作者：裴畔1,2, 丁永红1,2, 马铁华1,2
作者单位：1. 中北大学 仪器科学与动态测试教育部重点实验室, 山西 太原 030051;
2. 中北大学 电子测试技术国家重点实验室, 山西 太原 030051
关键词：机载无源定位;算法精度;平方根球形无味卡尔曼滤波;球面无味变换;鲁棒性;稳定性
摘要：
针对机载无源定位系统中，初始值误差和数值的舍入计算对无味卡尔曼滤波（un-scented Kalman filtering，UKF）算法的定位精度和滤波稳定性影响较大的问题，提出一种基于平方根球形无味的卡尔曼滤波算法（square root spherical unscented Kalman filter，Sqrt-UKFST）。该方法以单位超球体球面无味变换为基础，通过减少采样点数目和球面半径，保证所有采样点在一个单位超球体上，从而提高算法对初始值的鲁棒性，并采用平方根滤波提高算法的数值稳定性。对该算法进行100次Monte-Carlo实验，仿真结果表明，Sqrt-UKFST算法收敛速度快，滤波性能稳定；当初始状态估计误差较大时，Sqrt-UKFST算法的定位精度保持在30%以内，提高系统对初始值的鲁棒性。
Airborne passive location algorithm based on spherical square root unscented Kalman filter
PEI Pan1,2, DING Yonghong1,2, MA Tiehua1,2
1. Key Lab of Instrumentation Science & Dynamic Measurement, North University of China, Taiyuan 030051, China;
2. Key Laboratory of Electronic Measurement Technology, North University of China, Taiyuan 030051, China
Abstract: As the unscented Kalman filtering (UKF) in airborne passive location has greater impact on positioning accuracy and stability because of the initial value and numerical calculation error, an improved smoothing algorithm based on square root spherical unscented Kalman filter(Sqrt-UKFST) is presented. To guarantee that all sampling points on a unit hypersphere algorithm to improve the robustness of the initial value, the algorithm uses the unit hypersphere sphere tasteless converted by reducing the number of sampling points and the spherical radius.And the algorithm utilizes the square root matrix in the process of estimation to improve the stability of the filter. After 100 times Monte-Carlo experiments, simulation results show that the Sqrt-UKFST algorithm has better performance in the filter's stability, convergence velocity and the robustness of the initial value. When the initial state estimation reaches big error, the positioning precision maintained less than 30%.
Keywords: airborne passive location;algorithm accuracy;Sqrt-UKFST;spherical tasteless transformation;robustness;stability
2017, 43(2): 93-97 收稿日期: 2016-06-06;收到修改稿日期: 2016-08-07
基金项目: 国家自然科学基金项目（61471385）
作者简介: 裴畔(1991-),女,山西临汾市人,硕士研究生,专业方向为机载无源定位。
参考文献
[1] 刘学. 机载无源定位技术与跟踪算法研究[D]. 哈尔滨:哈尔滨工程大学,2012.
[2] 平殿发,司文健,苏峰. 基于多普勒变化率的机载无源定位方法研究[J]. 中国雷达,2010,29(4):4-6.
[3] 侯建民. 基于相位差变化率的空中运动单站对地面固定目标的无源定位[D]. 合肥:合肥工业大学,2015.
[4] 张志. 机载单站无源定位关键技术研究[D]. 南京:南京理工大学,2013.
[5] 申正义,闫抒升,王晓军,等. 修正的EKPF算法在固定单站被动目标跟踪中的应用[J]. 现代防御技术,2015(2):116-121,153.
[6] 黄耀光,李建新,高博. 基于UKF的单站无源定位改进算法[J]. 现代雷达,2012,34(11):45-48.
[7] QIU L B, SU H Y, HAO H, et al. Application of UKF algorithm in airborne single observer passive location[J]. Advanced Materials Research,2011(267):356-362.
[8] AI-HUSSEIN A, HALDAR A. Unscented Kalman filter with unknown input and weighted global iteration for health assessment of large structural systems[J]. Structural Control and Health Monitoring,2016,23(1):156-175.
[9] ZHAO H S, WEN Z Y, YU H P. A new method of multi-sensor data fusion based on multiscale analysis and UKF[J]. Internatonal Journal of Control and Automation,2016,9(2):329-342.
[10] 黄耀光,高博,李建新,等. 基于施密特正交变换UKF的单站无源定位算法[J]. 电光与控制,2013,20(02):37-40.
[11] 黄耀光,高博,李建新,等. 基于平方根UKF双向滤波的单站无源定位算法[J]. 数据采集与处理,2013,28(02):207-212.
[12] ZHAO K C, YOU Z. Square root spherical simplex unscented kalman filter for micro satellite attitude measurement[A]. 2nd International Conference on Information Engineering and Computer Science-Proceedings(ICIECS2010)[C]//2nd International Conference on Information Engineering and Computer Science-Proceedings.ICIECS,2010.
[13] HTET A, KAY S L, SHU T G. State-of-charge estimation of lithiumion battery using square root spherical unscented kalman filter(Sqrt-UKFST) in nanosatellite[J]. IEEE Journals & Magazines,2015,30(9):4774-4783.
[14] LI W X, HUANG C Q, WANG Y, et al. An improved airborne passive location & tracking algorithm using the rate-of-change of phase difference[J]. Journal of Electronics and Information Technology,2013,35(1):68-73.
[15] 万某峰,赵长胜. UKF滤波中蒙特卡洛采样策略比较分析[J]. 测绘通报,2012(12):37-39.
[16] 黄小平,王岩. 卡尔曼滤波原理及应用:Matlab仿真[M].北京:电子工业出版社,2015:71-79.
