目标无源定位与跟踪算法研究
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摘要
随着新技术、新方法在军事领域的应用,电子对抗、电子干扰、反辐射导弹等技术均有了长足的发展,这对电子侦察设备的生存能力和抗干扰能力提出了越来越高的要求。作为传统电子侦察设备的重要组成部分,有源定位系统由于自身的局限性已经不能满足现代战争的要求。单站无源定位系统以其隐蔽性好、抗干扰能力强、作用距离远等优点逐渐成为研究人员的关注焦点。论文基于只测角单站无源定位系统,研究了系统的可观测性以及滤波发散问题。主要工作如下:
(一)讨论了线性和非线性系统的可观测性以及参数估计的基本方法,深入分析了单站只测角无源定位系统的可观测性,研究了系统和目标的运动状态参数对系统定位精度的影响,得出了不同状态参数与定位精度的定性或定量的对应关系。
(二)针对单站只测角无源定位系统普遍存在的可观测性弱、目标初始状态估计误差大、滤波易发散的问题,论文提出了一种两阶段多模型扩展卡尔曼滤波算法。在估计误差比较大的滤波初始阶段,采用多个模型组成的模型集合加权来逼近目标的真实状态模型,可以有效地减小滤波的模型误差,避免滤波的发散;当滤波达到稳态后,改为采用单模型滤波以节省计算量和系统存储量。仿真结果表明,在初始状态估计比较精确的情况下,该算法定位精度与经典扩展卡尔曼滤波算法相当;在初始状态估计误差较大的情况下,采用经典扩展卡尔曼滤波算法滤波极易发散,而采用本文算法在保持较高定位精度的同时,可以快速收敛。
To deal with the wide application of electronic-counter, electronic jamming and anti-radiation missile, it is required to enhance the viability and antijamming ability of each electronic reconnaissance equipment. As an important part of the traditional electronic reconnaissance equipments, active locating system has not met the requirements of modern war because of its own drawbacks. Hence, single station passive locating system has gradually received extensive attention for the advantages of being hard to be detected, strong antijamming ability and long detecting range. Based on the single station bearings-only passive locating system (SSBOPLS), the system’s observability and filtering divergence are researched in this thesis. The main works can be summarized as follows.
Firstly, the observability of linear and nonlinear systems and the basis of parameter estimation are discussed. Particularly, the observability of single station bearings-only passive locating systems was analyzed and the influence of the moving state parameters of observer and target on the system locating accuracy is also researched. Based on that, the conclusion about the relationship between different moving state parameter and locating accuracy is made.
To solve the problem of filtering divergence in the case of low observability and large estimating error to the target’s original state in the SSBOPLS, this thesis presents a two-stage multiple mode extended Kalman filtering (EKF) algorithm. At the beginning of filtering, system often has large estimating error. In order to efficiently avoid filtering divergence, the algorithm uses a mode-set which contains multiple modes to approach the real target state mode. When filtering comes to steady-state, a single mode is applied in the algorithm to reduce the calculation complexity and the system storage. Simulation results indicate that the locating accuracy of the algorithm is similar to that of EKF when the original estimation is accurate. When the system has large original state estimating error, the proposed algorithm can still accurately track the target while EKF diverges.
(一)讨论了线性和非线性系统的可观测性以及参数估计的基本方法,深入分析了单站只测角无源定位系统的可观测性,研究了系统和目标的运动状态参数对系统定位精度的影响,得出了不同状态参数与定位精度的定性或定量的对应关系。
(二)针对单站只测角无源定位系统普遍存在的可观测性弱、目标初始状态估计误差大、滤波易发散的问题,论文提出了一种两阶段多模型扩展卡尔曼滤波算法。在估计误差比较大的滤波初始阶段,采用多个模型组成的模型集合加权来逼近目标的真实状态模型,可以有效地减小滤波的模型误差,避免滤波的发散;当滤波达到稳态后,改为采用单模型滤波以节省计算量和系统存储量。仿真结果表明,在初始状态估计比较精确的情况下,该算法定位精度与经典扩展卡尔曼滤波算法相当;在初始状态估计误差较大的情况下,采用经典扩展卡尔曼滤波算法滤波极易发散,而采用本文算法在保持较高定位精度的同时,可以快速收敛。
To deal with the wide application of electronic-counter, electronic jamming and anti-radiation missile, it is required to enhance the viability and antijamming ability of each electronic reconnaissance equipment. As an important part of the traditional electronic reconnaissance equipments, active locating system has not met the requirements of modern war because of its own drawbacks. Hence, single station passive locating system has gradually received extensive attention for the advantages of being hard to be detected, strong antijamming ability and long detecting range. Based on the single station bearings-only passive locating system (SSBOPLS), the system’s observability and filtering divergence are researched in this thesis. The main works can be summarized as follows.
