Localization

1
Localization

• Vinod Kulathumani
• West Virginia University

2
Localization

• Localization of a node refers to the problem of
  identifying its spatial co-ordinates in some
  co-ordinate system
• How do nodes discover their geographic positions
  in 2D or 3D space?
• Model static and mobile wireless sensor networks

3
Location Matters

• Sensor Net Applications
• Environment monitoring
• Event tracking
• Smart environment
• Geographic routing protocols
• GeoCast, GPSR, LAR, GAF, GEAR

4
Outline

• Range-based localization
• Time of arrival (GPS)
• Time difference of arrival (Acoustic)
• Angle of arrival
• RADAR
• Radio interferometric
• Doppler shift
• Converting estimated range into actual network
  position
• Range-free localization
• Centroid
• DV-HOP
• MDS-MAP
• APIT
• Localization in Mobile sensor networks

5
Range-based localization

• Distances between nodes to nodes/anchors measured
  wirelessly
• TOA (Time of Arrival )
• GPS
• TDOA (Time Difference of Arrival)
• Cricket
• AOA (Angle of Arrival )
• APS
• RSSI (Receive Signal Strength Indicator)
• RADAR
• Radio interferometric
• Doppler shift

6
Time of arrival (TOA)

• Example GPS
• Uses a satellite constellation of at least 24
  satellites with atomic clocks
• Satellites broadcast precise time
• Estimate distance to satellite using signal TOA
• Trilateration

• B. H. Wellenhoff, H. Lichtenegger and J. Collins,
  Global Positioning System Theory and Practice.
  Fourth Edition, Springer Verlag, 1997

7
Sound based TdoA
Because the speed of sound is much slower
(approximately 331.4m/s) than radio, it is
easier to be applied in sensor network. Some
hurdles are

• Line of sight path must exist between sender
  and receiver.
• Mono-direction.
• Short range.

8
Cricket

• Intended for indoors use where GPS don't work
• It can provide distance ranging and positioning
  precision of between 1 and 3 cm
• Active beacons and passive listeners
• http//cricket.csail.mit.edu/technology

9
Angle of arrival (AOA)

• Idea Use antenna array to measure direction of
  neighbors
• Special landmarks have compass GPS, broadcast
  location and bearing
• Flood beacons, update bearing along the way
• Once bearing of three landmarks is
  known,calculate position

"Medusa" mote
Dragos Niculescu and Badri Nath. Ad Hoc
Positioning System (APS) Using AoA, IEEE InfoCom
2003
10
Determining angles

• Directional antennas
• On the node
• Mechanically rotating or electrically steerable
• On several access points
• Rotating at different offsets
• Time between beacons allows to compute angles

11
RADAR

• Bahl MS research
• Offline calibration
• Tabulate ltlocation, RSSIgt to construct radio map
• Real-time location tracking
• Extract RSSI from base station beacons
• Find table entry best matching the measurement

12
Estimating distances RSSI

• Received Signal Strength Indicator
• Send out signal of known strength, use received
  signal strength and path loss coefficient to
  estimate distance
• Problem Highly error-prone process Shown PDF
  for a fixed RSSI

PDF
PDF
Distance
Signal strength
Distance
13
Problems with RSSI

• Sensors have wireless transceivers anyway, so why
  not just use the RSSI to estimate distances?
• Problem Irregular signal propagation
  characteristics (fading, interference, multi-path
  etc.)

