U.S. patent number 11,304,173 [Application Number 17/006,478] was granted by the patent office on 2022-04-12 for node location tracking method.
This patent grant is currently assigned to Korea Institute of Science and Technology. The grantee listed for this patent is KOREA INSTITUTE OF SCIENCE AND TECHNOLOGY. Invention is credited to Doik Kim, Jung Hee Kim.
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United States Patent |
11,304,173 |
Kim , et al. |
April 12, 2022 |
Node location tracking method
Abstract
Provided is a node location tracking method, including an
initial localization step of estimating initial locations of a
robot and neighboring nodes using inter-node measurement and a Sum
of Gaussian (SoG) filter, wherein the initial localization step
includes an iterative multilateration step of initializing the
locations of the nodes; and a SoG filter generation step of
generating the SoG filter.
Inventors: |
Kim; Doik (Seoul,
KR), Kim; Jung Hee (Seoul, KR) |
Applicant: |
Name |
City |
State |
Country |
Type |
KOREA INSTITUTE OF SCIENCE AND TECHNOLOGY |
Seoul |
N/A |
KR |
|
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Assignee: |
Korea Institute of Science and
Technology (Seoul, KR)
|
Family
ID: |
1000006236536 |
Appl.
No.: |
17/006,478 |
Filed: |
August 28, 2020 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20210266861 A1 |
Aug 26, 2021 |
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Foreign Application Priority Data
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Feb 21, 2020 [KR] |
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10-2020-0021369 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H04W
64/003 (20130101); G01S 5/0289 (20130101); G01S
5/0294 (20130101) |
Current International
Class: |
H04W
24/00 (20090101); H04W 64/00 (20090101); G01S
5/02 (20100101) |
Field of
Search: |
;455/456.1,556.1,462.1,41.2,41.3 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Gaussian Sum Filters for Space Surveillance: Theory and Simulations
; Joshua T. Horwood,* Nathan D. Aragon, .dagger. and Aubrey B.
Poore; Journal of Guidance, Control, and Dynamics; vol. 34, No. 6,
Nov.-Dec. 2011. cited by examiner .
A. Torres-Gonzalez et al., "Efficient Robot-Sensor Network
Distributed SEIF Range-Only SLAM," IEEE International Conference on
Robotics & Automation, 2014, pp. 1319-1326. cited by applicant
.
G. Vallicrosa et al., "AUV Single Beacon Range-Only SLAM with a SOG
Filter," IFAC--PapersOnLine, 2015, vol. 48, Issue 2, pp. 26-31.
cited by applicant .
Jose-Luis Blanco et al., "A Pure Probabilistic Approach to
Range-Only SLAM," IEEE International Conference on Robotics and
Automation, 2008, pp. 1436-1441. cited by applicant .
Jose-Luis Blanco et al., "Efficient Probabilistic Range-Only SLAM,"
IEEE/RSJ International Conference on Intelligent Robots and
Systems, 2008, pp. 1017-1022. cited by applicant .
Joseph Djugash et al., "Range-Only SLAM for Robots Operating
Cooperatively with Sensor Networks," Proceedings of the 2006 IEEE
International Conference on Robotics and Automation, 2006, pp.
2078-2084. cited by applicant .
N. M. Kwok et al., "Bearing-only SLAM Using a SPRT Based Gaussian
Sum Filter," Proceedings of the 2005 IEEE International Conference
on Robotics and Automation, 2005, pp. 1109-1114. cited by
applicant.
|
Primary Examiner: Arevalo; Joseph
Attorney, Agent or Firm: Rabin & Berdo, P.C.
Claims
What is claimed is:
1. A node location tracking method, comprising: an initial
localization step of estimating initial locations of a robot and
neighboring nodes using inter-node measurement and a Sum of
Gaussian (SoG) filter, and a movement based tracking step of
tracking a location or movement of the neighboring nodes using
measurement information between the robot and the neighboring nodes
and measurement information between the neighboring nodes, wherein
the initial localization step includes: an iterative
multilateration step of initializing the locations of the nodes;
and a SoG filter generation step of generating the SoG filter.