Firstly, the observability of linear and nonlinear systems and the basis of parameter estimation are discussed. Particularly, the observability of single station bearings-only passive locating systems was analyzed and the influence of the moving state parameters of observer and target on the system locating accuracy is also researched. Based on that, the conclusion about the relationship between different moving state parameter and locating accuracy is made.
To solve the problem of filtering divergence in the case of low observability and large estimating error to the target’s original state in the SSBOPLS, this thesis presents a two-stage multiple mode extended Kalman filtering (EKF) algorithm. At the beginning of filtering, system often has large estimating error. In order to efficiently avoid filtering divergence, the algorithm uses a mode-set which contains multiple modes to approach the real target state mode. When filtering comes to steady-state, a single mode is applied in the algorithm to reduce the calculation complexity and the system storage. Simulation results indicate that the locating accuracy of the algorithm is similar to that of EKF when the original estimation is accurate. When the system has large original state estimating error, the proposed algorithm can still accurately track the target while EKF diverges.
引文
[1] 刘福声,罗鹏飞.统计信号处理.长沙,国防科技大学出版社,1999
[2] 孙仲康,周一宇,何黎星.单多基地有源无源定位技术.北京,国防工业出版社,1996
[3] V.J.Aidala. Kalman Filter Behavior in Bearing-Only Tracking Applications. IEEE Transactions on Aerospace and Electronic Systems, Vol.15, No.1, Jan. 1979:29-39
[4] R.J.Webster. An exact trajectory solution from Doppler shift Measurement. IEEE Transactions on Aerospace and Electronic Systems, Vol.18, No.2, Mar. 1982:249-252
[5] Y.T.Chan, S.W.Rudnicki. Bearings-only and Doppler-bearing tracking using instrumental variables. IEEE Transactions on Aerospace and Electronic Systems, Vol.28, No.4, Oct. 1992:1076-1082
[6] Killint EW on the offensive. Journal of Electronics Defense, Jul. 1997:37-39
[7] Experimental passive range and ADA system shows promise. Journal of Electronics Defense, Dec. 1992:31-32
[8] EW101. Journal of Electronics Defense, Jan. 1998:14-19
[9] Advanced Digital Receiver Offers Precision Location. Identification. SIGNAL, Jul.1998:41-44
[10] A COTS solution for single platform passive targeting. Journal of Electronics Defense, Jul. 1996:42
[11] Litton develops phased interferometers for passive accurate target fixing. Aviation Week&Space Tech. Oct. 1990:73-74
[12] Jane's Radar and EW, 2000:477
[13] 许耀伟.一种快速高精度无源定位方法的研究[工学博士学位论文].长沙,国防科技大学研究生院,1998
[14] 安玮,孙仲康.利用多普勒变化率的单站无源定位测距技术.北京,雷达无源定位跟踪技术研讨会论文集,2001:41-45
[15] 郭福成.基于运动学原理的单站无源定位与跟踪关键技术研究[工学博士学位论文].长沙,国防科技大学研究生院,2002
[16] Martin J.Moorman. A New Estimator for Passive Tracking of Maneuvering Targets. Proc. IEEE 1992:1122-1124
[17] D.W.Whitcombe. Pseudo-state measurements applied to recursive nonlinear filtering. Proc.3rd.Symp.Nonlinear Estimation Theory and Its Application, 1972:278-281
[18] A.G.Lindgren, K.F.Gong. Position and Velocity Estimation Via Bearing Observations. IEEE Transactions on Automatic Control, Vol.26, No.3, April, 1981:488-493
[19] D.Lerro; Bar-Shalom Y. Bias compensation for improved recursive bearings-onlytarget state estimation. Proceedings of American Control Conference, Vol.1, 1995: 648-652
[20] V.J.Aidala, S.Hammel. Utilization of Modified Polar Coordinates for Bearings-Only Tracking. IEEE Transactions on Automatic Control, Vol.AC-28, No.3, Mar., 1983:283-294
