A TERM PAPER ON WIRELESS SENSORS BY ME
Advancements in
sensing, microelectronics and wireless communications technologies are paving the way for the development of
a new breed of integrated wireless sensing devices.
The relatively simple devices that we envision are akin to the sensory receptors of the nervous system in that they
are capable of detecting changes in the environment due to stimuli. In this paper, we examine the advancements
in location estimation using wireless
sensor networks which is one of its major applications. We try to extract few techniques described by the such as self configuration of wireless
sensor networks using Cramer-Rao’s
method, Probability grid and Experimental analysis of RSSI, Algorithms based on RSSI sampling, ROBUST position
estimation, Path loss location estimation and Nonparametric
Belief Propagation for Self-Localization.
This paper presents an overview of
research trends and challenges
in the design and implementation of large-scale location estimation using wireless sensor network
INTRODUCTION
A wireless sensor network (WSN) consists of spatially distributed autonomous sensors to monitor physical or environmental conditions,
such as temperature, sound, pressure, etc. and to cooperatively pass their data through the network to a main location. The WSN is built of "nodes" – from a few to several hundreds or even thousands, where each
node is connected to one (or sometimes several) sensors. Each such sensor network node has typically several
parts: a radio transceiver with an internal antenna or connection to an external antenna, a microcontroller, an electronic circuit for interfacing with the sensors
and an energy source, usually a battery or an embedded form of energy
harvesting. The WSN is built of "nodes"
– from a few to several hundreds or even thousands, where each node is connected to one (or sometimes several)
sensors. Each such sensor network node has typically
several parts: a radio transceiver with an internal antenna or connection to an external
antenna, a microcontroller, an electronic circuit for interfacing with the sensors and an energy source, usually a battery or an embedded form of energy
harvesting.
APPLICATIONS
1.
Area monitoring
Area monitoring is a common application of
WSNs. In area monitoring, the WSN is
deployed over a region where some phenomenon is to be monitored.
2.
Environmental/Earth monitoring
The
term Environmental Sensor Networks, has evolved to cover many applications of WSNs to earth
science research. This includes sensing volcanoes, oceans, glaciers, forests, etc.
3.
Water/Waste water
monitoring
Monitoring
the quality and level of water includes many activities such as checking the quality of underground or surface water and
ensuring a country’s water
infrastructure for the benefit of both human and animal. The area of water quality monitoring
utilizes wireless sensor networks and many manufacturers have launched fresh
and advanced applications for the purpose.
4. Agriculture
Using
wireless sensor networks within the agricultural industry is increasingly common; using a wireless network frees the farmer from
the maintenance of wiring
in a difficult environment. Gravity feed water systems can be monitored using pressure
transmitters to monitor water tank levels, pumps can be controlled using wireless
I/O devices and water use can be measured and wirelessly transmitted
back to a central control center for billing. Irrigation automation enables more efficient
water use and reduces waste.
5. Passive localization and tracking
The
application of WSN to the passive localization and tracking of non- cooperative targets (i.e., people
not wearing any tag) has been proposed by exploiting
the pervasive and low-cost nature of such technology and the properties
of the wireless links which are established in a meshed WSN infrastructure.
6. Passive localization and tracking
The
application of WSN to the passive localization and tracking of non- cooperative targets (i.e., people
not wearing any tag) has been proposed by exploiting
the pervasive and low-cost nature of such technology and the properties
of the wireless links which are established in a meshed WSN infrastructure.
7. Smart home monitoring
Monitoring
the activities performed in a smart home is achieved using wireless sensors embedded within everyday objects forming a WSN. State changes to objects based on human manipulation are captured by the
wireless sensors network
enabling activity-support services.
PLATFORMS
Hardware
One major challenge in a WSN is to produce low cost and tiny sensor nodes. There are an increasing number of small companies
producing WSN hardware and the commercial situation
can be compared to home computing in the 1970s. Many of the nodes are still in the research and development stage,
particularly their software. Also inherent to sensor network adoption is the use very low power methods for data
acquisition.
Software
Energy is the scarcest resource of WSN nodes, and it
determines the lifetime of WSNs. WSNs
are meant to be deployed in large numbers in various environments, including remote and hostile regions, where
ad-hoc communications are a key component.