Graph from Bahl, Padmadabhan RADAR An
In-Building RF-Based User Location and Tracking
System
14
Radio Interferometric Ranging (RIPS)

• RIPS a novel ranging technique that measures
  distance differences utilizing interfering radio
  signals

fCD (dAD-dBDdBC-dAC) mod ?
Interference superposition of two or more waves
resulting in a new wave pattern
q-range
15
Tracking with RIPS

• We use RIPS because of its high accuracy (cm),
  long range (200m), and low computation and low
  power requirements

Theory for Tracking

• radio-interferometric range, or q-range involves
  4 nodes A, B, C and D
• qABCD dAD-dBDdBC-dAC

• in tracking, we can assume that 3 nodes are
  anchors, thus we define t-range tACD
• tACD dAD-dAC qABCDdBD-dBC
• (qABCD is measured, dBD and dBC are given)

• the new equation defines a hyperbola in 2D
• note that C,D are receivers

t-range
q-range
hyperbola
16
Tracking with RIPS
Theory for Tracking

• RIPS measurement constrains the location of the
  target to a hyperbola
• if the target is a transmitter, a pair of
  receivers defines unique hyperbola
• e.g. using 12 anchors yields 55 hyperbolae from
  one measurement

Mobility Related and Other Ranging Errors

• an artefact of RIPS method is that phase offsets
  at multiple wavelengths need to be measured
• qABCD is the solution of a system of equations

Multipath, Measurement Errors fiCD are not
measured accurately, errors are
non-Gaussian Mobility qABCD changes as the
target moves Thus solution qABCD minimizes error
terms e1...en
17
Tracking with RIPS

• Localization with Non-Gaussian Ranging Errors

• ranging does not return a single q-range qABCD,
  but a set of q-ranges SABCD, one of them being
  the true range with high probability

• resulting ambiguity needs to be resolved by the
  localization algorithm

Disambiguation

• the true hyperbolae intersect at a single point
• improbable that a significant number of the false
  hyperbolae intersect at a single point
• localization algorithm simply finds a region
  which gets intersected by a large number of
  hyperbolas

refined search
18
Overview of our Tracking Application

• Sensor nodes
• XSM motes
• weather protected Mica2
• 7.3 MHz CPU, 4kB RAM, 38kbps radio
• TinyOS

• PC application
• regular laptop
• 1.5 GHz CPU, 512MB RAM
• java application calculates target location
• targets location and track are displayed in
  Google Earth

19
Evaluation Vanderbilt stadium

• we had Vanderbilt football stadium access
• placed 6 anchors on the field (tripods), and 6
  anchors in the stands
• covered an area of approximately 80m x 90m

20
Evaluation Google Earth

• we modelled Vanderbilt stadium in Google Earth
• we were showing target location and track in
  real-time
• large red balloon is the target, small red
  balloons are anchor nodes

21
Evaluation Results

• Results from our test runs
• 148 datapoints
• 37cm average and 1.5m maximum 2D error (61cm real
  error)
• target speed up to 2m/s
• 2.5 3 sec refresh rate

22
Tracking Mobile Nodes Using RF Doppler Shifts
Branislav Kusy Computer Science
Department Stanford University

• A novel tracking algorithm that utilizes RF
  Doppler shifts
• A technique that allows us to measure RF Doppler
  shifts using low cost hardware
• Mica2 8MHz CPU and 9kHz sampling rate

23
Utilizing doppler effect

• Single receiver allows us to measure relative
  speed.
• Multiple receivers allow us to calculate location
  and velocity

24
Doppler Effect

• Assume a mobile source transmits a signal with
  frequency f, and f is the frequency of received
  signal

source Jose Wudka, physics.ucr.edu
25
Can we Measure Doppler Shifts?
Typ. freq Dopp. Shift (_at_ 1 m/s)
Acoustic signals 1-5 kHz 3-15 Hz
Radio signals (mica2) 433 MHz 1.3 Hz
Radio signals (telos) 2.4 GHz 8 Hz

• Intriguing option if we can utilize radio
  signals, no extra HW is required

Solution radio interfereometry
26
Measuring Doppler shift
We use radio interferometry to measure Doppler
frequency shifts with 0.21 Hz accuracy.