2. A node location tracking method, comprising: an initial
localization step of estimating initial locations of a robot and
neighboring nodes using inter-node measurement and a Sum of
Gaussian (SoG) filter, wherein the initial localization step
includes: an iterative multilateration step of initializing the
locations of the nodes; and a SoG filter generation step of
generating the SoG filter; and wherein the iterative
multilateration step comprises initializing the locations of a
first three nodes to P.sub.0(n)=(x.sub.0(n), y.sub.0(n))=(0,0),
P.sub.1(n)=(x.sub.1(n), y.sub.1(n))=(d.sub.01,0),
P.sub.2(n)=(x.sub.2(n),
y.sub.2(n))={(d.sub.01.sup.2+d.sub.02.sup.2+d.sub.03.sup.2)/x.sub.1(n),
(d.sub.02.sup.2-x.sub.2.sup.2(n))}, and the location of another
node is initialized by the following Equation:
.function..times..function..function..times..times..times..times..times..-
function..+-..times..function. ##EQU00010## where m is an index of
the node other than the three nodes and is an integer of 3 or
greater, d.sub.01 is a distance between a 0.sup.th node and a first
node, d.sub.0m is a distance between the 0.sup.th node and an
m.sup.th node, and d.sub.1m is a distance between the first node
and the m.sup.th node.
3. A node location tracking method, comprising: an initial
localization step of estimating initial locations of a robot and
neighboring nodes using inter-node measurement and a Sum of
Gaussian (SoG) filter, wherein the initial localization step
includes: an iterative multilateration step of initializing the
locations of the nodes; and a SoG filter generation step of
generating the SoG filter; and wherein the generation of the SoG
filter is performed by generating a mean m.sup.k.sub.ij, a
covariance C.sup.k.sub.ij, and a weight w.sup.k.sub.ij of the
filter,
.function..times..times..times..times..times..pi..times..times..function.-
.times..times..times..times..times..pi..times..times..times..function..sig-
ma..sigma..function..times. ##EQU00011## where Vr is a radial unit
vector, Vt is a tangential unit vector, .sigma..sub.r.sup.2 is a
radial distribution, .sigma..sub.t.sup.2 is a tangential
distribution, and N is a number of Gaussian distributions.
4. The node location tracking method according to claim 3, wherein
the initial localization step further comprises a SoG filter
updating step that is performed by updating the weight, and the SoG
filter updating step comprises computing a likelihood
l.sub.ij,m.sup.k using a measured distance d.sub.mj obtained from
the neighboring nodes, and subsequently updating the weight
w.sup.k.sub.ij using the likelihood l.sub.ij,m.sup.k.
5. The node location tracking method according to claim 4, wherein
the initial localization step further comprises a SoG filter
merging step of merging a plurality of SoG filters of the
neighboring nodes to generate a Gaussian distribution, and the SoG
filter merging step is performed using [Equation 1] to [Equation
3]:
.function..times..times..times..times..times..times..times..times..times.-
.times..times..times..times..function..times..times..times..times..times..-
times..times..times..function..times..times..times..times..times..times..t-
imes..times..times..times..function..times..times..times..function..times.-
.times. ##EQU00012## wherein in [Equation 1] to [Equation 3],
P.sub.i(n+1) denotes an estimated location of an i.sup.th node at
an n+1.sup.th iteration, m.sup.k.sub.ij denotes a mean of the
filter, w.sup.k.sub.ji denotes the weight, C.sub.i(n+1) denotes a
covariance of a node newly estimated by the SoG filter merging
step, and C.sub.ji.sup.k denotes a covariance of
m.sup.k.sub.ji.
6. The node location tracking method according to claim 5, further
comprising: a weight transfer step of transferring a maximum weight
to surrounding weights with respect to an index k.sub.max having
the maximum weight in the SoG filter distribution using [Equation
4] and [Equation 5]:
.times..times..times..times..times..times..times..times..pi..times..t-
imes..sigma..times..function..times..times..sigma..times..times.
##EQU00013## wherein in [Equation 4] and [Equation 5], d.sub.kmax-k
denotes a distance between m.sup.kmax.sub.ij and m.sup.k.sub.ij,
m.sup.kmax.sub.ij is a mean of the SoG filter having the maximum
weight, and .sigma. is a spread of the Gaussian distribution.