Operating systems
Operating
systems for
wireless sensor network nodes are typically less complex than general-purpose operating systems. They
more strongly resemble embedded systems, for two
reasons. First, wireless sensor networks are typically deployed with a
particular application in mind,
rather than as a general platform. Second, a need for low costs and low power leads most wireless sensor
nodes to have low-power microcontrollers ensuring that mechanisms such as virtual memory are either
unnecessary or too expensive to implement.
Literature
Review
Neiyer Correal et.al. Proposed the challenges and
opportunities in the wireless sensor networks
[1]. As advancements in sensing, microelectronics and wireless communications technologies are paving the way
for the development of a new breed
of integrated wireless sensing devices.
The relatively simple devices that we envision are akin to the
sensory receptors of the nervous system in that they are capable of detecting changes in the environment due to stimuli. As
are their biological counterparts,
these \RF neurons" or
neuRFon devices are endowed with the ability to associate, producing efficient sensory networks. These pervasive
wireless sensor networks may potentially have
an unprecedented impact on the way we interact with our surroundings, by providing
a sensory fabric, linking cyberspace to our surrounding environment. Many issues
must be addressed in order to bring this unconventional communication centric vision to mainstream. This paper
presented an overview of research trends and challenges in the design and implementation of large-scale wireless embedded networks.
As the technological
advances are making ultra low-power low-cost wireless devices on a chip
feasible. In order to achieve a vision of pervasive wireless sensor networking researchers must address many
technological challenges. This paper provides an
overview of key research areas in academic, government, and industry, with a slant toward position location. It is our position that position location is a key application enabler. Research into
accurate location techniques, free of
infrastructure, will translate into
greater ease of installation and usefulness of sensor data. Paramount to the success of the wireless sensor network
concept is achieving unprecedented
end-to- end energy efficiency across
all layers of the system architecture. Integral
to achieving this goal is the
development of experimental test beds, as they are invaluable to the exploration
of the design space and the minimization of technical risks. As implementations
reduce in size and energy consumption, prototypes will demonstrate compelling
applications and point in new directions for further applications.
Neal
Patwari et.al. proposed Relative Location Estimation in Wireless Sensor
Networks
[2]. Self-configuration in wireless sensor
networks is a general class of estimation of problems which we study via the
Cramer-Rao bound (CRB). Specifically, we consider sensor location estimation
when sensors measure received signal strength (RSS) or time of-arrival (TOA)
between themselves and neighboring sensors. A small fraction of sensors in the
network have known location while the remaining locations must be estimated. We
derive CRBs and maximum likelihood estimators (MLEs) under Gaussian and
lognormal models for the TOA and RSS measurements, respectively. An extensive
TOA and RSS measurement campaign in an indoor office area illustrates MLE
performance. Finally, relative location estimation algorithms are implemented
in a wireless sensor network test bed and deployed in indoor and outdoor
environments. The measurements and test bed experiments demonstrate 1 m RMS
location errors using TOA, and 1 m to 2 m RMS location errors using RSS.
This
article has been to show the accuracy with which wireless sensor networks can
estimate the relative sensor locations. The results should help researchers determine
if the accuracy possible from relative location estimation can meet their
application requirements. This article began by proving that location
estimation variance bounds (CRB) decrease as more devices are added to the
network. Next, it was shown that CRBs can be readily calculated for arbitrary numbers
and geometries of devices, and several examples were presented. Sensor location
estimation with approximately 1 m RMS error has been demonstrated using TOA
measurements. However, despite the reputation of RSS as a coarse means to
estimate range, it can nevertheless achieve an accuracy of about 1 m RMS in a
test bed experiment. Fading outliers can still impair the RSS relative location
system, implying the need for a robust estimator. Future experimentation is needed
to verify the variance of location estimators due to the non-ergodic nature of
shadowing. Analysis can quantify the effect of ‘nuisance’ channel parameters,
and can be extended to consider the effects of multi-user interference on
sensor location estimation.
