引入斜距和高程预测的BLUE跟踪方法
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摘要
最佳线性无偏估计(BLUE:Best Linear Unbiased Estimation)算法用于目标跟踪时,受斜距、高程参量间的"共线"效应影响,对近程目标估计误差会增大甚至发散。针对此问题,在量测转换模型中引入斜距、高程预测,构建斜距、高程参量有偏估计,抑制"共线"效应。基于非线性参数误差最小准则推导斜距、高程估计的权值和偏置,建立基于非线性观测和状态预测融合估计的量测转换模型。基于该模型的BLUE算法能更精确的捕捉转换量测误差特性,以较小计算代价获得性能提升,数值仿真鲁棒性好,有很好应用前景。
BLUE(Best linear unbiased estimation) filter can be used for target tracking. Influenced by the colinearity between the slant range measurement and the altitude measurement, BLUE filter's estimation may degrade or diverge for close-range target tracking. To solve this problem, the biased weighted estimates of slant range and altitude were employed in the converted measurements to alleviate the colinearity. The bias and weighing of the slant range and altitude parameters were derived based on the minimum mean square error criteria. The converted measurement model with the fusion of nonlinear measurement and state prediction was built. The improved BLUE algorithm was able to estimate the statistics of the converted measurements more accurately, hence the filtering accuracy was improved. Simulation results verified this model can greatly improve the performances with minor computational burden. It was also shown to have excellent robustness in numerical examples, which proved it to be a practical approach.
BLUE(Best linear unbiased estimation) filter can be used for target tracking. Influenced by the colinearity between the slant range measurement and the altitude measurement, BLUE filter's estimation may degrade or diverge for close-range target tracking. To solve this problem, the biased weighted estimates of slant range and altitude were employed in the converted measurements to alleviate the colinearity. The bias and weighing of the slant range and altitude parameters were derived based on the minimum mean square error criteria. The converted measurement model with the fusion of nonlinear measurement and state prediction was built. The improved BLUE algorithm was able to estimate the statistics of the converted measurements more accurately, hence the filtering accuracy was improved. Simulation results verified this model can greatly improve the performances with minor computational burden. It was also shown to have excellent robustness in numerical examples, which proved it to be a practical approach.
引文
[1] Julier S J, Uhlmann J K. Reduced sigma point filters for the propagation of means and covariances through nonlinear transformations[C]//Proceeding of the American Control Conference, 2002: 887-892.
[2] Ienkaran A, Simon H. Cubature Kalman filters[J]. IEEE Trans. on Automatic Control, 2009, 54(6): 1254-1269.
[3] 程水英, 张剑云. 粒子滤波评述[J]. 宇航学报, 2008, 29(4): 1099-1111. Cheng Shuiying, Zhang Jianyun. Commentaries of particle filter[J]. Journal of Astronautics, 2008, 29(4): 1099-1111.(in Chinese)
[4] Mo Longbin, Song Xiaoquan, Zhou Yiyu, et al. Unbiased converted measurements for tracking[J]. IEEE Trans. on AES, 1998, 34(3): 1023-1027.
[5] Duan Zhansheng, Han Chongzhao, Li Xiaorong. Comments on “Unbiased converted measurements for tracking”[J]. IEEE Trans. on AES, 2004, 40(4): 1374-1377.
[6] Zhao Zhanlue. Best linear unbiased filtering with nonlinear measurements for target tracking[J]. IEEE Trans. on AES, 2004, 40(4): 1324-1336.
[7] Katkuri J R, Jilkov V P. A comparative study of nonlinear filters for target tracking in mixed coordinates[C]//2010 42nd Southeastern Symposium on System Theory, 2010: 202-207.
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[9] Zhang Yunjun, Geng Zhi.Detection of target maneuver from bearings-only measurements[J]. IEEE Trans. on AES, 2013, 49(3): 2028-2034.
[10] 盛琥, 王金根, 陈治平, 等. 基于高程补偿的BLUE算法在塔康中的应用研究[J]. 系统工程与电子技术, 2016, 36(8): 1752-1757.Sheng Hu, Wang Jingen, Chen Zhiping, et al. Application research of altitude compensation based BLUE algorithm in TACON[J]. Systems Engineering and Electronics, 2016, 36(8): 1752-1757.(in Chinese)
[11] 王炜, 李丹, 姜礼平, 等.可处理多普勒量测的最佳线性无偏估计算法[J]. 电子与信息学报, 2015, 37(6): 1336-1342.Wang Wei, Li Dan, Jiang Lipin, et al. The Best Linear Unbiased Estimation Algorithm with Doppler Measurements[J]. Journal of Electronics & Information Technology, 2015, 37(6): 1336-1342.(in Chinese)
[12] 李为, 李一平, 封锡盛. 基于卡尔曼滤波预测的无偏量测转换方法[J]. 控制与决策, 2015, 30(2): 229-235.Li Wei, Li Yipin, Feng Xisheng. Tracking with prediction-conditioned unbiased converted measurements[J]. Control and Decision, 2015, 30(2): 229-235.(in Chinese)
[13] Sheng Hu, Zhao Wenbo, Wang Jingen. Interacting multiple model tracking algorithm fusing input estimation and best linear unbiased estimation filter[J]. IET Radar, Sonar & Navigation, 2017, 11(1): 70-77.