7. The node location tracking method according to claim 2, further
comprising: a movement based tracking step of estimating the
location or movement of the neighboring nodes using movement of the
robot from the initial position value of the robot or the
neighboring nodes estimated in the initial localization step.
8. The node location tracking method according to claim 7, wherein
the movement based tracking step comprises a SoG filter resetting
step, a SoG filter updating step, a SoG filter merging step and a
weight transfer step.
9. The node location tracking method according to claim 6, wherein
.sigma. is 3.
Description
CROSS-REFERENCE TO RELATED APPLICATION
This application claims priority to Korean Patent Application No.
10-2020-0021369, filed on Feb. 21, 2020, and all the benefits
accruing therefrom under 35 U.S.C. .sctn. 119, the contents of
which in its entirety are herein incorporated by reference.
BACKGROUND
1. Field
The present disclosure relates to a node location tracking method,
and more particularly, to a node location tracking method for
tracking a node's location without moving a robot.
2. Description of the Related Art
Location recognition technology in sensor network environments is
technology that estimates relative positions using information such
as distances or angles from a known location, and calculates the
locations of nodes using them.
Common methods for measuring locations in sensor network
environments come in a variety of technologies, for example,
methods using infrared, ultrasound, Radio Frequency Identification
(RFID), Ultra WideBand (UWB), Received Signal Strength Indication
(RSSI), camera sensors and light.
Among the above-described technologies, the location measurement
technology using the RSSI of the sensor nodes is not easy to use
due to abrupt changes in RSSI depending on the characteristics of
surrounding environments. To measure the distance using the
irregular RSSI values, many studies are being performed.
Additionally, to detect the locations of the nodes, event
detection, location awareness dependent computing and geographic
tracking are necessary. There are many studies on reliability and
data robustness from the point of view of sensor networks, but for
location awareness, methods and systems for ensuring confidence of
the received signals are challenging.
The traditional location tracking algorithms keep track of the
locations of neighboring nodes by moving a robot. The location
tracking by the robot's movement is affected by both odometry
errors and measurement errors.
Additionally, such location tracking algorithms are applied only
when neighboring nodes are in a static state.
SUMMARY
The present disclosure is directed to providing a node location
tracking method for tracking a node's location without moving a
robot.
The present disclosure is further directed to providing a node
location tracking method for tracking a location using signal
information between a robot and neighboring nodes as well as signal
information between neighboring nodes.
To solve the above-described problem, a node location tracking
method of the present disclosure includes an initial localization
step of estimating initial locations of a robot and neighboring
nodes using inter-node measurement and a Sum of Gaussian (SoG)
filter, wherein the initial localization step includes an iterative
multilateration step of initializing the locations of the nodes,
and a SoG filter generation step of generating the SoG filter.
The iterative multilateration step may include initializing the
locations of first three nodes to P.sub.0(n)=(x.sub.0(n),
y.sub.0(n))=(0,0), P.sub.1(n)=(x.sub.1(n), y.sub.1(n))=(d.sub.01,
0), P.sub.2(n)=(x.sub.2(n),
y.sub.2(n))={(d.sub.01.sup.2+d.sub.02.sup.2+d.sub.03.sup.2)/x.sub.1(n),
(d.sub.02.sup.2-x.sub.2.sup.2(n))}, and the location of other node
may be initialized by the following Equation:
.function..times..function..function..times..times..times..times..times..-
function..+-..times..function. ##EQU00001##
Here, m is an index of the node other than the three nodes and is
an integer of 3 or greater, d.sub.01 is a distance between the
0.sup.th node and the first node, d.sub.0m is a distance between
the 0.sup.th node and the m.sup.th node, and d.sub.1m is a distance
between the first node and the m.sup.th node.
According to an example related to the present disclosure, the
generation of the SoG filter may be performed by generating a mean
m.sup.k.sub.ij, a covariance C.sup.k.sub.ij, and a weight
w.sup.k.sub.ij of the filter,
.function..times..times..times..times..times..pi..times..times..function.-
.times..times..times..times..times..pi..times..times..times..function..sig-
ma..sigma..function..times. ##EQU00002## where Vr is a radial unit
vector, Vt is a tangential unit vector, .sigma..sub.r.sup.2 is a
radial distribution, .sigma..sub.t.sup.2 is a tangential
distribution, and N is the number of Gaussian distributions.