Radu
Stoleru et.al. proposed Location
Estimation Scheme for Wireless Sensor Networks
using probability grid [3]. Location information is of paramount
importance for Wireless Sensor
Networks (WSN). The accuracy of collected data can significantly be affected by an imprecise positioning
of the event of interest. Despite the importance of location information, real system implementations, that do not
use specialized hardware for
localization purposes, have not been successful. In this paper, they proposed a
location estimation scheme that uses a
probabilistic approach for estimating the location
of anode in a sensor network. Our localization scheme makes use of additional knowledge of topology
deployment. We assume a sensor network is deployed in a controlled manner, where the goal of the deployment is to form a
grid topology. We evaluate our
localization scheme through simulations, showing localization errors as low as 3% of radio range. We outperform similar
localization schemes by obtaining 50% less
error in localization, when compared to them. We also evaluate our localization
solution and the DV-Hop scheme in a real implementation, obtaining an average
error in location of 79% of radio
range, outperforming DV-Hop by approximately 40%. We analyze the significant differences in performance between simulations and a real
implementation and stress the importance
of further evaluations of real
implementations. The result is an
effective and realistic protocol that works in an actual implementation, under certain assumptions,
because it exploits deployment information.
In
this paper they presented a localization scheme, called the Probability Grid
that can be used in WSN which have been deployed
in a grid topology. This scheme was inspired
by a similar solution, called DV-Hop, from Rutgers, which use shop count, from anchors to sensor nodes, as a measure of
distance to known locations. The DV-Hop scheme
is more general than this solution, since it does not use the knowledge about deployment topology. However, this
generality does not help, since the errors are high in practical deployments. Probability Grid is more resistant than
DV-Hop to situations when the hop count
is not a very accurate measure of the distance between two points. This is due to the fact that in real
deployments, the radio range is not circular. Previous research has shown the presence of long links, backward
links or stragglers and a significant deviation
from a circular radio pattern. Using a probabilistic approach, the Probability Grid
considers the hop count for a particular distance to be a discrete random
variable that has a Poisson
distribution. Our solution is completely distributed and does not require special infrastructure. It only
requires, as similar solutions do, to have a small percentage of the nodes, called anchors, aware of their position.
They planned to extend their
work in the following directions: a) empirically obtain a real distribution of
hop counts for different distances. In simulations and limited experimental
verification, a Poisson distribution
proved satisfactory, however, from an empirically obtained distribution, we expect higher accuracy
in a real system deployment; b) each node, through
beaconing, can acquire additional
information about its neighbors positions. This
can serve as a reinforcement of accuracy of its own location computation and eliminate cases where multiple nodes localize themselves
to the same position in the grid; c)
employ local flooding from anchors to the adjacent nodes. They observed that
the contribution made to the precision in position, made by anchors
further away is much smaller
than the contribution made by the anchors closer to the node; d) investigate
the possibility of regionally centralizing the hop
count information, in an attempt to better compute
the optimal positioning of nodes in the
grid, in order to decrease the total degree
of uncertainty/entropy. Entropy based approach for target localization is proposed by Wang et al. Their entropy-based
sensor selection heuristic objective is to reduce
the entropy of the target location distribution. Similarly, they plan on using
the centralized approach in order to
reduce the entropy of the sensor location distribution.
Mohit
Saxena et.al. proposed Experimental Analysis of RSSI-based Location
In
this work, their major objective has been to quantify how good and accurate is
the RSSI model in a wireless sensor network to estimate the location of a cooperative
target. They have classified their observations in two broad categories, the
first ones are based on a calibration based analysis and the second ones are
based on a full - fledged scheme for location estimation, the k - nearest
signal space neighbor match algorithm. Our results are encouraging and we are able
to achieve an accuracy of nearly 1.1 meters with 90% probability in indoor
environment. In the first set of results, they quantified the relationship between
relative error and actual distance which we empirically prove to be multiplicative.
Once we have a good quantification of the signal strength model, we implemented
a location estimation scheme on this basis. The first relationship which comes
to surface is the variation of accuracy with changes in the control parameter
k. Next they investigated the impact of variation in mote orientations on the
accuracy of location estimation. Appropriate choice of k within the OCV ranges
proved to give more accurate results. Choosing maximal signal strength
fingerprints while building the offline signal space, makes the location
estimation more independent of user orientation. They also observe that the
performance of our system improves as the size of the radio map is enhanced by
increasing the number of grid points - N. One of the extensions to this system
built using a WSN could be to analyze how the accuracy levels vary as we increase
the number of targets being tracked at the same time from one to more. As they
increase the number of motes being tracked, the number of packets being sampled
at the base station will increase manifold, which can in turn result in the
degradation of sensitivity of the location estimates of the objects. they would
also like to investigate the performance of our system under phenomena such as
shadowing and signal contention between different motes and interference with other
low-power wireless devices, which work on the same frequency channels.
