Algorithm development for source localization in wireless sensor networks
無線傳感器網絡中的源定位算法研究
Student thesis: Doctoral Thesis
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Award date  15 Feb 2013 
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Permanent Link  https://scholars.cityu.edu.hk/en/theses/theses(21450148be5a4a0c885ccf631f81c1da).html 

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Abstract
Source localization has been one of the fundamental and important problems in a
variety of fields ranging from radar, sonar, and, navigation, to telecommunications,
mobile communications, and wireless sensor networks.
A sensor with a known position is called the anchor and a sensor with an unknown
position is named the source. In this thesis, several algorithms are devised to locate
the source(s) with the use of the noisy distance measurements between the source(s)
and anchors.
Locating a source with timedifferenceofarrival (TDOA) measurements, which is
one of the standard measurements for positioning, is investigated in many research
works. One of the TDOAbased positioning algorithms, the linear least squares (LLS)
technique, is widely used because of its computational efficiency. Twostep weighted
least squares (WLS) and constrained WLS (CWLS) are two common LLS schemes
where an additional variable is introduced to obtain linear equations. However, they
both have the same measurement matrix that becomes illconditioned when the sensor
geometry is a uniform circular array and the source is close to the array center. In
this thesis, a new CWLS estimator is proposed to circumvent this problem. The main
strategy is to separate the source coordinates and the additional variable to different
sides of the linear equations where the latter is first solved via a quadratic equation.
In doing so, the matrix to be inverted has a smaller condition number than that
of the conventional LLS approaches, so that it can provide a superior performance
in different geometry settings. Numerical examples are also included to evaluate the
proposed location estimator by comparing with the existing twostep WLS and CWLS
algorithms as well as the CramérRao lower bound (CRLB).
Employing received signal strength (RSS) measurements, which utilizes the signal
strength received at an array of spatially separated sensors, is considered to be more cost effective than other measurements in hardware. Therefore, being able to
locate a source using RSS measurements in an accurate and lowcomplexity manner
is desirable. Assuming that the source transmit power is known, a twostep WLS
estimator for RSSbased positioning is devised by utilizing the mean and variance of
the squared distance estimates according to the RSS measurements. The first step
estimator is a best linear unbiased estimator without considering the relationship
between unknown parameters while the second one is its improved version by exploiting
the known relationship between the parameter estimates. This algorithm is
then extended to unknown pathloss factor case with relaxation technique. Furthermore,
given that the transmit power is unknown, the differential RSS information
is employed to devise a computationally attractive localization method based on the
twostep WLS approach. The main ingredients in the first step development are to
obtain the unbiased estimates of the ratios of squared ranges and the second step is
to exploit the relationship between the extra variable and the source location. Theoretical
performance analysis of the proposed algorithms is also produced to evaluate
their statistical properties.
In many scenarios, there is more than one source to be located, so it is desirable
to investigate algorithms to estimate the positions of multiple sources for RSSbased
positioning problems. Assuming that the transmit powers are unknown, a twostep
WLS algorithm is devised with noncollaborative RSS measurements in which only
the oneway distances between sources and anchors are used. This twostep WLS
method is different from the proposed one in the single source case; the former utilizes
the RSS measurements directly while the latter employs the differential RSS
information. Moreover, when the pathloss factors are unknown, two nonlinear least
squares (NLS) algorithms are devised. The first one is the maximumlikelihood (ML)
method which is directly devised for all unknown parameters while the second algorithm
is a combination of the LLS and ML techniques. The nuisance parameters,
transmit powers and pathloss factors, are first removed from the RSS measurements
using the separable LLS technique, then the resulting problem is a nonlinear function
of the source positions and can be handled by the ML principle. Numerical examples
show that the second algorithm has a better performance than the first one.
Multidimensional scaling (MDS) algorithm, which transforms the pairwise distance
information into the relative coordinates of sensors, is one of the collaborative
schemes in which all pairwise distances between sources and sources, sources and
anchors, anchors and anchors are employed. Two weighted MDS (WMDS) methods
are proposed to locate the sources for the scenarios of known and unknown transmit
power assuming that the path loss factors are known. By utilizing the unbiased
estimates of the squared ranges, a WMDS algorithm is devised for known transmit
power case, while the other WMDS algorithm is devised for unknown transmit power
case with the use of unbiased estimates of the ratios of squared distances and of the
selected reference squared distance. Simulation results show that these two proposed
WMDS algorithms are comparable to their corresponding CRLBs at sufficiently small
noise conditions.
 Wireless localization, Wireless sensor networks