校正源状态扰动下Taylor 级数迭代定位方法

doi:10.3969/j.issn.0255-8297.2015.03.006

应用科学学报 ›› 2015, Vol. 33 ›› Issue (3): 274-289.doi: 10.3969/j.issn.0255-8297.2015.03.006

校正源状态扰动下Taylor 级数迭代定位方法

张杰，蒋建中，郭军利

解放军信息工程大学信息系统工程学院，郑州450002

收稿日期:2014-09-04 修回日期:2015-01-06 出版日期:2015-05-30 发布日期:2015-01-06
作者简介:蒋建中，教授，研究方向：通信中的信号处理，E-mail: jiang3721@163.com
基金资助:
国家自然科学基金(No.61104036)资助

Source Localization Using Taylor Series Iteration with Perturbation Calibration of Emitter States

Institute of Information System Engineering, PLA Information Engineering University,
Zhengzhou 450002, China

Received:2014-09-04 Revised:2015-01-06 Online:2015-05-30 Published:2015-01-06

摘要/Abstract

摘要： 目前绝大部分的定位算法只适用于特定的定位场景，而基于Taylor 级数迭代的定
位算法适用于任意定位体制. 为此，针对具有一般普适意义的定位方程，给出一种系统分析
Taylor 级数迭代定位算法的理论框架，分别在校正源状态无误差(情况a) 和校正源状态有误
差(情况b)条件下推导了基于Taylor级数展开的定位方法及其相关性能. 对于情况(a)，给出
了相应的克拉美罗界. 对于情况(b)，首先给出其克拉美罗界，并与情况(a)进行比较. 其次推
导出忽略校正源状态误差时的均方误差理论值，并与克拉美罗界进行比较，发现忽略校正源
状态误差无法达到最优定位精度. 针对上述不足，提出了一种基于Taylor 级数迭代的两步最
优融合算法，并证明其精度可达到克拉美罗界. 最后，利用仿真实验场景验证该算法的性能以
及理论分析的正确性.

关键词: 无源定位, 克拉美罗界, 校正源, Taylor 级数迭代, 两步最优融合定位

Abstract: While most passive localization algorithms are only applicable to certain applications,
the Taylor series iteration (TSI) algorithm is suitable for arbitrary settings. For
this reason, a theoretical framework for deriving localization performance of TSI is discussed.
Two cases, with and without calibration state error, are considered. In the former
case, the corresponding Cramér-Rao lower bound (CRLB) is derived. In the latter case,
the corresponding CRLB is derived and compared with the former case. Mean square error
(MSE) is derived theoretically. Comparison between the theoretical MSE with the CRLB
indicates that accuracy of the source location cannot reach the optimal accuracy without
considering the calibration state error. To overcome the shortcoming, a two-step optimal
fusion localization method based on TSI is proposed, with accuracy reaching that of CRLB.
Passive localization is simulated to verify performance of the proposed algorithm, showing
validity of the theoretical analysis in this paper.

Key words: passive localization, Cramér-Rao lower bound, calibration emitters, Taylor series iteration, two-step optimal fusion localization

中图分类号:

TN911.7

张杰，蒋建中，郭军利. 校正源状态扰动下Taylor 级数迭代定位方法[J]. 应用科学学报, 2015, 33(3): 274-289.

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校正源状态扰动下Taylor 级数迭代定位方法

Source Localization Using Taylor Series Iteration with Perturbation Calibration of Emitter States

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