[21] T.L.Song, J.L.Speyer. A Stochastic Analysis of a Modified Gain Extend Kalman Filter with Application to Estimation with Bearing Only Measurements. IEEE Transactions on Automatic Control, Vol.30, No.10,1985:940~949
[22] M.Pachter, P.R.Chandler. Universal linearization concept for extended Kalman filters. IEEE Transactions on Aerospace and Electronic Systems, Vol.29, No.3, July, 1993:946-962
[23] J.R.Guerci, R.Goetz, J.Dimodica, A method for improving extended Kalman filter performance for angle-only passive ranging. IEEE Transactions on Aerospace and Electronic Systems, Vol.30, No.4, Oct., 1994:1090-1093
[24] S.L.Fagin. Comments on a Method for Improving Extended Kalman Filter Performance for Angle-Only Passive Ranging, IEEE Transactions on Aerospace and Electronic Systems, Vol.31, No.3, July. 1995
[25] 邓新蒲.运动单观测器无源定位与跟踪方法研究[工学博士学位论文].长沙,国防科技大学研究生院,2000
[26] Avitzour. A stochastic simulation Bayesian approach to multitarget tracking. IEE Proceedings on Radar, Sonar and Navigation. UK:IEE,1995
[27] B.P.Carlin, N.G.Polson, D.S.Stoffer. A Monte Carlo Approach to Nonnormal and Nonlinear State-space Modeling. JASA. 1992 ,87 (418):493～500
[28] A.Doucet, N.Gordon, V.Krishnamurthy. Particle Filters for State Estimation of Jump Markov Linear Systems. IEEE Trans. On Signal Processing, Vol.49, 2001:613-624
[29] J.Carpenter, P.Clifford, F.Fearnhead. Improved Particle Filter for Nonlinear Problems. IEE proc. Radar, Sonar, Navigation, 1999, 146(1)
[30] 周宏仁,敬忠良,王培德.机动目标跟踪.北京,国防工业出版社,1991
[31] Y.T.Chan, J.B.Plant, A.G.C.Hu. A Kalman filter based tracking scheme with input estimation. IEEE Transactions on Aerospace and Electronic Systems, 1979, 15(2):237-244
[32] Y.Bar-Shalom, K.Birmiwal. Variable dimension filter for maneuvering target tracking. IEEE Transactions on Aerospace and Electronic Systems, 1982, 18(5):611-619
[33] H.A.P.Blom, Y.Bar-Shalom. The Interacting Multiple Model Algorithm for Systems with Markovian Switching Coefficients. IEEE Trans. AC, 1988, 33(4):780
[34] X.R.Li, Y.Bar-Shalom. Multiple Model Estimation with Variable Structure. IEEETrans. AC, 1996, 41(4):478-493
[35] X.R.Li. Model-set Sequence-conditioned Estimation for Variable-structure MM Estimation. SPIE, 1998, 3373:546-558
[36] 孙仲康,陈辉煌.定位导航与制导,北京,国防工业出版社,1987
[37] 袁天鑫.最佳估计原理.北京,国防工业出版社,1979
[38] S.C.Nardone, A.Lindgren, K.F.Gong. Fundamental Properties and Performance of Conventional Bearings-Only Target Motion Analysis. IEEE Transactions on Automatic Control, Vol.AC-29, No.9, Sept., 1984:755-787
[39] Martin J.Moorman. A Stochastic Perturbation Analysis of Bias in the Extended Kalman Filter as Applied to Bearings-Only Estimation. Proc.31stDecision and Control, 1992:3778-3783
[40] Y.Bar-Shalom. Tracking a maneuvering target using input estimation versus interacting multiple model algorithm. IEEE Transactions on Aerospace and Electronic Systems. Vol.25, No.2, Mar. 1989:296-300
[41] X.R.Li, Y.Bar-Shalom. Performance prediction of the interacting multiple model algorithm. IEEE Transactions on Aerospace and Electronic Systems, Vol.29, No.3, Jul., 1993:755-771
[42] E.Mazor, A.Averbuch, Y.Bar-Shalom, J.Dayan. Interacting multiple model methods in target tracking: A survey. IEEE Transactions on Aerospace and Electronic Systems, Vol.34, No.1, Jan., 1998:103-122
[43] 刘忠.纯方位目标运动分析与被动定位算法研究[工学博士学位论文].武汉,华中科技大学研究生院,2002
[44] P.S.Maybeck, K.P.Hentz. Investigation of Moving-Bank Multiple Model Adaptive Algorithm. AIAA J.Guidance, Control, and Dynamics, Vol.10, Jan.,1987: pp.90-96