• 2 nodes T, A transmit sine waves _at_430 MHz
• fT, fA
• Node Si receives interference signal (in
  stationary case)
• fi fT fA
• T is moving, fi is Doppler shifted
• fi fT fA ?fi,T
• (one problem we dont know the value fT-fA
  accurately)

T
Si
?fi,T
Beat frequency is estimated using the RSSI signal.
27
Formalization
We want to calculate both location and velocity
of node T from the measured Doppler shifts.

• Unknowns
• Location, velocity of T, and fT-fA
• x(x,y,vx,vy,f)
• Knowns (constraints)
• Locations (xi,yi) of nodes Si
• Doppler shifted frequencies fi
• c(f1,,fn)
• Function H(x)c

28
Tracking as Optimization Problem

• Non-linear Least Squares (NLS)
• Minimize objective function H(x) c
• Whats the effect of measurement errors?

29
Improving Accuracy

• State Estimation Kalman Filter
• Measurement error is Gaussian
• Model dynamics of the tracked node (constant
  speed)
• Accuracy improves, but maneuvers are a problem

30
Resolving EKF Problems

• Combine Least Squares and Kalman Filter
• Run standard KF algorithm
• Detect maneuvers of the tracked node
• Update KF state with NLS solution

Dilemma how much to trust our measurements
31
Tracking Algorithm
Infrastructure nodes record Doppler shifted beat
frequency.
Doppler shifted frequencies
32
Experimental Evaluation

• Vanderbilt football stadium
• 50 x 30 m area
• 9 infrastructure XSM nodes
• 1 XSM mote tracked
• position fix in 1.5 seconds

Non-maneuvering case
32
33
Experimental Evaluation

• Vanderbilt football stadium
• 50 x 30 m area
• 9 infrastructure XSM nodes
• 1 XSM mote tracked
• position fix in 1.5 seconds

Maneuvering case
Only some of the tracks are shown for clarity.
34
From ranging to self-localization

• Ranging can be wrt anchors
• Actual location coordinates received directly
• Ranging can be amongst non-anchors
• A relative location can be obtained
• Can be done centralized or distributed
• Consider a centralized scheme Sensys 2004, Moore
  et. Al.
• If ranging is precise rigid localization can be
  done
• If ranging is imprecise
• Flip ambiguities can arise
• Avoid this using robust quadrilaterals

35
Trilateration without noise

• If three anchors are not on the same line,
  trilateration with accurate distance measurements
  gives a unique location

36
Trilateration with noise

• There can be flip ambiguity

37
Use robust quads

• Four nodes with fixed pair wise distances
• Smallest rigid graph that can be formed

38
Robustness

• If error is bounded, there can be no flips

39
Robustness

• If error is bounded, there can be no flips

40
Connecting quads

• Robust quads that share 3 nodes can be merged

41
Summary of steps step 1

• Each node x gets the distance measurements
  between each pair of 1-hop neighbors.
• Identify the set of robust quadrilaterals.
• Merge the quads if they share 3 nodes.
• Estimate the positions of as many nodes as
  possible by iterative trilateration.
• Note Local coordinate system rooted at x.

42
Step 2 global alignment

• Align neighboring local coordinates systems.
• Find the set of nodes in common between two
  clusters.
• Compute the translation, rotation that best align
  them.

43
Range-free localization

• Range-based localization
• Required Expensive hardware
• Limited working range ( Dense anchor requirement)
• Range-free localization
• Simple hardware
• Less accuracy

44
Range-free Centroid

• Idea Do not use any ranging at all, simply
  deploy enough beacons
• Anchors periodically broadcast their location
• Localization
• Listen for beacons
• Average locations of all anchors in range
• Result is location estimate
• Good anchor placement is crucial!