Javad Rezazadeh et.al.
proposed Fundamental Metrics for Wireless Sensor Networks localization [5].
Localization in wireless sensor networks (WSNs) is a broad topic that has
received considerable attention from the research community. The approaches
suggested to estimate location are implemented with different concepts, functionalities,
scopes and technologies. This paper introduces a methodological approach to the
evaluation of localization algorithms and contains a discussion of evaluation
criteria and performance metrics followed by statistical empirical simulation
models and metrics that affect the performance of the algorithms and hence
their assessment. The major contribution of this paper is to analyze and
identify relevant metrics to compare different approaches on the evaluation of
localization schemes.
In this paper they
presented, different methods to implement localization and the main metrics that a system designer has to take
into account to understand and value the different
location-sensing systems. In the simulation results of various localization schemes, where the accuracy was examined
through the trade-offs between accuracy and measurement
performance, percentage of anchors, deployment of anchors, density of non anchors, etc. Besides randomly generated
networks, a typical deployment of nodes is the grid
of non-anchor nodes within a particular area. The localization accuracy of a
solution is usually quantified
using the average Euclidean distance between the estimated locations and the true locations normalized
to the radio range or other system metrics. For mobility-assisted localization, the effect of node density is not
as important as in static localization
scenarios. In addition, communication computation cost may not be of same importance to the off-line simulations as to
the real implementations.
Charalampos
Papamanthou et.al. proposed Algorithms
for Location Estimation
Based on RSSI sampling [6].In
this paper, they re-examine the RSSI measurement mode for location estimation and provide the first detailed
formulation of the probability distribution of the position of a
sensor node [5]. They also show how
to use this probabilistic model to
efficiently compute a good estimation of
the position of the sensor node by sampling multiple readings from the
beacons (where we do not merely use
the mean of the samples) and then minimizing a function with an acceptable computational effort. The results of the simulation of our method in TOSSIM indicate that the location of the sensor node can be
computed in a small amount of time and that the
quality of the solution is competitive with previous approaches.
In this paper, they have
analyzed the RSSI model for location estimation in sensor networks. Given a normal distribution for the error
in dBm, they computed the correct
probability distribution of the sensor’s location and then they adopted this probability distribution in a theoretical
analysis of sampling the measurements for location
estimation. They finally gave a simple algorithm that can be executed on sensor
nodes; its complexity, for a
constant number of beacons, is proportional to the size of the sample. Location estimation in sensor networks
presents several trade-offs. If higher accuracy
is desired, one has to deploy more beacons or use more samples. Using a large number of beacons and samples causes
significant energy consumption. The energy- optimal
case occurs when only three beacons are
deployed and an estimation of the actual
point is based on the probability
distribution computed by taking into consideration
only one measurement. This solution, however, gives unacceptable errors. Additionally, performing computations with the exact
probability distribution is unrealistic,
since it involves complex formulas.
Hence, they were to depend on few measurements,
off-line computed data must be stored as tables within the sensor, which immediately creates a storage problem. However, one can use more samples, thus increasing energy consumption.
They
studied the problem of secure position determination and location verification in wireless sensor networks.
We proposed a sensor initiated localization algorithm
called Robust Position Estimation (ROPE), that achieves robust sensor localization and verification of sensor
location claims even in the presence of malicious adversaries. Compared to previously proposed schemes, ROPE
allows sensors to estimate their
own location without the assistance of a central authority, while being resistant
to severe types of attacks such as the
wormhole attack, node impersonation and jamming of transmissions. We introduced a new metric called Maximum Spoofing
Impact (MSI) for evaluating the impact of
possible attacks, and showed that ROPE limits the MSI even for low densities of reference points.
Guoqiang
Mao et.al. proposed Path
Loss Exponent Estimation for Wireless Sensor
Network Localization [8].The wireless received signal strength (RSS) based localization techniques have attracted significant
research interest for their simplicity. The
RSS based localization techniques can be divided into two categories: the
distance estimation based and the RSS
profiling based techniques. The path loss exponent (PLE) is a key parameter in the distance
estimation based localization algorithms, where distance is estimated from the RSS. The PLE measures the rate at
which the RSS decreases with
distance, and its value depends on the specific propagation environment. Existing techniques on PLE estimation rely on
both RSS measurements and distance measurements
in the same environment to calibrate the PLE. However distance measurements can be difficult and expensive
to obtain in some environments. In this paper
they proposed several techniques for online calibration of the PLE in wireless sensor networks
without relying on distance measurements. They demonstrated that it is possible to estimate the PLE using only
power measurements and the geometric constraints
associated with planarity in a wireless sensor network. This may have a significant impact on distance-based wireless
sensor network localization.