[45] V.P.Jilkov. Design and Comparison of Mode-Set Adaptive IMM algorithm for Maneuvering Target Tracking. IEEE Transactions on Aerospace and Electronic Systems, 1999, 35(1):343-350
[46] W.D.Blair, G.A.Watson. Interacting Multiple Bias Model Algorithm with application to Tracking Maneuvering Targets. Proc. 31st IEEE Conf. on Decision and Control, 1992:3790-3795
[47] 钟晓军,王国宏,陈士举,蒋凤新.伪线性滤波在导弹纯方位跟踪中的应用.飞航导弹,2004,05:55-58
[48] J.M.Passerieux, D.Van.Cappel. Optimal observer maneuver for bearings-only tracking. IEEE Transactions on Aerospace and Electronic Systems,Vol.34, No.3, Jul, 1998:777-788
[49] Rao.S.Koteswara. Algorithm for detection of maneuvering targets in bearings-only passive target tracking. IEE. Proc. Radar, Sonar, Navig. Vol.146, No.3, Jun, 1999:141-146
[2] 孙仲康,周一宇,何黎星.单多基地有源无源定位技术.北京,国防工业出版社,1996
[3] V.J.Aidala. Kalman Filter Behavior in Bearing-Only Tracking Applications. IEEE Transactions on Aerospace and Electronic Systems, Vol.15, No.1, Jan. 1979:29-39
[4] R.J.Webster. An exact trajectory solution from Doppler shift Measurement. IEEE Transactions on Aerospace and Electronic Systems, Vol.18, No.2, Mar. 1982:249-252
[5] Y.T.Chan, S.W.Rudnicki. Bearings-only and Doppler-bearing tracking using instrumental variables. IEEE Transactions on Aerospace and Electronic Systems, Vol.28, No.4, Oct. 1992:1076-1082
[6] Killint EW on the offensive. Journal of Electronics Defense, Jul. 1997:37-39
[7] Experimental passive range and ADA system shows promise. Journal of Electronics Defense, Dec. 1992:31-32
[8] EW101. Journal of Electronics Defense, Jan. 1998:14-19
[9] Advanced Digital Receiver Offers Precision Location. Identification. SIGNAL, Jul.1998:41-44
[10] A COTS solution for single platform passive targeting. Journal of Electronics Defense, Jul. 1996:42
[11] Litton develops phased interferometers for passive accurate target fixing. Aviation Week&Space Tech. Oct. 1990:73-74
[12] Jane's Radar and EW, 2000:477
[13] 许耀伟.一种快速高精度无源定位方法的研究[工学博士学位论文].长沙,国防科技大学研究生院,1998
[14] 安玮,孙仲康.利用多普勒变化率的单站无源定位测距技术.北京,雷达无源定位跟踪技术研讨会论文集,2001:41-45
[15] 郭福成.基于运动学原理的单站无源定位与跟踪关键技术研究[工学博士学位论文].长沙,国防科技大学研究生院,2002
[16] Martin J.Moorman. A New Estimator for Passive Tracking of Maneuvering Targets. Proc. IEEE 1992:1122-1124
[17] D.W.Whitcombe. Pseudo-state measurements applied to recursive nonlinear filtering. Proc.3rd.Symp.Nonlinear Estimation Theory and Its Application, 1972:278-281
[18] A.G.Lindgren, K.F.Gong. Position and Velocity Estimation Via Bearing Observations. IEEE Transactions on Automatic Control, Vol.26, No.3, April, 1981:488-493
[19] D.Lerro; Bar-Shalom Y. Bias compensation for improved recursive bearings-onlytarget state estimation. Proceedings of American Control Conference, Vol.1, 1995: 648-652
[20] V.J.Aidala, S.Hammel. Utilization of Modified Polar Coordinates for Bearings-Only Tracking. IEEE Transactions on Automatic Control, Vol.AC-28, No.3, Mar., 1983:283-294
[21] T.L.Song, J.L.Speyer. A Stochastic Analysis of a Modified Gain Extend Kalman Filter with Application to Estimation with Bearing Only Measurements. IEEE Transactions on Automatic Control, Vol.30, No.10,1985:940~949
[22] M.Pachter, P.R.Chandler. Universal linearization concept for extended Kalman filters. IEEE Transactions on Aerospace and Electronic Systems, Vol.29, No.3, July, 1993:946-962
[23] J.R.Guerci, R.Goetz, J.Dimodica, A method for improving extended Kalman filter performance for angle-only passive ranging. IEEE Transactions on Aerospace and Electronic Systems, Vol.30, No.4, Oct., 1994:1090-1093
[24] S.L.Fagin. Comments on a Method for Improving Extended Kalman Filter Performance for Angle-Only Passive Ranging, IEEE Transactions on Aerospace and Electronic Systems, Vol.31, No.3, July. 1995