The initial localization step may further include a SoG filter
updating step that is performed by updating the weight, and the SoG
filter updating step may include computing a likelihood
l.sub.ij,m.sup.k using a measured distance d.sub.mj obtained from
the neighboring nodes, and subsequently updating the weight
w.sup.k.sub.ij using the likelihood l.sub.ij,m.sup.k.
The initial localization step may further include a SoG filter
merging step of merging a plurality of SoG filters of the
neighboring nodes to generate a Gaussian distribution, and the SoG
filter merging step may be performed using [Equation 1] to
[Equation 3]:
.function..times..times..times..times..times..times..times..times..times.-
.times..times..times..times..function..times..times..times..times..times..-
times..times..times..function..times..times..times..times..times..times..t-
imes..times..times..times..function..times..times..times..function..times.-
.times. ##EQU00003##
In [Equation 1] to [Equation 3], P.sub.i(n+1) denotes an estimated
location of the i.sup.th node at the n+1.sup.th iteration,
m.sup.k.sub.ij denotes a mean of the filter, w.sup.k.sub.ji denotes
the weight, C.sub.i(n+1) denotes a covariance of the node newly
estimated by the SoG filter merging step, and C.sup.k.sub.ij
denotes covariance of m.sup.k.sub.ij.
The initial localization step may further include a weight transfer
step of transferring a maximum weight to its surrounding weights
with respect to an index k.sub.max having the maximum weight in the
SoG filter distribution using [Equation 4] and [Equation 5]:
.times..times..times..times..times..times..times..times..pi..times..times-
..sigma..times..function..times..times..sigma..times..times.
##EQU00004##
In [Equation 4] and [Equation 5], d.sub.kmax-k denotes a distance
between m.sup.kmax.sub.ij and m.sup.k.sub.ij, m.sup.kmax.sub.ij is
a mean of the SoG filter having the maximum weight, and .sigma. is
a spread of the Gaussian distribution, and may be, for example,
3.
According to another example related to the present disclosure, the
node location tracking method of the present disclosure may further
include a movement based tracking step of estimating the location
or movement of the neighboring nodes more accurately using movement
of the robot from the initial position value of the robot or the
neighboring nodes estimated in the initial localization step.
The movement based tracking step may include a SoG filter resetting
step, a SoG filter updating step, a SoG filter merging step and a
weight transfer step.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a flowchart showing a node location tracking method of
the present disclosure.
FIG. 2 is a conceptual diagram showing a relationship between a
robot and neighboring nodes in a node location tracking method of
the present disclosure.
FIG. 3 is a graph showing a relationship between a robot, a
receiver and neighboring nodes in a node location tracking method
of the present disclosure.
FIG. 4A is a graph showing a Sum of Gaussian (SoG) filter resetting
step.
FIG. 4B is a graph showing a SoG filter updating and merging
step.
FIG. 4C is a graph showing a SoG filter resetting and updating
step.
FIG. 5A is a graph showing the results of Experiment 1 about
position error performance of a node location tracking method of
the present disclosure and different methods.
FIG. 5B is a graph showing the results of Experiment 2 about
position error performance of a node location tracking method of
the present disclosure and different methods.
FIG. 6 is a graph showing node movements in a node location
tracking method of the present disclosure.
FIG. 7 is a graph showing a SoG filter generation step.
FIG. 8 is an algorithm showing a SoG filter updating step.
FIGS. 9A and 9B are graphs showing a weight distribution between
two nodes.
FIG. 10 is an algorithm showing a SoG filter updating step.
FIG. 11 is a graph showing a comparison of performance with/without
a weight transfer step.
DETAILED DESCRIPTION
Hereinafter, the disclosed embodiments will be described in detail
with reference to the accompanying drawings, and identical or
similar elements are given identical or similar reference signs and
redundant descriptions are omitted herein. As used herein, the
suffix "unit" is only given or used to ease the drafting of the
specification, and does not have any meaning or role for
identifying itself. Additionally, in describing the embodiments
disclosed herein, when it is determined that a certain detailed
description of relevant known technology may make the key subject
matter of the disclosed embodiments ambiguous, the detailed
description is omitted herein. Additionally, the accompanying
drawings are provided for an easy understanding of the disclosed
embodiments, and the technical spirit disclosed herein is not
limited by the accompanying drawings, and it should be understood
that the present disclosure covers all modifications, equivalents
or alternatives falling in the spirit and technical scope of the
present disclosure.
