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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