Chapter 7
Localization & Positioning
1
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Goals of this chapter


Means for a node to determine its physical position with
respect to some coordinate system (50, 27) or symbolic
location (in a living room)
Using the help of



2
Anchor nodes that know their position
Directly adjacent nodes
Over multiple hops
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Outline





3
7.1 Properties of localization and positioning
procedures
7.2 Possible approaches
7.3 Mathematical basics for the lateration problem
7.4 Positioning in multi-hop environments
7.5 Positioning assisted by anchors
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7.1 Properties of localization and
positioning procedures

Physical position versus logical location







4
Coordinate system: position
Symbolic reference: location
Absolute versus relative coordinate
Centralized or distributed computation
Localized versus centralized computation
Limitations: GPS for example, does not work indoors
Scale (indoors, outdoors, global, …)
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Properties of localization and positioning
procedures (cont.)

Accuracy


Precision


5
how close is an estimated position to the real
position?
the ratio with which a given accuracy is reached
Costs, energy consumption, …
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7.2 Possible approaches

Proximity


(Tri-/Multi-) lateration and angulation




The most evident form of it is to analyze pictures taken by a camera
Other measurable characteristic ‘fingerprints’ of a given location can be
used for scene analysis e.g., RADAR
Bounding box

6
Lateration : when distances between nodes are used
Angulation: when angles between nodes are used
Scene analysis


A node wants to determine its position or location in the proximity of an
anchor
to bound the possible positions of a node
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Proximity (range-free approach)

7
Using information of a node’s neighborhood

Exploit finite range of wireless communication

e.g., easy to determine location in a room with
infrared (room number announcements)
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Trilateration and triangulation (range-based
approach)

(Tri-/Multi-)lateration and angulation



Using geometric properties
Lateration: distances between entities are used
Angulation: angle between nodes are used
(x = 5, y = 4)
r2
r3
(x = 8, y = 2)
r1
(x = 2, y = 1)
8
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Trilateration and triangulation (cont.)
Determining distances



9
To use (multi-)lateration, estimates of distances to
anchor nodes are required.
This ranging process ideally leverages the facilities
already present on a wireless node, in particular, the
radio communication device.
The most important characteristics are Received
Signal Strength Indicator (RSSI), Time of Arrival
(ToA), and Time Difference of Arrival (TDoA).
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Distance estimation
RSSI (Received Signal Strength Indicator)

10
Send out signal of known strength, use received signal
strength and path loss coefficient to estimate distance
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Distance estimation
RSSI (cont.)

Problem: Highly error-prone process :



11
Caused by fast fading, mobility of the environment
Solution: repeated measurement and filtering out incorrect
values by statistical techniques
Cheap radio transceivers are often not calibrated
 Same signal strength result in different RSSI
 Actual transmission power different from the intended power
 Combination with multipath fading
 Signal attenuation along an indirect path is higher than along
a direct path
 Solution: No!
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Distance estimation
PDF
PDF
RSSI (cont.)
Distance
Distance
PDF of distances in a given RSSI value
12
Signal strength
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Distance estimation
ToA (Time of arrival )

Use



13
time of transmission,
propagation speed
Problem: Exact time synchronization
 Usually, sound wave is used
 But propagation speed of sound depends on
temperature or humidity
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Distance estimation
TDoA (Time Difference of Arrival )

Use two different signals with different propagation
speeds



14
Compute difference between arrival times to compute
distance
Example: ultrasound and radio signal (Cricket System)
 Propagation time of radio negligible compared to
ultrasound
Problem: expensive/energy-intensive hardware
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Scene analysis

RADAR system: Comparing the received signal
characteristics from multiple anchors with
premeasured and stored characteristics values.


15
Radio environment has characteristic “fingerprints”
The necessary off-line deployment for measuring the
signal landscape cannot always be accommodated in
practical systems.
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Bounding Box



16
The bounding box method proposed in uses squares
instead of circles as in tri-lateration
to bound the possible positions of a node.
For each reference node i, a bounding box is defined
as a square with its center at the position of this node
(xi, yi), with sides of size 2di (where d is the estimated
distance) and with coordinates (xi –di, yi–di) and (xi+di,
yi+di).
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Bounding Box (cont.)

