation matrices among the coordinates and LOS rate decoupling expressions are deduced.
Secondly, classical tracking method of missile and target are studied. Tracking simulations, using pursuit guidance law and proportion guidance law, are accomplished in order to get LOS rate, body LOS rate and correlative coordinate transformation matrix.
Thirdly, the outliers existing in measurements are analyzed. Through amending“innovation”in the equations of Kalman filter, outlier-eliminating Kalman filtering algorithm is achieved. Simulation results show that outlier-eliminating Kalman filtering algorithm , which based on“innovation”amending, can effectively eliminate both the isolated outliers and patch-type outliers.
Finally, through analyzing background noise, Gaussian-Laplace noise model is established. Then state equations and measurement equations are established in order to distill the LOS rate. As traditional extended Kalman filter(EKF) can adapt to neither complicated nonlinear equations nor nonGaussian noise, LOS rate estimation using particle filter(PF) and unscented Kalman filter(UKF) are studied.
Simulation results show that LOS rate estimation, using UKF method for strapdown imaging guidance system, can meet both real-time and precision requirements.
引文
1姚郁,章国江.捷联成像制导系统的若干问题探讨.红外与激光工程. 2006, 35(1): 1~6
2苏身榜.捷联寻的制导技术及其在国外的发展.航空兵器. 1994(2): 45~50
3 GUO-JIANG ZHANG, YU YAO. Line of Sight Rate Estimation of Strapdown Imaging Guidance System Based on Unscented Kalman Filter. Proceedings of the Fourth International Conference on Machine Learning and Cybernetics. Guangzhou: 18-21. August 2005. 1574~1578
4陶迪.自寻的导弹捷联导引系统实现比例导引设计与研究.哈尔滨工程大学硕士论文. 2005:1~3
5陈哲.捷联式惯性导航原理.航空专业教材编审组. 1986
6 NESLINE. F W, ZARCHAN. P. Line-of-sight reconstruction for faster homing guidance. Journal of Guidance, Control , and Dynamics, 1984, 8(1) : 3~8
7 LIN Zhe, YAO Yu, MA Ke mao. The design of LOS reconstruction filter for strap down imaging seeker. IEEE 2005 International Conference on Machine Learning and Cybernetics. 2005, 4: 2272~2277
8钱杏芳.导弹飞行力学.北京理工大学出版社. 2003:28~103
9程国采.战术导弹导引方法.国防大学出版社. 1996:30~62
10周荻.寻的导弹新型导引规律.国防工业出版社. 2002:5~26
11秦永元,张洪钺,汪叔华.卡尔曼滤波与组合导航原理.西北工业大学出版社. 1998:10~40
12付梦印,邓志红,张继伟. Kalman滤波理论及其在导航系统中的应用.科学出版社. 2003:30~55
13 Greg Welch, Gary Bishop. An Introduction to the Kalman Filter. University of North Carolina, Department of Computer Science, TR 95-041. 1995
14柳海峰,姚郁,等. Kalman滤波新息正交性抗野值法研究.电机与控制学报. 2003, 7 (1) : 40~42
15胡峰,孙国基. Kalman滤波的抗野值修正.自动化学报. 1999, 25(5):692~698.