Anchors
Nirupama Bulusu, John Heidemann and Deborah
Estrin. Density Adaptive Beacon Placement,
Proceedings of the 21st IEEE ICDCS, 2001
45
Hop-Count Techniques
r
DV-HOP Niculescu Nath, 2003 Amorphous Nagpal
et. al, 2003
4
1
2
7
3
1
4
3
5
2
4
8
3
3
6
4
4
5
Works well with a few, well-located seeds and
regular, static node distribution. Works poorly
if nodes move or are unevenly distributed.
46
MDS
47
Obtaining a Coordinate System from Distance
Measurements Introduction to MDS
MDS maps objects from a high-dimensional space to
a low-dimensional space, while preserving
distances between objects. similarity between
objects coordinates of points

• Classical metric MDS
• The simplest MDS the proximities are treated as
  distances in an Euclidean space
• Optimality LSE sense. Exact reconstruction if
  the proximity data are from an Euclidean space
• Efficiency singular value decomposition, O(n3)

48
LOCALIZATION USING MDS-MAP (Shang, et al.,
Mobihoc03)

• The basic MDS-MAP algorithm
• Given connectivity or local distance measurement,
  compute shortest paths between all pairs of
  nodes.
• Apply multidimentional scaling (MDS) to construct
  a relative map containing the positions of nodes
  in a local coordinate system.
• Given sufficient anchors (nodes with known
  positions), e.g, 3 for 2-D or 4 for 3-D networks,
  transform the relative map and determine the
  absolute the positions of the nodes.
• It works for any n-dimensional networks, e.g.,
  2-D or 3-D.

49
Applying Classical MDS

• Create a proximity matrix of distances D
• Convert into a double-centered matrix B
• Take the Singular Value Decomposition of B
• Compute the coordinate matrix X (2D coordinates
  will be in the first 2 columns)

NxN matrix of 1s
NxN identity matrix
NxN matrix of 1s
50
Example Localization Using Multidimensional
Scaling (MDS) (Yi Shang et. al)

• The basic MDS-MAP algorithm
• Compute shortest paths between all pairs of
  nodes.
• Apply classical MDS and use its result to
  construct a relative map.
• Given sufficient anchor nodes, transform the
  relative map to an absolute map.

51
MDS-MAP ALGORITHM

• Compute all-pair shortest paths. O(n3)
• Assigning values to the edges in the connectivity
  graph
• Known connectivity only all edges have value 1
  (or R/2)
• Known neighbor distances the edges have the
  distance values
• Apply classical MDS and use its result to
  construct a 2-D (or 3-D) relative map. O(n3)
• Given sufficient anchor nodes, convert the
  relative map to an absolute map via a linear
  transformation. O(nm3)
• Compute the LSE transformation based on the
  positions of anchors. O(m3), m is the number
  of anchors
• Apply the transformation to the other unknown
  nodes. O(n)

52
MDS-MAP (P) The Distributed Version

• Set-up the range for local maps Rlm ( of hops
  to consider in a map)
• Compute maps of individual nodes
• Compute shortest paths between all pairs of nodes
• Apply MDS
• Least-squares refinement
• Patch the maps together
• Randomly pick a node and build a local map, then
  merge the neighbors and continue until the whole
  network is completed
• If sufficient anchor nodes are present, transform
  the relative map to an absolute map
• MDS-MAP(P,R) Same as MDS-MAP(P) followed by a
  refinement phase

53
MDS-MAP(P) (Shang and Ruml, Infocom04)

• The basic MDS-MAP works well on regularly shaped
  networks, but not on irregularly shaped networks.
• MDS-MAP(P) (or MDS-MAP based on patches of local
  maps)
• For each node, compute a local relative map using
  MDS
• Merge/align local maps to form a big relative map
• Refine the relative map based on the relative
  positions (optional). (When used, referred to as
  MDS-MAP(P,R) )
• Given sufficient anchors, compute absolute
  positions
• Refine the positions of individual nodes based on
  the absolution positions (optional)