Using range to anchors to determine a bounding box

Use center of box as
position estimate
B
C
d
A
17
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References
18

N. Bulusu, J. Heidemann, and D. Estrin. “GPS-Less Low Cost
Outdoor Localization For Very Small Devices,” IEEE Personal
Communications Magazine, 7(5): 28–34, 2000.

C. Savarese, J. Rabay, and K. Langendoen. “Robust Positioning
Algorithms for Distributed Ad-Hoc Wireless Sensor Networks,” In
Proceedings of the Annual USENIX Technical Conference, Monterey,
CA, 2002.

A. Savvides, C.-C. Han, and M. Srivastava. “Dynamic Fine-Grained
Localization in Ad-Hoc Networks of Sensors,” Proceedings of the
7th Annual International Conference on Mobile Computing and
Networking, pages 166–179. ACM press, Rome, Italy, July 2001.

S. Simic and S. Sastry, “Distributed localization in wireless ad hoc
networks,” UC Berkeley, Tech. rep. UCB/ERL M02/26, 2002.
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7.3 Mathematical basics for the
lateration problem
19
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Solution with three anchors and correct
distance values

Assuming distances to three points with known
location are exactly given

Solve system of equations (Pythagoras!)



20
(xi , yi) : coordinates of anchor point i,
ri : distance to anchor i
(xu, yu) : unknown coordinates of node
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Solution with three anchors and correct
distance values (cont.)
21
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Trilateration as matrix equation

Rewriting as a matrix equation:
2( x3  x1 ) xu  2( y3  y1 ) yu  (r12  r32 )  ( x12  x32 )  ( y12  y32 )
2( x3  x2 ) xu  2( y3  y2 ) yu  (r22  r32 )  ( x22  x32 )  ( y22  y32 )
 x3  x1
2
 x3  x2
22
y3  y1   xu  (r12  r32 )  ( x12  x32 )  ( y12  y32 )
 2 2




y3  y2   yu  (r2  r3 )  ( x22  x32 )  ( y22  y32 )
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Solving with distance errors
_

What if only distance estimation ri  ri   i available?
Use multiple anchors, overdetermined system of
equations

Use (xu, yu) that minimize mean square error,


23
i.e,
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Minimize mean square error

Look at square of the of Euclidean norm expression


24
(note that for all vectors v)
Look at derivative with respect to x, set it equal to 0
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7.4 Positioning in multi-hop
environments
25
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Connectivity in a multi-hop network
26

Assume that the positions of n anchors are known and
the positions of m nodes is to be determined, that
connectivity between any two nodes is only possible if
nodes are at most R distance units apart, and that the
connectivity between any two nodes is also known

The fact that two nodes are connected introduces a
constraint to the feasibility problem – for two
connected nodes, it is impossible to choose positions
that would place them further than R away
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Multi-hop range estimation

How to estimate range to a node to which no direct
radio communication exists?


No RSSI, TDoA, …
But: Multi-hop communication is possible
B
A
X
C
27
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Multi-hop range estimation (cont.)

Idea 1: (DV-Hop) Start by counting hops between
anchors then divide known distance



28
Count Shortest hop numbers between all two nodes.
Each anchors estimate hop length and propagates to the
network.
Node calculates its position based on average hop length and
shortest path to each anchor.
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DV Hop

L1 calculates average hope length :
100  40
 17.5
62

29
( xi  x j ) 2  ( yi  y j ) 2
h
i
So do L2 and L3 :
40  75
 16.42
25

ci


75  100
 15.90
65
Node A uses trilateration to estimate it’s position by multiplying the
average hope length of every received anchor to shortest path
length it assumed.
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DV-Distance