[25] 邓新蒲.运动单观测器无源定位与跟踪方法研究[工学博士学位论文].长沙,国防科技大学研究生院,2000
[26] Avitzour. A stochastic simulation Bayesian approach to multitarget tracking. IEE Proceedings on Radar, Sonar and Navigation. UK:IEE,1995
[27] B.P.Carlin, N.G.Polson, D.S.Stoffer. A Monte Carlo Approach to Nonnormal and Nonlinear State-space Modeling. JASA. 1992 ,87 (418):493～500
[28] A.Doucet, N.Gordon, V.Krishnamurthy. Particle Filters for State Estimation of Jump Markov Linear Systems. IEEE Trans. On Signal Processing, Vol.49, 2001:613-624
[29] J.Carpenter, P.Clifford, F.Fearnhead. Improved Particle Filter for Nonlinear Problems. IEE proc. Radar, Sonar, Navigation, 1999, 146(1)
[30] 周宏仁,敬忠良,王培德.机动目标跟踪.北京,国防工业出版社,1991
[31] Y.T.Chan, J.B.Plant, A.G.C.Hu. A Kalman filter based tracking scheme with input estimation. IEEE Transactions on Aerospace and Electronic Systems, 1979, 15(2):237-244
[32] Y.Bar-Shalom, K.Birmiwal. Variable dimension filter for maneuvering target tracking. IEEE Transactions on Aerospace and Electronic Systems, 1982, 18(5):611-619
[33] H.A.P.Blom, Y.Bar-Shalom. The Interacting Multiple Model Algorithm for Systems with Markovian Switching Coefficients. IEEE Trans. AC, 1988, 33(4):780
[34] X.R.Li, Y.Bar-Shalom. Multiple Model Estimation with Variable Structure. IEEETrans. AC, 1996, 41(4):478-493
[35] X.R.Li. Model-set Sequence-conditioned Estimation for Variable-structure MM Estimation. SPIE, 1998, 3373:546-558
[36] 孙仲康,陈辉煌.定位导航与制导,北京,国防工业出版社,1987
[37] 袁天鑫.最佳估计原理.北京,国防工业出版社,1979
[38] S.C.Nardone, A.Lindgren, K.F.Gong. Fundamental Properties and Performance of Conventional Bearings-Only Target Motion Analysis. IEEE Transactions on Automatic Control, Vol.AC-29, No.9, Sept., 1984:755-787
[39] Martin J.Moorman. A Stochastic Perturbation Analysis of Bias in the Extended Kalman Filter as Applied to Bearings-Only Estimation. Proc.31stDecision and Control, 1992:3778-3783
[40] Y.Bar-Shalom. Tracking a maneuvering target using input estimation versus interacting multiple model algorithm. IEEE Transactions on Aerospace and Electronic Systems. Vol.25, No.2, Mar. 1989:296-300
[41] X.R.Li, Y.Bar-Shalom. Performance prediction of the interacting multiple model algorithm. IEEE Transactions on Aerospace and Electronic Systems, Vol.29, No.3, Jul., 1993:755-771
[42] E.Mazor, A.Averbuch, Y.Bar-Shalom, J.Dayan. Interacting multiple model methods in target tracking: A survey. IEEE Transactions on Aerospace and Electronic Systems, Vol.34, No.1, Jan., 1998:103-122
[43] 刘忠.纯方位目标运动分析与被动定位算法研究[工学博士学位论文].武汉,华中科技大学研究生院,2002
[44] P.S.Maybeck, K.P.Hentz. Investigation of Moving-Bank Multiple Model Adaptive Algorithm. AIAA J.Guidance, Control, and Dynamics, Vol.10, Jan.,1987: pp.90-96
[45] V.P.Jilkov. Design and Comparison of Mode-Set Adaptive IMM algorithm for Maneuvering Target Tracking. IEEE Transactions on Aerospace and Electronic Systems, 1999, 35(1):343-350
[46] W.D.Blair, G.A.Watson. Interacting Multiple Bias Model Algorithm with application to Tracking Maneuvering Targets. Proc. 31st IEEE Conf. on Decision and Control, 1992:3790-3795
[47] 钟晓军,王国宏,陈士举,蒋凤新.伪线性滤波在导弹纯方位跟踪中的应用.飞航导弹,2004,05:55-58
[48] J.M.Passerieux, D.Van.Cappel. Optimal observer maneuver for bearings-only tracking. IEEE Transactions on Aerospace and Electronic Systems,Vol.34, No.3, Jul, 1998:777-788
[49] Rao.S.Koteswara. Algorithm for detection of maneuvering targets in bearings-only passive target tracking. IEE. Proc. Radar, Sonar, Navig. Vol.146, No.3, Jun, 1999:141-146