54
SOME IMPLEMENTATION DETAILS OF MDS-MAP(P)

• For each node, compute a local relative map using
  MDS
• Size of local maps fixed or adaptive
• Merge/align local maps to form a big relative map
• Sequential or distributed scaling or not
• Refine the relative map based on the relative
  positions
• Least squares minimization what information to
  use
• Given sufficient anchors, compute absolute
  positions
• Anchor selection centralized or distributed
• Refine the positions of individual nodes based on
  the absolution positions
• Minimizing squared errors or absolute errors

55
AN EXAMPLE OF C-SHAPE GRID NETWORKS
Known 1-hop distances with 5 range error
Connectivity information only
MDS-MAP(P) without both optional refinement steps.
56
RANDOM UNIFORM PLACEMENT
Connectivity information only
Known 1-hop distances with 5 range error
200 nodes 4 random anchors
57
RANDOM C-SHAPE PLACEMENT
Connectivity information only
Known 1-hop distances with 5 range error
160 nodes 4 random anchors
58
APIT
59
Overview of APIT

• APIT employs a novel area-based approach. Anchors
  divide terrain into triangular regions
• A nodes presence inside or outside of these
  triangular regions allows a node to narrow the
  area in which it can potentially reside.
• The method to do so is called Approximate Point
  In Triangle Test (APIT).

60
Perfect PIT Test

• Proposition 1 If M is inside triangle ABC, when
  M is shifted in any direction, the new position
  must be nearer to (further from) at least one
  anchor A, b or C

A
M
C
B
61
Continued

• Proposition 2 If M is outside triangle ABC, when
  M is shifted, there must exist a direction in
  which the position of M is further from or closer
  to all three anchors A, B and C.

A
M
C
B
62
Perfect PIT Test

• If there exists a direction such that a point
  adjacent to M is further/ closer to points A, B,
  and C simultaneously, then M is outside of ABC.
  Otherwise, M is inside ABC.
• Perfect PIT test is infeasible in practice.

63
Departure Test.

• Experiments show that, the receive signal
  strength is decreasing in an environment without
  obstacles.
• Therefore further away a node is from the anchor,
  weaker the received signal strength.

M
N
A
64
Appropriate PIT Test.

• Use neighbor information to emulate the movements
  of the nodes in the perfect PIT test.
• If no neighbor of M is further from/ closer to
  all three anchors A, B and C simultaneously, M
  assumes that it is inside triangle ABC.
  Otherwise, M assumes it resides outside this
  triangle.

65
Inside Case
Outside Case
66
Error Scenarios for APIT test.
In to out error
Out to in error
67

• However, from experimental results it is seen
  that the error percentage is small as the density
  increases.

68
APIT aggregation

• Represent the maximum area in which a node will
  likely reside using a grid SCAN algorithm.
• For inside decision the grid regions are
  incremented.
• For outside decision the grid regions are
  decremented.

69
Algorithm

• Anchor Beaconing
• Individual APIT Test
• Triangle Aggregation
• Center of Gravity Estimation

• Pseudo Code
• Receive beacons (Xi,Yi)
• from N anchors
• N anchors form triangles.
• For ( each triangle Ti ? )
• InsideSet ? Point-In-Triangle-Test (Ti)
• Position COG ( nTi ?InsideSet)

70
APIT Aggregation
High Possibility area
Grid-Based Aggregation
With a density 10 nodes/circle, Average 92
A.P.I.T Test is correct Average 8 A.P.I.T Test
is wrong
Low possibility area
Localization Simulation example
71
Evaluation

• Radio Model Continuous Radio Variation Model.
• Degree of Irregularity (DOI ) is defined as
  maximum radio range variation per unit degree
  change in the direction of radio propagation

a
DOI 0 DOI
0.05 DOI 0.2
72
Simulation Setup

• Setup
• 1000 by 1000m area
• 2000 4000 nodes ( random or uniform placement )
• 10 to 30 anchors ( random or uniform placement )
• Node density 6 20 node/ radio range
• Anchor percentage 0.52
• 90 confidence intervals are within in 510 of
  the mean
• Metrics
• Localization Estimation Error ( normalized to
  units of radio range)
• Communication Overhead in terms of message