The terms "first", "second", and the like may be used to describe
various elements, but the elements are not limited by the terms.
These terms are used to distinguish one element from another.
It will be understood that when an element is referred to as being
"connected to" another element, the element can be connected to the
other element, but intervening elements may be present.
Unless the context clearly indicates otherwise, the singular forms
include the plural forms as well.
It should be understood that the term "comprises" or "includes"
when used in this specification, specifies the presence of stated
features, integers, steps, operations, elements, components or
groups thereof, but does not preclude the presence or addition of
one or more other features, integers, steps, operations, elements,
components, or groups thereof.
FIG. 1 is a flowchart showing a node location tracking method S100
of the present disclosure, FIG. 2 is a conceptual diagram showing a
relationship between a robot 1 and neighboring nodes 3 in the node
location tracking method S100 of the present disclosure, and FIG. 3
is a graph showing a relationship between the robot 1, a receiver 5
and the neighboring nodes 3 in the node location tracking method
S100 of the present disclosure.
Hereinafter, the node location tracking method S100 of the present
disclosure will be described with reference to FIGS. 1 to 3.
Referring to FIG. 1, the node location tracking method S100 of the
present disclosure includes an initial localization step S10.
Referring to FIG. 2, as opposed to the traditional location
tracking methods, the node location tracking method S100 of the
present disclosure tracks the location using measurement
information between the robot 1 and the neighboring nodes 3 as well
as measurement information between the neighboring nodes 3.
Accordingly, it is possible to track the movement of the robot 1
and the neighboring nodes 3 using the measurement information
between the neighboring nodes 3. Additionally, in FIG. 2, the
two-way arrows indicate that the measurement information is
provided between the nodes 3 and between the robot 1 and the nodes
3.
Additionally, referring to FIG. 3, in the node location tracking
method S100 of the present disclosure, the receiver 5 (or a
receiver node) tracks the location upon receiving the measurement
information from not only the robot 1 but also the neighboring
nodes 3.
In the initial localization step S10, the initial locations of the
robot 1 and the neighboring nodes 3 are estimated using inter-node
measurement and a Sum of Gaussian (SoG) filter.
The initial localization step S10 may include an iterative
multilateration step S12 for initializing the location of the
node.
The initialization in the iterative multilateration step S12 may be
understood as initial estimation of node location.
P.sub.i(n) denotes the estimated location of the i.sup.th node at
the n.sup.th iteration, and d.sub.ij denotes the estimated distance
between the i.sup.th node and the j.sup.th node.
For example, the locations of the first three nodes may be
initialized to P.sub.0(n)=(x.sub.0(n), y.sub.0(n))=(0,0),
P.sub.1(n)=(x.sub.1(n), y.sub.1(n))=(d.sub.01, 0),
P.sub.2(n)=(x.sub.2(n),
y.sub.2(n))={(d.sub.01.sup.2+d.sub.02.sup.2+d.sub.03.sup.2)/x.sub.1(n),
(d.sub.02.sup.2-x.sub.2.sup.2(n))}.
Subsequently, the location of the node other than the three nodes
may be initialized to P.sub.m(n) of one of the following two
candidates, in which {circumflex over
(d)}.sub.2m=.parallel.p.sub.m(n)-p.sub.2(n).parallel. is closer to
the measurement d.sub.2m.
.function..times..function..function..times..times..times..times..times..-
function..+-..times..function. ##EQU00005##
{circumflex over (d)}.sub.2m is the initialized distance between
the location p.sub.n(n) of the m.sup.th node and the location
p.sub.2(n) of the second node. Here, m is an index of the node
other than the three nodes, and may be understood as an integer of
3 or greater.
Additionally, d.sub.01 may be the distance between the 0.sup.th
node and the first node, d.sub.0m may be the distance between the
0.sup.th node and the m.sup.th node, and d.sub.1m may be the
distance between the first node and the m.sup.th node.
