无源定位观测方程的两类伪线性化方法及渐近最优闭式解

doi:10.3969/j.issn.0372-2112.2015.04.014

电子学报 ›› 2015, Vol. 43 ›› Issue (4): 722-729.DOI: 10.3969/j.issn.0372-2112.2015.04.014

无源定位观测方程的两类伪线性化方法及渐近最优闭式解

王鼎¹, 张瑞杰², 吴瑛¹

1. 解放军信息工程大学信息系统工程学院, 河南郑州 450000;
2. 解放军信息工程大学四院, 河南郑州 450000

收稿日期:2013-06-13 修回日期:2014-06-22 出版日期:2015-04-25
- 作者简介:
- 王鼎男,1982年生于安徽芜湖,博士,现为信息工程大学信息系统工程学院讲师,主要从事阵列信号处理、无源定位方面的相关研究.E-mail:wang_ding814@aliyun.com;张瑞杰 女,1984年生于河南郑州,博士,现为信息工程大学四院讲师,主要从事网络舆情分析、图像场景分类与检索、无源定位等方面的相关研究.E-mail:rjz_wonder@163.com;吴瑛女,1960年生于河南郑州,硕士,现为信息工程大学信息系统工程学院教授,博士生导师,主要从事现代信号处理的相关研究.E-mail:hnwuying22@163.com
- 基金资助:
- 国家自然科学基金 (No.61201381)

Two Pseudo-Linearization Processing Methods and the Asymptotically Optimal Closed-Form Solutions for Passive Location

WANG Ding¹, ZHANG Rui-jie², WU Ying¹

1. Institute of Information Systems Engineering, Information Engineering University of PLA, Zhengzhou, Henan 450000, China;
2. The Fourth Institute of Information Engineering University of PLA, Zhengzhou, Henan 450000, China

Received:2013-06-13 Revised:2014-06-22 Online:2015-04-25 Published:2015-04-25

摘要/Abstract

摘要：

为避免无源定位中的迭代运算,该文针对两类特殊的无源定位(非线性)观测方程,分别提出将其进行伪线性化处理,从而实现目标位置闭式解算的理论分析框架.首先,在不限定具体物理观测量的前提下,归纳总结出两类将非线性观测方程转化为伪线性观测方程的数学模型,并推导出用于目标定位的加权线性最小二乘闭式解.接着,利用一阶误差分析方法定量分析两类闭式解的理论定位方差,并证明其参数估计性能均能够达到相应的克拉美罗界(在门限效应发生前),从而证明闭式解的渐近最优性.最后,文中以AOA/TOA联合定位和AOA/TDOA/FDOA联合定位为算例,分别阐述两类伪线性化无源定位方法的具体应用,并通过仿真实验验证文中理论分析的有效性.

关键词: 无源定位, 伪线性方程, 最优闭式解, 理论框架, 克拉美罗界

Abstract:

In order to avoid the iterative computations in passive location,two theoretical analysis frameworks used to solve two kinds of location equations are presented via converting the nonlinear measurement equations into the pseudo-linear equalities.First,two kinds of mathematical model for the pseudo-linearization of two nonlinear measurement equations are formulated,which are not limited to specific physical measurements,and then the corresponding weighted linear least squares (WLS) solutions are derived.Subsequently,the theoretical estimation variances of the two analytical solutions are derived through first-order perturbation analysis methodology,and their theoretical location performances are proved to be able to attain the corresponding Cramér-Rao bound (CRB) before the threshold effect occurs and,hence,the asymptotical optimality of the two pseudo-linearization location methods are verified.Finally,the AOA/TOA location and AOA/TDOA/FDOA location are taken as examples to describe the application of the two pseudo-linearization location methods,and the simulation experiments are conducted to corroborate the effectiveness of the theoretical analysis in this paper.

Key words: passive location, pseudo-linear equation, optimal closed-form solution, theoretical framework, Cramér-Rao bound (CRB)

中图分类号:

TN911.7

王鼎, 张瑞杰, 吴瑛. 无源定位观测方程的两类伪线性化方法及渐近最优闭式解[J]. 电子学报, 2015, 43(4): 722-729.

WANG Ding, ZHANG Rui-jie, WU Ying. Two Pseudo-Linearization Processing Methods and the Asymptotically Optimal Closed-Form Solutions for Passive Location[J]. Acta Electronica Sinica, 2015, 43(4): 722-729.

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无源定位观测方程的两类伪线性化方法及渐近最优闭式解

Two Pseudo-Linearization Processing Methods and the Asymptotically Optimal Closed-Form Solutions for Passive Location

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