基于两步最小二乘定位的偏差改进算法

doi:10.7527/S1000-6893.2015.0182

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基于两步最小二乘定位的偏差改进算法

张杰, 蒋建中, 郭军利

信息工程大学信息系统工程学院, 郑州 450002

收稿日期:2015-01-30 修回日期:2015-06-15 出版日期:2016-02-15 发布日期:2015-07-19
通讯作者: 张杰,男,硕士研究生。主要研究方向:无源定位。Tel:0371-81622197,E-mail:hpzj242411@163.com E-mail:hpzj242411@163.com
作者简介:蒋建中,男,硕士,教授。主要研究方向:通信中的信号处理。Tel:0371-81622197,E-mail:jiang3721@sina.com;郭军利,男,硕士,副教授。主要研究方向:通信中的信号处理。Tel:0371-81622197,E-mail:gjl@163.com
基金资助:
国家自然科学基金(61104036)

Improved bias algorithm for localization using two-step least square

ZHANG Jie, JIANG Jianzhong, GUO Junli

College of Information System Engineering, University of Information and Engineering, Zhengzhou 450002, China

Received:2015-01-30 Revised:2015-06-15 Online:2016-02-15 Published:2015-07-19
Supported by:
National Natural Science Foundation of China(61104036)

摘要/Abstract

摘要：

针对传统最小二乘(LS)定位算法在噪声较大时会出现有偏估计的问题。首先详细推导了传统两步最小二乘算法在时差角度联合定位场景下的理论偏差,给出了出现偏差的原因;其次对误差均值加入二次约束条件,提出一种基于时差角度联合定位的改进算法,并详细推导新算法的理论偏差以及均方误差。相比于其他加限制条件的方法,新算法能有效降低估计偏差,另外由于其不需要进行特征值分解且能得到闭式解,计算复杂度较小。仿真结果表明,新算法在保持原有均方误差(MSE)的前提下能显著降低估计偏差,其定位偏差与最大似然估计器相当。

关键词: 多站无源定位, 有偏估计, 加权最小二乘, 时差角度联合定位, 均方误差

Abstract:

Bias of a source location estimate using classical least square(LS) algorithm is significant when the noise is large. This paper started by deriving the theoretical bias of the time-differences-of-arrival(TDOA) and angle-of-arrival(AOA) positioning which used the classical two-step LS algorithm and found the reason which caused the bias. Then the improved TDOA and AOA algorithm was proposed by adding the quadratic constraints to the expectation of the error. Compared to other methods with constraints, the novel algorithm can reduce the bias considerably. Furthermore, because the new algorithm does not require eigenvalue decomposition and can obtain the closed-form solution, it has little computation load. Simulation shows that the new method can reduce the bias significantly and obtain the original mean-square error(MSE). The improved algorithm is able to lower the bias to the same level as the maximum likelihood estimator.

Key words: multi-station passive localization, bias estimate, weighted least square, TDOA and AOA jointed localization, mean-square error

中图分类号:

张杰, 蒋建中, 郭军利. 基于两步最小二乘定位的偏差改进算法[J]. 航空学报, 2016, 37(2): 695-705.

ZHANG Jie, JIANG Jianzhong, GUO Junli. Improved bias algorithm for localization using two-step least square[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(2): 695-705.

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

基于两步最小二乘定位的偏差改进算法

Improved bias algorithm for localization using two-step least square

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