FIG. 4A is a graph showing a SoG filter resetting step S21, FIG. 4B
is a graph showing a SoG filter updating step S16 and a SoG filter
merging step S17, and FIG. 4C is graph showing a SoG filter
resetting step S21 and a SoG filter updating step S16.
Hereinafter, a SoG filter generation step S15, a SoG filter
updating step S16 and a SoG filter merging step S17 of the present
disclosure will be described with reference to FIGS. 4A to 4C.
Referring to FIG. 1, the initial localization step S10 may further
include a SoG filter generation step S15, a SoG filter updating
step S16, a SoG filter merging step S17 and a weight transfer step
S18.
The SoG filter generation step S15 may be performed by generating
the mean m.sup.k.sub.ij, the covariance C.sup.k.sub.ij and the
weight w.sup.k.sub.ij of the filter.
.function..times..times..times..times..times..pi..times..times..function.-
.times..times..times..times..times..pi..times..times..times..function..sig-
ma..sigma..function..times. ##EQU00006##
Here, Vr denotes a radial unit vector, Vt denotes a tangential unit
vector, .sigma..sub.r.sup.2 denotes a radial distribution,
.sigma..sub.t.sup.2 denotes a tangential distribution, and N
denotes the number of Gaussian distributions. N may be defined by
the user's settings in each node.
FIG. 3 may be understood as a graph about the SoG filter generation
step S15, and shows the measured distance of the robot 1 and the
receiver 5.
FIG. 5A is a graph showing the results of Experiment 1 about
position error performance of the node location tracking method
S100 of the present disclosure and other methods, and FIG. 5B is a
graph showing the results of Experiment 2 about position error
performance of the node location tracking method S100 of the
present disclosure and other methods.
Experiment 1 of FIG. 5A is conducted in an area of 3.6 m.times.4.8
m, and Experiment 2 of FIG. 5B is conducted in an area of 6.6
m.times.8.4 m.
In FIGS. 5A and 5B, the node location tracking method S100 of the
present disclosure is efficient Cooperative Dynamic Range Only
(eCDRO)-Simultaneous Localization and Mapping (SLAM). Additionally,
in FIGS. 5A and 5B, EPRO-SLAM and RBPF-RO-SLAM may be understood as
the traditional location tracking method. In FIGS. 5A and 5B, it
can be understood that the location tracking method S100
(eCDRO-SLAM) of the present disclosure has a low position error
when the robot moves, and even when the robot does not move.
FIG. 6 is a graph showing node movements in the node location
tracking method S100 of the present disclosure, and shows an
example in which each node moves near the square of 1 m to 2 m.
FIG. 7 is a graph showing the step S15 of generating the SoG filter
7. Describing the SoG filter 7 with reference to FIG. 7, FIG. 7
shows a plurality of ellipses 7a, and the SoG filter 7 may be
understood as a set of ellipses 7a. Each ellipse 7a is a Gaussian
indicating a probability distribution associated with the location
of the node. The SoG filter 7 may be understood as a set of
Gaussians. The shape of Gaussian of the SoG filter 7 is not
necessarily limited to the elliptical shape.
The mean m.sup.k.sub.ij denotes the center of the ellipses 7a in
FIG. 7, the covariance C.sup.k.sub.ij denotes the extent to which
each ellipse 7a spreads wide, and the weight w.sup.k.sub.ij denotes
the number of ellipses 7a.
The accuracy of the initialized location in the Iterative
multilateration may be improved by the SoG filter generation step
S15.
The SoG filter updating step S16 may be performed by performing
weight updates. The SoG filter updating step S16 is shown in FIGS.
4B and 4C. In the weight updates, the likelihood is computed using
the measured distance d.sub.mj, obtained from the neighboring
nodes, and subsequently, the weight w.sup.k.sub.ij is updated using
the likelihood l.sub.ij,m.sup.k. Here, m denotes an index of the
neighboring nodes, and k denotes an index of the SoG filter
node.
FIG. 8 shows an algorithm showing the SoG filter updating step
S16.
FIG. 8 shows an example of computing the likelihood
l.sub.ij,m.sup.k using the measured distance d.sub.mj, obtained
from the neighboring nodes, and subsequently, updating the weight
w.sup.k.sub.ij using the likelihood l.sub.ij,m.sup.k.