16胡奕明,秦永元.目标跟踪系统Kalman滤波野值修正算法研究.弹箭与制导学报. 2006:330~334
17高宁,等.抗野值自适应卡尔曼滤波方法的研究.中国惯性技术学报. 2003
18左东广,韩崇昭,等.闪烁噪声机动目标跟踪的模型集交互跟踪算法.系统仿真学报. April 2004. Vol. 16 No. 4.pp.767~771
19 N.P.Kostantinos, H.Dimitris. Advanced Signal Processing Handbook. BocaRaton: CRC Press LLC, 2001
20宋小全,孙仲康.非高斯噪声下的机动目标跟踪.电子学报. 1998,26(9):40~46
21戴丁樟.粒子滤波算法研究及其在目标跟踪中的应用.哈尔滨工业大学硕士论文. 2006:32~36
22 Richard Lewis. Optimal Estimation with An Introduction to Stochastic Control Theory, John Wiley & Sons, Inc. 1986
23 R. E. Kalman. A New Approach to Linear Filtering and Prediction Problems. Transaction of the ASME-Journal of Basic Engineering, pp. 35~45.March 1960
24胡士强,敬忠良.粒子滤波算法综述.控制与决策. 2005, 20(4): 361~365
25 Gordon N, Salmond D. Novel Approach to Non-linear and Non-Gaussian Bayesian State Estimation. Proc of Institute Electric Engineering, 1993, 140(2): 107~113
26 Liu J S, Chen R. Sequential Monte Carlo Methods for Dynamical Systems. J of the American Statistical Association, 1998, 93(5): 1032~1044
27 J. B. Kuipers. SPASYN - An Electromagnetic Relative Position and Orientation Tracking System. IEEE Transactions on Instrumentation and Measurement. Vol. IM-29, No. 4, pp. 462~466. 1980
28 Peter S. Maybeck. Stochastic Models, Estimation, and Control, Volume 1, Academic Press, Inc. 1979
29 D. L. Alspach, H. W. Sorenson. Nonlinear Bayesian Estimation Using Gaussian Sum Approximation. IEEE Trans. Automat. Contr., vol. 20, pp. 439~447, 1972
30 B. D. O. Anderson, J. B. Moore. The Kalman-Bucy Filter As A True Time-varying Wiener Filter. IEEE Trans. Syst. Man Cybern. vol. 1, pp.119~128, 1971
31 C. Andrieu, A, Doucet. Recursive Monte Carlo Algorithms for Parameter Estimation in General State Space Models. Proc. IEEE Signal Processing Workshop on Statistical Signal Processing. pp.14~17, 2001
32 C. Andrieu, N. de Freitas, A. Doucet. Rao-Blackwellised Particle Filtering via Data Augmentation. Adv. Neural Inform. Process. Syst. 14, Cambridge, MA: MIT Press, 2002
33 C. Andrieu, N. de Freitas, A. Doucet and M. I. Jordan. An Introduction to MCMC for Machine Learning. Machine Learning. vol. 50, no. 1/2, pp. 5~43, 2003
34 M. S. Arulampalam, S. Maskell, N. Gordon and T. Clapp. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans. Signal Processing. vol. 50, no. 2, pp. 174~188, Feb. 2002
35 D. Avitzour. A Stochastic Simulation Bayesian Approach to Multitarget Tracking. IEE Proc.-F. vol. 142, pp. 41~44, 1995
36 B. Azimi-Sadjadi. Approximate Nonlinear Filtering With Applications toNavigation. Dept. Elect. Comput. Engr. Univ. Maryland, College Park, 2001.
37 Y. Boers. On The Number of Samples To Be Drawn in Particle Filtering. Proc. IEE Colloquium on Target Tracking: Algorithms and Applications. Ref. No. 1999/090, 1999/215, pp. 5/1~5/6, 1999
38 E. Bolviken, P. J. Acklam, N. Christophersen, J-M. Stordal. Monte Carlo Filters for Nonlinear State Estimation. Automatica. vol. 37, pp.177~183, 2001
39潘泉,杨峰,叶亮,等.一类非线性滤波器-UKF综述.控制与决策. May 2005. Vol. 120 No. 5.pp.482~494
40王淑一,程杨,杨涤,等. UKF方法及其在跟踪问题中的应用.飞行力学. 2003, 21 (2) : 59~62