73
Error Reduction by Increasing Anchors
AH1028,ND 8, ANR 10, DOI 0
Placement Uniform
Placement Random
74
Error Reduction by Increasing Node Density
AH16, Uniform, AP 0.62, ANR 10
DOI0.1
DOI0.2
75
Error Under Varying DOI
ND 8, AH16, AP 2, ANR 10
Placement Uniform
Placement Random
76
Localization in mobile sensor networks
Does mobility help or hurt? Following is a
solution from MOBICOM 06 U. Virginia

• (Reasonably) Accurate Localization in Mobile
  Networks
• Low Density, Arbitrarily Placed Seeds
• Range-free no special hardware
• Low communication (limited addition to normal
  neighbor discovery)

77
Our Approach Monte Carlo Localization

• Adapts an approach from robotics localization
• Take advantage of mobility
• Moving makes things harderbut provides more
  information
• Properties of time and space limit possible
  locations cooperation from neighbors

Frank Dellaert, Dieter Fox, Wolfram Burgard and
Sebastian Thrun. Monte Carlo Localization for
Mobile Robots. ICRA 1999.
78
MCL Initialization
Nodes actual position
Initialization Node has no knowledge of its
location. L0 set of N random locations in
the deployment area
79
MCL Step Predict
Nodes actual position
Predict Node guesses new possible locations
based on previous possible locations and maximum
velocity, vmax
80
Prediction
p(lt lt-1) c if d(lt, lt-1) lt vmax
0 if d(lt, lt-1) vmax
Assumes node is equally likely to move in any
direction with any speed between 0 and vmax. Can
adjust probability distribution if more is known.
81
MCL Step Predict
Filter
Nodes actual position
r
Seed node knows and transmits location
Predict Node guesses new possible locations
based on previous possible locations and maximum
velocity, vmax
Filter Remove samples that are inconsistent
with observations
82
Filtering
S
S
Indirect Seed If node doesnt hear a seed, but
one of your neighbors hears it, node must be
within distance (r, 2r of that seeds location.
Direct Seed If node hears a seed, the node must
(likely) be with distance r of the seeds location
83
Resampling
Use prediction distribution to create enough
sample points that are consistent with the
observations.
84
Recap Algorithm
Initialization Node has no knowledge of its
location. L0 set of N random locations in
the deployment area Iteration Step Compute
new possible location set Lt based on Lt-1,
the possible location set from the previous time
step, and the new observations. Lt
while (size (Lt) lt N) do R l l is
selected from the prediction distribution
Rfiltered l l where l ? R and filtering
condition is met Lt choose (Lt ?
Rfiltered, N)
85
Homework 9 Due Monday Nov 10

• Present a summary of the following paper (lt 2
  pages)
• A Wireless Sensor Network for Real-time Indoor
  Localisation and Motion Monitoring IPSN 2008
• Lasse Klingbeil, Tim Wark (CSIRO ICT Centre)
• Optional reading
• Belief propagation techniques for localization
• Ihler et al IPSN 2004

86
WSN for Indoor Localization

• CSIRO Australia

87
Goals

• Low cost indoor tracking
• Range free localization
• No special hardware for precise range estimation
• No system calibration
• Low network overhead

88
Contributions

• Localization using combination of
• Local mobility model (accelerometer, gyroscope)
• Range free localization
• Map information
• Actual real time implementation
• Root mean square error (over time) around 2m

89
Network model

• Static wireless infrastructure base station
• Act as seed nodes for localization
• Coarse grained position measurement
• If mobile node can hear seed node
• Distance modeled as a sigmoid probability density
  fn
• Provide communication infrastructure
• Mobile network
• Data transferred to seed nodes
• Single hop (data buffered until seed node met)
• Implicit acknowledgement and retransmissions