In the algorithm of FIG. 8, in the third line, d.sub.ij,m.sup.k may
be a vector indicating the distance between and m.sub.ij.sup.k and
p.sub.m(n). m.sub.ij.sup.k is a vector indicating the mean distance
between the i.sup.th node and the j.sup.th node in the Gaussian k
index, and p.sub.m(n) is a vector indicating the location at the
m.sup.th node.
In the fourth line, the likelihood l.sub.ij,m.sup.k is computed,
d.sub.mj denotes the distance between the m.sup.th node and the
j.sup.th node, and .sigma. is the user parameter, and may be, for
example, 3.
In the second to fifth lines, the likelihood l.sub.ij,m.sup.k is
computed based on d.sub.ij,m.sup.k value.
As shown in the sixth to eighth lines, the likelihood
l.sub.ij,m.sup.k is normalized.
As shown in the ninth to eleventh lines, the likelihood
l.sub.ij,m.sup.k is multiplied by the weight w.sup.k.sub.ij, and as
shown in the twelfth to fourteenth lines, the weight w.sup.k.sub.ij
for the likelihood is normalized.
In the present disclosure, the SoG filter updating step S16 only
relies on the measurement rate, thereby achieving fast weight
convergence.
In the SoG filter updating step S16, the mean and the covariance of
the filter may be updated using an Extended Kalman Filter (EKF)
before the weight updates. The EKF is well known in the art, and
its detailed description is omitted herein.
FIGS. 9A and 9B are graphs showing a weight distribution between
two nodes.
The weight distribution between two nodes has a symmetric property
as shown in FIGS. 9A and 9B. Accordingly, after w.sup.k.sub.ij is
computed, the same value as w.sup.k.sub.ij may be applied using the
modular operation, and since w.sup.k.sub.ij is not separately
computed, it is possible to update the weight with half the
computational amount.
FIG. 10 is an algorithm showing the SoG filter updating step
S16.
In the algorithm of FIG. 10, referring to the eleventh to
fourteenth lines, mod is the modular operation and may find an
index of w.sup.k.sub.ji corresponding to the index k of
w.sup.k.sub.ij. Additionally, the same value as w.sup.k.sub.ij may
be applied without needing to calculating w.sup.k.sub.ij, thereby
reducing the required computational amount by half.
In the SoG filter merging step S17, the plurality of SoG filters of
the neighboring nodes is merged into a Gaussian distribution using
the following [Equation 1] to [Equation 3] to estimate the location
of the node.
.function..times..times..times..times..times..times..times..times..times.-
.times..times..times..times. ##EQU00007##
Here, p.sub.i(n+1) is the location of the node newly estimated by
the SoG filter merging step S17.
C.sub.ji.sup.k=(m.sub.ji.sup.k-p.sub.i(n+1))(m.sub.ji.sup.k-p.sub.i(n+1))-
.sup.T [Equation 2]
Here, C.sub.ji.sup.k denotes the covariance of m.sup.k.sub.ji.
.function..times..times..times..times..times..times..times..times..functi-
on..times..times..times..times..times..times. ##EQU00008##
Here, C.sub.i(n+1) is the covariance of the node newly estimated by
the SoG filter merging step S17.
Additionally, in the SoG filter merging step S17, Gaussian
distribution having a low weight w.sup.k.sub.ij is not included in
the computation, thereby achieving efficient computation. For
example, under the condition of |w.sub.ij.sup.k|< , =0.00001/N,
Gaussian distribution having a low weight w.sup.k.sub.ij may be not
included in the computation.
Due to non-convexity of anchor-free localization, a local solution
may be obtained after the SoG filter merging step S17, and to
resolve the non-convexity, the weight transfer step S18 may be
performed.
In the weight transfer step S18, the maximum weight may be
transferred to its surrounding weights with respect to the index
k.sub.max having the maximum weight in SoG filter distribution
using [Equation 4] and [Equation 5].
.times..times..times..times..times..times..times..times..pi..times..times-
..sigma..times..function..times..times..sigma..times..times.
##EQU00009##
In [Equation 4] and [Equation 5], d.sub.kmax-k denotes the distance
between m.sup.kmax and m.sup.k.sub.ij, m.sup.kmax.sub.ij denotes
the mean of the SoG filter having the maximum weight, and .sigma.
is the spread of the Gaussian distribution, and may be, for
example, 3.