41 D. F. Allinger, S. K. Mitter. New Results in Innovations Problem for Nonlinear Filtering. Stochastics, vol. 4, pp. 339~348, 1981
42 Joseph J, La Viola Jr. A Comparison of Unscented and Extended Kalman Filtering for Estimating Quaternion Motion. Proceedings of American Control Conference, 2003, pp. 2435~2440
43 M. C. VanDyke, J. L. Schwartz, C. D. Hall. Unscented Kalman Filtering for Spacecraft Attitude State and Parameter Estimation. http: //www. Space-flight.org/AAS_meetings/2004_winter/w2004_program.pdf, 2004203210
44 Yong R, Chen Y Q. Better Proposal Distributions: Object Tracking Using Unscented Particle Filter. Proc of the 2001 IEEE Computer Society Conf on Computer Vision and Pattern Recognition, 2001. Kauai, H I, 2001: 786~793
45 S.J. Julier, J. K. Uhlmann and H. Durrant-Whyte. A New Approach for Filtering Nonlinear System. Proceedings of the American Control Conference, 1995, pp. 1628~1632
2苏身榜.捷联寻的制导技术及其在国外的发展.航空兵器. 1994(2): 45~50
3 GUO-JIANG ZHANG, YU YAO. Line of Sight Rate Estimation of Strapdown Imaging Guidance System Based on Unscented Kalman Filter. Proceedings of the Fourth International Conference on Machine Learning and Cybernetics. Guangzhou: 18-21. August 2005. 1574~1578
4陶迪.自寻的导弹捷联导引系统实现比例导引设计与研究.哈尔滨工程大学硕士论文. 2005:1~3
5陈哲.捷联式惯性导航原理.航空专业教材编审组. 1986
6 NESLINE. F W, ZARCHAN. P. Line-of-sight reconstruction for faster homing guidance. Journal of Guidance, Control , and Dynamics, 1984, 8(1) : 3~8
7 LIN Zhe, YAO Yu, MA Ke mao. The design of LOS reconstruction filter for strap down imaging seeker. IEEE 2005 International Conference on Machine Learning and Cybernetics. 2005, 4: 2272~2277
8钱杏芳.导弹飞行力学.北京理工大学出版社. 2003:28~103
9程国采.战术导弹导引方法.国防大学出版社. 1996:30~62
10周荻.寻的导弹新型导引规律.国防工业出版社. 2002:5~26
11秦永元,张洪钺,汪叔华.卡尔曼滤波与组合导航原理.西北工业大学出版社. 1998:10~40
12付梦印,邓志红,张继伟. Kalman滤波理论及其在导航系统中的应用.科学出版社. 2003:30~55
13 Greg Welch, Gary Bishop. An Introduction to the Kalman Filter. University of North Carolina, Department of Computer Science, TR 95-041. 1995
14柳海峰,姚郁,等. Kalman滤波新息正交性抗野值法研究.电机与控制学报. 2003, 7 (1) : 40~42
15胡峰,孙国基. Kalman滤波的抗野值修正.自动化学报. 1999, 25(5):692~698.
16胡奕明,秦永元.目标跟踪系统Kalman滤波野值修正算法研究.弹箭与制导学报. 2006:330~334
17高宁,等.抗野值自适应卡尔曼滤波方法的研究.中国惯性技术学报. 2003
18左东广,韩崇昭,等.闪烁噪声机动目标跟踪的模型集交互跟踪算法.系统仿真学报. April 2004. Vol. 16 No. 4.pp.767~771
19 N.P.Kostantinos, H.Dimitris. Advanced Signal Processing Handbook. BocaRaton: CRC Press LLC, 2001
20宋小全,孙仲康.非高斯噪声下的机动目标跟踪.电子学报. 1998,26(9):40~46
21戴丁樟.粒子滤波算法研究及其在目标跟踪中的应用.哈尔滨工业大学硕士论文. 2006:32~36
22 Richard Lewis. Optimal Estimation with An Introduction to Stochastic Control Theory, John Wiley & Sons, Inc. 1986
23 R. E. Kalman. A New Approach to Linear Filtering and Prediction Problems. Transaction of the ASME-Journal of Basic Engineering, pp. 35~45.March 1960
24胡士强,敬忠良.粒子滤波算法综述.控制与决策. 2005, 20(4): 361~365
25 Gordon N, Salmond D. Novel Approach to Non-linear and Non-Gaussian Bayesian State Estimation. Proc of Institute Electric Engineering, 1993, 140(2): 107~113
26 Liu J S, Chen R. Sequential Monte Carlo Methods for Dynamical Systems. J of the American Statistical Association, 1998, 93(5): 1032~1044