30
Idea 2: If range estimates between neighbors exist, use
them to improve total length of route estimation in
previous method (DV-Distance)
Distance between neighboring nodes is measured
using radio signal strength and is propagated in meters
rather than in hops.
The algorithm uses the same method to estimate but
shortest distance length are assumed.
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Multi-hop range estimation (cont.)
DV-Based Scheme
•
•
Must work in a network which is dense enough DVhop approach used the hop of the shortest path to
approximately estimate the distance between a pair of
nodes
Drawback: Requires lots of communications
anchor
anchor
31
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Discussion

Number of anchors



Uniformly distributed network


32
Euclidean method increase accuracy as the number of
anchors goes up
The “distance vector”-like methods are better suited for a
low-ratio of anchors
Distance vector methods perform less well in non-uniformly
networks
Euclidean method is not very sensitive to this effect
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7.5 Positioning assisted by anchors
33
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APIT (Approximate Point in Triangle)




By pure connectivity information
Idea: decide whether a node is within or outside of a
triangle formed by any three anchors
However, moving a sender node to determine its
position is hardly practical !
Solution:

34
inquire all its neighbors about their distance to the given
three corner anchors
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APIT (cont.)

Inside a triangle

Irrespective of the direction of
the movement, the node must
be closed to at least one of the
corners of the triangle
A
M
B
35
C
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APIT (cont.)

Outside a triangle:

There is at least one direction
for which the node’s distance
to all corners increases
M
B
36
A
C
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APIT (cont.)

Approximation: Normal nodes test only directions
towards neighbors
A
A
1
1
3
M
2
3
M
4
2
4
B
C
B
A. Inside Case
37
C
B. OutSide Case
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APIT (cont.)

Grid-Based Aggregation

Narrow down the area where the normal node can potentially
reside
0
0
0
0
0
10
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
12 1
1
1
1
0
0
0
0
1
2
2
1
1
01 -1 0
0
1
1
2
2
1
1
0
-1 -1 0
0
0
2
2
2
1
0
-1 -1 -1
0
0
1
1
1
0
0
-1 -1 -1
anchor node
normal node
38
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MCL (Monte-Carlo Localization)

Assumptions




Time is divided into several time slots
Moving distance in each time slot is randomly chosen from
[0 , Vmax ]
Each anchor node periodically forwards its location to twohop neighbors
Notation

39 2016/3/12
R - communication range
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39
MCL (cont.)

Each normal node maintains 50 samples in each time
slot



40 2016/3/12
Samples represent the possible locations
The sample selection is based on previous samples
Sample (x , y) must satisfy some constraints
 Located in the anchor constraints
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40
MCL (cont.)

Anchor constraints


Near anchor constraint
 The communication region of
one-hop anchor node ( near
anchor )
Farther anchor constraint
 The region within ( R , 2R ]
centered on two-hop anchor
( farther anchor )
Near anchor constraint
R
A1
N1
Farther anchor constraint
R
R
A1
N1
N2
41 2016/3/12
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41
MCL (cont.)
Environment
Anchor node
Normal node
A4
N1
A1
A2
A3
42 2016/3/12
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42
MCL (cont.)
Initial Phase
Sample in the last time slot
Anchor node
Normal node
A4
N1
A1
A2
A3
43 2016/3/12
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43
MCL (cont.)
Sample in this time slot
Sample in the last time slot
Anchor node
Normal node
Prediction Phase & Filtering
Phase
Vmax
A4
R
RA
N1
1
A2
R
A3
44 2016/3/12
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44
MCL (cont.)
Sample in this time slot
Sample in the last time slot
Anchor node
Normal node
Prediction Phase & Filtering
Phase
Vmax
A4
Vmax
R
RA
N1
1
A2
Vmax
45 2016/3/12
R
A3
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45
MCL (cont.)
Sample in this time slot
Estimative position
Anchor node
Normal node
Estimative Location

the average of samples
A4
A1
EN1
N1
A2
A3
46 2016/3/12
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46
MCL (cont.)
Sample in this time slot
Sample in the last time slot
Anchor node
Normal node
Repeated Prediction Phase
& Filter Phase
In the next time slot
Vmax
A1
A4
N1
A2
R
A3
47 2016/3/12
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47
DRLS
Distributed Range-Free Localization Scheme