FIG. 11 is a graph showing a comparison of performance with/without
the weight transfer step S18.
Referring to FIG. 11, a position error of improved high probability
may be obtained by performing the weight transfer step S18. In FIG.
11, the blue line indicates a position error when the weight
transfer step S18 is not performed, and the red line indicates a
position error when the weight transfer step S18 is performed.
The node convergence determination process includes calculating an
average location of nodes, and determining whether the nodes are
converged.
The average location of nodes may be calculated by [Equation 6].
{tilde over (p)}.sub.i(n+1)=.alpha.{tilde over
(p)}.sub.i(n)+(1-.alpha.)p.sub.i(n) [Equation 6]
Here, {tilde over (p)}.sub.i(n) denotes the average location of
nodes, and a may be a value close to 1, and denotes, for example, a
value between 0.9 and 0.95.
The node convergence determination process may be performed by
[Equation 7]. .parallel.{tilde over (p)}.sub.i(n+1)-{tilde over
(p)}.sub.i(n).parallel.<.epsilon. [Equation 7]
Here, .epsilon. may be 10.sup.-4 to 10.sup.-3.
When the condition of [Equation 7] is satisfied, the corresponding
node is determined to be converged, and when the condition of
[Equation 7] is not satisfied, the location of the corresponding
node may be continually estimated upon receipt of newly measured
location information. When all the nodes are converged, the
procedure is shifted to the moving step.
The node location tracking method S100 of the present disclosure
may further include a movement based tracking step S20.
In the movement based tracking step S20, the locations or the
movements of the neighboring nodes 3 are estimated more accurately
using the movement of the robot 1 from the initial position values
of the robot 1 and the neighboring nodes 3 estimated in the initial
localization step S10, and the movement based tracking step S20 may
be performed after the initial localization step S10.
Referring to FIG. 1, the movement based tracking step S20 may
include a SoG filter resetting step S21, a SoG filter updating step
S22, a SoG filter merging step S24 and a weight transfer step
S27.
Additionally, the movement based tracking step S20 may comprise the
plurality of steps included in the initial localization step
S10.
In the SoG filter resetting step S21 of resetting the SoG filter 7
generated in FIG. 3 or FIG. 7, resetting is performed based on the
changed position value of the receiver 5 or the robot 1 by the
location movement of the receiver or the robot 1.
Referring to FIG. 4A, shown is an example of the step of resetting
the SoG filter 7 by the movement of the receiver 5.
In the movement based tracking step S20, the SoG filter updating
step S22, the SoG filter merging step S24 and the weight transfer
step S27 are performed in the same way as the SoG filter updating
step S16, the SoG filter merging step S17 and the weight transfer
step S18 in the initial localization step S10 as described above,
and a reference is made to the description in the initial
localization step S10 described previously.
The node location tracking method of the present disclosure is not
affected by odometry errors, and is only affected by measurement
errors, and accordingly, it is possible to minimize position
errors, and achieve more accurate estimation irrespective of the
size of the wireless network.
The node location tracking method of the present disclosure is only
affected by measurement errors, thereby achieving fast node
localization.
The node location tracking method of the present disclosure
includes SoG filter updates, and thus it is possible to track the
movements of the neighboring nodes, and it can be used in
applications where node movements are necessary.
The method of the present disclosure may be used in applications
where node movements are necessary, for example, location tracking
of moving goods in the warehouse, search and rescue in disaster
environments, activity analysis of humans or moving objects in
ambient intelligence and autonomous underwater vehicle (AUV)
systems in underwater environments.
The node location tracking method S100 of the present disclosure as
described hereinabove is not limited to the configuration and
method of the embodiments described above, and some or all the
embodiments may be selectively combined to make various
modification.
It is obvious to those skilled in the art that the present
disclosure may be embodied in other particular forms without
departing from the spirit and essential features of the present
disclosure. Therefore, the above detailed description should not be
interpreted as being limiting in all aspects and should be
considered as being exemplary. The scope of the present disclosure
should be determined by the reasonable interpretation of the
appended claims, and the scope of the present disclosure covers all
modifications within the equivalent scope of the present
disclosure.
* * * * *