27 J. B. Kuipers. SPASYN - An Electromagnetic Relative Position and Orientation Tracking System. IEEE Transactions on Instrumentation and Measurement. Vol. IM-29, No. 4, pp. 462~466. 1980
28 Peter S. Maybeck. Stochastic Models, Estimation, and Control, Volume 1, Academic Press, Inc. 1979
29 D. L. Alspach, H. W. Sorenson. Nonlinear Bayesian Estimation Using Gaussian Sum Approximation. IEEE Trans. Automat. Contr., vol. 20, pp. 439~447, 1972
30 B. D. O. Anderson, J. B. Moore. The Kalman-Bucy Filter As A True Time-varying Wiener Filter. IEEE Trans. Syst. Man Cybern. vol. 1, pp.119~128, 1971
31 C. Andrieu, A, Doucet. Recursive Monte Carlo Algorithms for Parameter Estimation in General State Space Models. Proc. IEEE Signal Processing Workshop on Statistical Signal Processing. pp.14~17, 2001
32 C. Andrieu, N. de Freitas, A. Doucet. Rao-Blackwellised Particle Filtering via Data Augmentation. Adv. Neural Inform. Process. Syst. 14, Cambridge, MA: MIT Press, 2002
33 C. Andrieu, N. de Freitas, A. Doucet and M. I. Jordan. An Introduction to MCMC for Machine Learning. Machine Learning. vol. 50, no. 1/2, pp. 5~43, 2003
34 M. S. Arulampalam, S. Maskell, N. Gordon and T. Clapp. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans. Signal Processing. vol. 50, no. 2, pp. 174~188, Feb. 2002
35 D. Avitzour. A Stochastic Simulation Bayesian Approach to Multitarget Tracking. IEE Proc.-F. vol. 142, pp. 41~44, 1995
36 B. Azimi-Sadjadi. Approximate Nonlinear Filtering With Applications toNavigation. Dept. Elect. Comput. Engr. Univ. Maryland, College Park, 2001.
37 Y. Boers. On The Number of Samples To Be Drawn in Particle Filtering. Proc. IEE Colloquium on Target Tracking: Algorithms and Applications. Ref. No. 1999/090, 1999/215, pp. 5/1~5/6, 1999
38 E. Bolviken, P. J. Acklam, N. Christophersen, J-M. Stordal. Monte Carlo Filters for Nonlinear State Estimation. Automatica. vol. 37, pp.177~183, 2001
39潘泉,杨峰,叶亮,等.一类非线性滤波器-UKF综述.控制与决策. May 2005. Vol. 120 No. 5.pp.482~494
40王淑一,程杨,杨涤,等. UKF方法及其在跟踪问题中的应用.飞行力学. 2003, 21 (2) : 59~62
41 D. F. Allinger, S. K. Mitter. New Results in Innovations Problem for Nonlinear Filtering. Stochastics, vol. 4, pp. 339~348, 1981
42 Joseph J, La Viola Jr. A Comparison of Unscented and Extended Kalman Filtering for Estimating Quaternion Motion. Proceedings of American Control Conference, 2003, pp. 2435~2440
43 M. C. VanDyke, J. L. Schwartz, C. D. Hall. Unscented Kalman Filtering for Spacecraft Attitude State and Parameter Estimation. http: //www. Space-flight.org/AAS_meetings/2004_winter/w2004_program.pdf, 2004203210
44 Yong R, Chen Y Q. Better Proposal Distributions: Object Tracking Using Unscented Particle Filter. Proc of the 2001 IEEE Computer Society Conf on Computer Vision and Pattern Recognition, 2001. Kauai, H I, 2001: 786~793
45 S.J. Julier, J. K. Uhlmann and H. Durrant-Whyte. A New Approach for Filtering Nonlinear System. Proceedings of the American Control Conference, 1995, pp. 1628~1632