90
On board processing

• Step detection
• Using accelerometer (25Hz sampling)
• Threshold on FIR averaging filter
• Constant stride length at every step constant
• Angle estimation
• Using magnetometer and gyroscope
• Low weight given to magnetometer
• Data transmitted step angle

91
Angle estimation error
92
Data transmission

• Mobile node beacons top most event periodically
• A static node that hears, forwards to base
• Currently base assumed one hop
• Mobile node overhears implicit ack
• Multiple static nodes can forward which one is
  seed?
• Mobile node maintains nearest seed variable
• Updated whenever implicit ack received
• Reset to null after 1 second of no ack
• Sent along with event data
• Message considered by base if sending node
  nearest node

93
Monte Carlo Localization

• Position Xk at time tk
• (Px,Py)k
• Modeled as p(Xk), a probability distribution for
  Xk
• Represented by N particles (Xki, wki), i1..N
• Initially (k0)
• All N particles drawn uniformly from entire area
• At every locally detected step
• Mobile node buffers estimated angle of movement

94
Monte Carlo Localization

• Update step
• For every step event received by base (when
  mobile node within range of anchor)
• Calculate Xk1i for i1..N
• Use Gaussian error model around the estimated
  angle and constant stride length
• Update wk1i as follows
• Set to 0 if estimated position is a wall
• Else set to 1

95
Monte Carlo Localization

• Correction step
• If any step even occurred within range of seed
  node (indicated by nearest seed variable not
  NULL)
• Correct wsi (i1 .. N) for that time as follows
• wsi wsi f(d)
• ddist(seed node, Xsi )
• f(d) models probability of mobile node being at
  Xsi given position of seed node
• Renormalize wsi so that they add to 1
• Resample
• Get number of non zero weight particles back to N
• Number of points around around Xi proportional to
  wi

96
Monte Carlo estimation

• At any time
• Location mean of all N particle locations
• Confidence estimate standard deviation across
  particles

97
Simulation model

• Topology
• 50m X 60m area with walls
• Motion model
• Walk in a straight line
• Steps drawn from random distribution
• Upon hitting wall change direction randomly
• Motion detection
• Step detection probability 100
• Angle errors Gaussian with standard deviation
  10 degree
• Network
• Nominal range 5m (used in distance estimation)
• Transmission range uniformly distributed
• 5(1 r) to 5(1 r)
• Lossy

98
Sample path and map
99
Simulation parameters

• Seed density
• Number of particles
• Map availability
• Packet loss rate
• Degree of irregularity r
• Metric
• Root mean square of the error along path

100
RMS estimation error Vs seed distance

• N 500
• No loss in transmissions
• r0.3

101
Max estimation error Vs seed distance

• N 500
• No loss in transmissions
• r0.3

102
Estimation error Vs N

• With map
• No loss in transmissions
• r0.3

103
Estimation error over time

• With map
• No loss in transmissions
• Seed distance 10m
• r 0.3

104
Estimation error Vs r, loss

• With map, seed distance 10m, N500

105
Experimental evaluation

• Platform
• Fleck mote
• Atmega-128 micro-controller
• 915MHz radio
• 3 single axis gyroscopes
• 2 dual axis accelerometer
• Magnetometer
• Topology
• Office building (area not known)
• 9 seed nodes (5-10m apart)

106
Map (hard to read)
107
Measured latency and error
108
Experiment - summary

• Latency
• Standard deviation (from 0) 1.3
• Maximum 8 seconds
• Estimation error with map
• Standard deviation (from 0) 1.2m
• Maximum 2.5m
• Estimation error without map
• Standard deviation (from 0) 2.5m
• Maximum 5.2m

109
Comments

• What value did gyroscope add?
• Not clear from analysis / simulation
• Radio error bounded by 3m
• RMS estimation error approx. 1-1.5m
• Max estimation error approx. 2.5-3m
• Map is confusing
• Allowed space Vs error?
• Experiments dont tell much