In
this paper, they presented some techniques for online calibration of path loss exponent in wireless sensor networks
without relying on distance measurements. Specifically,
techniques were proposed which are based on different assumptions about
knowledge
of distance information. The first technique assumes that the probability distribution of distance between
neighboring sensors is known. Then an algorithm similar to the quantile-quantile plot was proposed, which can estimate the
path loss exponent accurately
using a small number of received power measurements. However this assumption of knowing the distance distribution
can be unrealistic in some applications. This
has motivated us to find a more generic technique without using any distance information. Then they presented a
technique based on the Cayley-Menger determinant, which estimates the path loss exponent using only power
measurements and the geometric
constraints associated with planarity in a wireless sensor network. The technique can give an accurate
estimate of alpha when there is no noise in power measurements, but it has a large bias in the presence of noise. A
pattern matching technique approximately
correcting the bias is proposed based on the empirical observation that the relationship between E(^alpha), sigma db
and alpha is independent of the
distribution of the vertices of various quadrilaterals and the shape of the
area in which vertices of the
quadrilaterals are located. They also presented an improvement of the earlier technique using data fusion. The proposed algorithms may have
significant impact on
distance-based wireless sensor network localization, where distance is estimated from the received signal
strength measurements. In this paper, we observed the empirical law that the relationship between E(^alpha), sigma
dB and alpha is independent of the
distribution of the vertices of the quadrilaterals and is also independent of
the shape of the area in which the
vertices of the quadrilaterals are located. It is desirable to obtain an analytical expression of
the relationship between E(^alpha), sigma dB and alpha. This is the direction of our future research. Furthermore,
the proposed algorithm relies on
the log-normal propagation model in Eq.
1 and Eq. 2 in the sense that the maximum
likelihood estimator shown in Eq. 11 may have a different form when the received signal strength has a
different model. Although the log-normal propagation model is a popular model for wireless networks, there are
environments in which the log- normal
propagation model is not the best model. In that case, a technique needs to be developed to select the best model and choose
the best estimator for distance to replace Eq.
11 accordingly. Therefore how to develop an algorithm for environments in which
the log-normal propagation model does
not apply is also a future research topic.
Om
Prakash Sahu et.al. proposed Practical Solution for Location Estimation in Manually Deployed Wireless Sensor
Networks [9]. This paper addresses the existing research and adds another aspect of functionality by
incorporating pertinent sensor nodes to
provide a dynamic location discovery and estimation. The software used provides
an easy graphical user
interface to visualize a particular location in accordance with geographical latitude and longitude. A simple real time location
estimation technique is worked out for
wireless sensor networks based on manual deployment of sensors. The proposed scheme finds more efficient
solutions with less quantity of sensors as compared to existing deployment schemes. The set up is evaluated exclusively
in real environments using IRIS
sensor nodes supported by a global positioning system module to provide visualization of an outdoor location.
The results are offered by Google Earth application.
The
technique to deploy sensor nodes manually is currently used in several projects, and there are scenarios of
real system deployments, where manual deployment is the only solution. Results show that the deployed nodes estimate
their relative latitude and
longitude positions for a reference point. The average localization error is
mainly due to the limitations of
the devices used, because for location information, the nodes completely rely on the global positioning
system and localizing themselves in the middle of
their proximate placements or reference points.
In
future, performance evaluation and scalability will be done through simulation.
The experience from the current deployment
of the sensors can be used further to address the
aerial deployment. Considering the rate, altitude, and trajectory of sensor
nodes the actual location information
at the time of initial deployment, can also be obtained using our solution, giving a starting
point towards a better and precise localization scheme. The authors are working towards making it more
common and adaptable for other user communities
also.
Alexander
T.Ihler et al. proposed Nonparametric Belief Propagation for Self- Localization of Sensor Networks [10]. Automatic
self-localization is a critical need for the
effective use of ad hoc sensor networks in military or civilian applications.