[14] 盛琥, 王金根, 王立明, 等. 量测转换卡尔曼滤波在塔康导航中的应用[J]. 信号处理, 2015, 31(1): 34-38.Sheng Hu, Wang Jingen, Wang Liming, et al. Application of Converted Measurements Kalman Filter for TACAN Navigation[J]. Journal of Signal Processing, 2015, 31(1): 34-38.(in Chinese)
[2] Ienkaran A, Simon H. Cubature Kalman filters[J]. IEEE Trans. on Automatic Control, 2009, 54(6): 1254-1269.
[3] 程水英, 张剑云. 粒子滤波评述[J]. 宇航学报, 2008, 29(4): 1099-1111. Cheng Shuiying, Zhang Jianyun. Commentaries of particle filter[J]. Journal of Astronautics, 2008, 29(4): 1099-1111.(in Chinese)
[4] Mo Longbin, Song Xiaoquan, Zhou Yiyu, et al. Unbiased converted measurements for tracking[J]. IEEE Trans. on AES, 1998, 34(3): 1023-1027.
[5] Duan Zhansheng, Han Chongzhao, Li Xiaorong. Comments on “Unbiased converted measurements for tracking”[J]. IEEE Trans. on AES, 2004, 40(4): 1374-1377.
[6] Zhao Zhanlue. Best linear unbiased filtering with nonlinear measurements for target tracking[J]. IEEE Trans. on AES, 2004, 40(4): 1324-1336.
[7] Katkuri J R, Jilkov V P. A comparative study of nonlinear filters for target tracking in mixed coordinates[C]//2010 42nd Southeastern Symposium on System Theory, 2010: 202-207.
[8] Jiao Lianmeng, Pan Quan, Liang Yan.Nonlinear tracking algorithm with range-rate measurements based on unbiased measurement conversion[C]//2012 15th International Conference on Information Fusion, 2012: 1400-1405.
[9] Zhang Yunjun, Geng Zhi.Detection of target maneuver from bearings-only measurements[J]. IEEE Trans. on AES, 2013, 49(3): 2028-2034.
[10] 盛琥, 王金根, 陈治平, 等. 基于高程补偿的BLUE算法在塔康中的应用研究[J]. 系统工程与电子技术, 2016, 36(8): 1752-1757.Sheng Hu, Wang Jingen, Chen Zhiping, et al. Application research of altitude compensation based BLUE algorithm in TACON[J]. Systems Engineering and Electronics, 2016, 36(8): 1752-1757.(in Chinese)
[11] 王炜, 李丹, 姜礼平, 等.可处理多普勒量测的最佳线性无偏估计算法[J]. 电子与信息学报, 2015, 37(6): 1336-1342.Wang Wei, Li Dan, Jiang Lipin, et al. The Best Linear Unbiased Estimation Algorithm with Doppler Measurements[J]. Journal of Electronics & Information Technology, 2015, 37(6): 1336-1342.(in Chinese)
[12] 李为, 李一平, 封锡盛. 基于卡尔曼滤波预测的无偏量测转换方法[J]. 控制与决策, 2015, 30(2): 229-235.Li Wei, Li Yipin, Feng Xisheng. Tracking with prediction-conditioned unbiased converted measurements[J]. Control and Decision, 2015, 30(2): 229-235.(in Chinese)
[13] Sheng Hu, Zhao Wenbo, Wang Jingen. Interacting multiple model tracking algorithm fusing input estimation and best linear unbiased estimation filter[J]. IET Radar, Sonar & Navigation, 2017, 11(1): 70-77.
[14] 盛琥, 王金根, 王立明, 等. 量测转换卡尔曼滤波在塔康导航中的应用[J]. 信号处理, 2015, 31(1): 34-38.Sheng Hu, Wang Jingen, Wang Liming, et al. Application of Converted Measurements Kalman Filter for TACAN Navigation[J]. Journal of Signal Processing, 2015, 31(1): 34-38.(in Chinese)
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