48
There are three phases in the DRLS algorithm.

Phase 1 – Beacon exchange

Phase 2 – Using improved grid-scan algorithm to get initial
estimative location

Phase 3 – Refinement
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DRLS (cont.)
Beacon Exchange

Beacon exchange via two-hop flooding
A4
Normal node
Near anchor
N3
Farther anchor
A3
A1
N2
A2
N1
49
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DRLS (cont.)
Improved Grid-Scan Algorithm

Calculate the overlapping rectangle
up side
N
A1
50
A3
A2
left side down side right side
Anchor node
Normal node
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DRLS (cont.)
Improved Grid-Scan Algorithm

Divide the ER into small grids

The initial value of the grid is 0
A1
51
0
0
N 0
0
0
0
0
0
0
0
0
0
0
0
0
0
A3
A2
Anchor node
Normal node
Estimative location
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DRLS (cont.)
Improved Grid-Scan Algorithm

Initial estimative location

Apply centroid formula to grids with the maximum grid
value
A1
52
1
2
N 3
3
N’ 3
2
2
2
1
2
2
3
3
3
2
2
A3
A2
Anchor node
Normal node
Estimative location
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DRLS (cont.)
Refinement

Repulsive virtual force (VF)


53
Induced by farther anchor nodes
Dinvasion : the maximum distance that the farther
anchor invades the estimative region along the
direction from the farther anchor towards the initial
estimative location
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DRLS (cont.)
Refinement




VFi : virtual force induced by farther anchor i
Dinvasioni : the maximum distance that
the farther anchor i invades the estimative
region along the direction from i towards
A4
the initial estimative location
Vi,j : the unit vector in the
DinvasionA4
direction from the farther anchor
VFA5 A2
VFA3
i towards the initial estimative
N’ N
location j
A1
DinvasionA5
A3 VFA4
VFi = Vi,j˙Dinvasioni
A5
54
estimative region
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DRLS (cont.)
Refinement


Resultant Virtual Force (RVF)
RVF = ΣVFi
A4
A2
A3
A1
RVF
N’ N’N
A5
55
estimative region
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DRLS (cont.)
Refinement


Di : the moving distance caused by the farther anchor i
Dimax : the maximum moving
distance caused by the farther
anchor i
Di
Dimax
=
Dinvasioni
a
A4
DinvasionA3max
A2
b
c
A3
e
d
N’
A1
Dinvasionimax
L3
f
N
DA3max
A5
DinvasionA3
56
estimative region
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DRLS (cont.)
Refinement


Dmovei : the moving vector caused by the
farther anchor i
Vi,j : the unit vector in the
A4
direction from the farther anchor
i towards the initial estimative
Dinvasion
location j
DmoveA5 A2
DmoveA3
Dmovei = Vi,j˙Di
N’ N
A4

A1
A3 DmoveA4
DinvasionA5
A5
estimative region
57
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DRLS (cont.)
Refinement

Dmove: the final moving vector
Dmove = Σ Dmovei
A4
A2
A3
A1
Dmove
N’ N’N
A5
estimative region
58
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IMCL
Improved MCL Localization Scheme

Improvements



59
Dynamic number of samples
 According to the overlapping region of anchor constraints
Restricted samples
 Anchor constraints
 The estimative locations of neighboring normal nodes
Predicted moving direction of the normal node
 Be used to increase the localization accuracy
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IMCL (cont.)
60

Phase 1- Sample Selection Phase

Phase 2- Neighbor Constraints Exchange
Phase

Phase 3- Refinement Phase
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IMCL (cont.)
Sample Selection Phase

Dynamic sample number


Sampling Region
 The overlapping region
of anchor constraints
 Difficult to calculate
Estimative Region (ER)
 A rectangle surrounding
the sampling region
R
R
A3
R
N
A1
A2
ER
61
2016/3/12
IMCL (cont.)
Sample Selection Phase