In general, self-localization involves
the combination of absolute location information (e.g., from a global positioning system) with relative
calibration information (e.g., distance measurements
between sensors) over regions of the network. Furthermore, it is generally desirable to distribute the computational
burden across the network and minimize the amount
of inter sensor communication. They demonstrated that the information used for sensor localization is fundamentally local
with regard to the network topology and use this
observation to reformulate the problem within a graphical model framework. We then present and demonstrate the utility of nonparametric belief
propagation (NBP), a recent generalization
of particle filtering, for both estimating sensor locations and representing location uncertainties.
NBP has the advantage that it is easily implemented in a distributed fashion, admits a wide variety of statistical
models, and can represent multimodal
uncertainty. Using simulations of small to moderately sized sensor networks, we show that NBP may be made robust to
outlier measurement errors by a simple model augmentation,
and that judicious message construction can result in better estimates. Furthermore, we provide an analysis of
NBP’s communications requirements, showing that
typically only a few messages per sensor are required, and that even low
bit-rate approximations of these
messages can be used with little or no performance impact.
They proposed a novel
approach to sensor localization, applying a graphical model framework and
using a nonparametric message-passing algorithm to solve the ensuing inference problem. The methodology has
a number of advantages. First, it is easily
distributed (exploiting local computation
and communications between nearby sensors),
potentially reducing the amount of communications required. Second, it computes and makes
use of estimates of the uncertainty, which may subsequently be used to determine the reliability of each
sensor’s location estimate. The estimates easily accommodate complex, multimodal
uncertainty. Third, it is straightforward to incorporate
additional sources of information, such as a model of the probability of obtaining a distance measurement
between sensor pairs. Finally, in contrast to other methods, it is easily extensible to non-Gaussian noise
models, which may be used to model
and increase robustness to measurement outliers. In empirical simulations,
NBP’s performance is comparable
to the centralized MAP estimate, while additionally representing the inherent uncertainties. They have also shown how
modifications to the NBP algorithm can
result in improved performance. The NBP
framework easily accommodates an outlier
process model, increasing the method’s robustness to a few large errors in distance
measurements for little to no computation and communication overhead. Also, carefully chosen proposal
distributions can result in improved small- sample
performance, reducing the computational costs associated with calibration. Finally, appropriate message
schedules require very few message transmissions, and reduced-complexity representations may be applied to lessen the cost of each
message transmission with little or no
impact on the final solution. There
remain many open directions for
continued research. First, other message-passing inference algorithms (e.g., max-product) might improve performance if
adapted to high-dimensional non-Gaussian problems.
Also, alternative graphical model representations may bear investigating; it may be possible to retain fewer edges,
or improve the accuracy of BP by clustering nodes.
Given its promising initial performance and many possible avenues of improvement, NBP appears to provide a
useful tool for estimating unknown sensor locations
in large ad hoc networks.
DISCUSSION AND
CONCLUSION
Technological
advances are making ultra low-power, low-cost wireless devices on a chip feasible. In order to achieve a vision of pervasive
wireless sensor networking researchers must
address many technological challenges. This paper provides an overview of key
re-
Search areas in academia,
government, and industry towards position location. This article began by proving that location
estimation variance bounds (CRB) decrease as more
devices are added to the network. Next, it was shown that CRBs can be readily calculated for arbitrary numbers and
geometries of devices, and several examples were presented. Sensor location estimation with approximately
1 m RMS error has been demonstrated
using TOA measurements. In the next paper Using a probabilistic approach, the Probability Grid considers the
hop count for a particular distance to be a
Discrete random variable, that has a
Poisson distribution. Another techniques objective has
been to quantify how good and accurate is the RSSI model in a wireless sensor network to estimate the location of a
cooperative target. In this article the next one was different methods to implement localization and the main metrics
that a system designer has to
take into account to understand and value the different location-sensing
systems. In the next part we studied
the problem of secure position determination and location
Verification in wireless sensor
networks. The next part presented some techniques for online calibration of path loss exponent in wireless sensor
networks without relying on distance
measurements. Specifically, techniques were proposed which are based on different assumptions about knowledge
of distance information. In the last part a novel approach
to sensor localization, applying a graphical model framework and using a nonparametric message-passing
algorithm to solve the ensuing inference problem.
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