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Algorithm and Accuracy Analysis of Weighted Maximum Likelihood Estimation

in Multi-station DF Crossing Localization

Zong Junjun

1, a *

,Cui Xunxue

2,b

,Yang Hui

3,c

,Gao Bin

4,d

1,2,,3,4

New Star Research Institute of Applied Technology, Hefei, 230031,P.R.China

a

zjj_2008@163.com,

b

cuixx_2013@163.com,

c

sanpedroman@163.com,

d

563321248@qq.com

Corresponding Author: Zong Junjun.Tel:18909699781. E-mail:zjj_2008@163.com

Keywords: passive localization; direction-finding (DF); crossing localization; weighted maximum

likelihood estimation (WMLE); error analysis

Abstract: In order to solve the non uniform environment of the target area influencing the variance

of DF error, the weighted maximum likelihood estimation (WMLE) algorithm was proposed. In this

algorithm, the effect of the target distance was introduced into MLE. we construct the weighted

vector to make up for the effect when the target distance increase the variance of the DF error

become worse. Theoretical analysis showed that the algorithm of WMLE could further improve the

accuracy of the multi-station DF crossing localization.

Passive acoustic localization has received good attention in the world and obtained considerable

development in the military fields, for its good concealment, strong confidentiality and less

susceptible to interference. Among its many location methods, multi-station DF crossing location is

one of the important. It is a kind of method, by using multi-station DF information to obtain the

location of target, also known as triangulation method. The location accuracy is mainly affected by

the DF’s accuracy, array’s quantity, base-station’s configuration, localization’s algorithm and other

factors, especially when the sensor’s device and array’s configuration was constrained, location

algorithm would become the main factors affecting the location accuracy.

Recently years, many mature localization algorithms have been formed, such as least squares

estimation (LSE), pseudo-linear estimation (PLE), maximum likelihood estimation (MLE). Among

them, the performance of MLE is excellent. When using the MLE to locate the sound point of the

burst, we usually assume the variance (

σ

) of DF error is unchanged. But actually, target region isn’t

an uniform environment,

σ

will be influenced by the target distance. Obviously, from the control

of estimation error, MLE isn’t an effective method. This article according to the point of the account

source, based on the view of Dogancay’s MLE, we construct the WMLE, namely, by setting the

weighted function to compensate for the effect of heterogeneous environment on DF error.

Location Principle

In figure 1, The station position is represented by

(, ,)

T

k kkk

S xyz=

( )

1, 2, ,kn= 

, where

T

denotes matrix transpose. The true location of the stationary target is represented by

4th International Conference on Computer, Mechatronics, Control and Electronic Engineering (ICCMCEE 2015)

© 2015. The authors - Published by Atlantis Press

971

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