The number of samples ( k )
R
k ≦ Max_Num

ERArea 
k = Max _ Num 

ER
Threshold 

R
A3
R
N
A1
A2
ER
• ERArea
— the area of ER
• ERThreshold — the threshold value
• Max_Num — the upper bound of sample number
In our simulations, ERThreshold = 4R2
62
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IMCL (cont.)
Sample Selection Phase

Using the prediction and filtering phase of MCL


63
Samples are randomly selected from the region
extended Vmax from previous samples
Filter new samples
 Near anchor constraints
 Farther anchor constraints
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IMCL (cont.)
Effective Location Estimation

An additional normal nodes constraint


Samples must locate on the communication region of
neighboring normal nodes
The localization error may increase
Send the possible location
region to neighbors instead
of the estimative position
EN1
N1
EN2
N2
N3
64
2016/3/12
IMCL (cont.)
Neighbor Constraints Exchange Phase

The possible location region

The distribution of samples are selected in phase I
135°
90°
180°
45°
0°
(Cx ,Cy)
225°
Step 1: Sensor A constructs a coordinate
axis and uses (Cx ,Cy) as origin
Step 2: The coordinate axis is separated
into eight directions
315°
270°
65
Central position in phase 1
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IMCL (cont.)
Neighbor Constraints Exchange Phase
135°
Step 3: The samples are also divided
into eight groups according to
the angle θ with (Cx , Cy)
90°
45°
θ
180°
(Sx ,Sy)
Sy  Cy
  tan (
)
Sx  Cx
1
0°
(Cx ,Cy)
225°
315°
270°
Valid samples in current time slot
66
Central position in phase 1
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IMCL (cont.)
Neighbor Constraints Exchange Phase
135°
90°
180°
45°
Step 4: Using the longest distance
within group as radius to perform
sector
0°
225°
315°
the possible location region
described by eight sectors and (Cx ,
Cy)
270°
Sample in the this time slot
67
Central position in phase 1
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IMCL (cont.)
Neighbor Constraints Exchange Phase

Neighbor constraint

Extend R from the possible located region
90°
45°
135°
Each sensor broadcasts its
neighbor constraint region once
R
0°
180°
(Cx ,Cy)
Neighbor constraint
315°
225°
68
270°
2016/3/12
IMCL (cont.)
Refinement Phase

Samples are filtered



When sample is not satisfy the constraints

69
Neighbor constraints
 Receive from neighboring normal nodes
Moving constraint
 Predict the possible moving direction
Normal node generates a valid sample to replace it
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IMCL (cont.)
Refinement Phase

Neighbor constraints


70
Sample S1 is a valid sample
 Satisfied both neighbor
constraints of N2 and N3
Sample S2 is a invalid sample
 Only satisfied the neighbor
constraint of N3
S2
S1
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IMCL (cont.)
Refinement Phase

Moving constraint

The prediction of nodes moving direction is [θ±ΔΦ ]
In time slot t if (Cx , Cy) is
located in {θ±ΔΦ} from Et-2
Prediction is right
ΔΦ
θ
Et-2
71
Et-1 (Cx , Cy) if (Cx , Cy) is located outside of
{θ±ΔΦ} from Et-2
ΔΦ
Prediction is wrong
Thus, we do not adopt the moving
(Cx , Cy)
constraint!
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IMCL (cont.)
Refinement Phase



Sample 1
Sample 2
ΔΦ
θ
Et-1
If prediction is right, sample must
be located in {θ±ΔΦ} from Et-2
Sample 1 satisfies moving
constraint
Sample 2 does not satisfy moving
constraint
(Cx , Cy)
ΔΦ
Et-2
72
2016/3/12
IMCL (cont.)
Estimative Position

Normal node calculates the estimative position Et (Ex ,
Ey) of samples
k

Ex =
 x coordinate of sample i
i 1
k
k

Ey =
 y coordinate of sample i
i 1
, k  sample number
k
73
2016/3/12
Conclusions

Determining location or position is a really important
function in WSN, but fraught with many errors and
shortcomings



74
Range estimates often not sufficiently accurate
Many anchors are needed for acceptable results
Anchors might need external position sources (GPS)
2016/3/12
References

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