RADIO INTERFEROMETRIC
GEOLOCATION
By: Kate Hayes
OUTLINE
• Introduction
• Theoretical background behind radio interferometry
• Analyzing sources of error
• Prototype implementation
• Technique discussion for distance
• Localization algorithm
• Field Experiments
• Conclusion
http://thor.he.net/~gludlow/rip.gif
INTRODUCTION TO STATE OF THE
ART
• Acoustic WSNs have limited range of high
accuracy
• Acoustic WSNs need special
actuator/detector pairs which adds to the
cost
• A number of applications require privacy
making the very limited Ultrasound signal
the only option
• Most WSNs are only available in 2D
• There seems to be the ability to have
adequate accuracy or acceptable range
but not both simultaneously
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RADIO INTERFEROMETRY
• Radio interferometry is traditionally used
in physics, geodesy, and astronomy
http://fas.org/irp/imint/docs/rst/Intro/vlbi_concept.jpg
• The method uses two or more directional
antennae to measure the radio signal
from a single source and performing
cross-correlation
• A radio interferometer is very expensive
requires tunable, directional antennae;
high sampling rates; and high precision
time synchronization
• This device is not directly applicable to
WSNs
http://perg.phys.ksu.edu/vqm/laserweb/ch-10/10-1.gif
RADIO INTERFEROMETRIC
POSITIONING SYSTEM (RIPS)
• Radio Interferometric Positioning System (RIPS) is the novel
idea to use the concepts behind interferometry and
apply them to WSNs
• The main idea is to use two nodes as transmitters that
create the interference pattern which is measured by
two receivers
• The frequencies emitted by the transmitters are almost
the same, which when combined create a low
frequency envelope
• The two receivers measure the wave packet’s phase
difference and use this to determine the relative position
of the four nodes
• The key attribute is that the phase offset of a low
frequency signal is measured and it corresponds to the
wavelengths of a high-frequency carrier signal
PHASE OFFSET
http://hyperphysics.phyastr.gsu.edu/hbase/sound/imgsou/beat4.gif
http://medias.audiofanzine.com/images/thumbs3/642
391.jpg
• The composite (addition of the two transmitters
signals) signal has a low beat frequency
• Relative phase offset is measured rather than the
phase offset so that timing synchronization can
be avoided
• Relative phase offset between two receivers
depends on only on the four distances between
the receivers and transmitters and the
wavelength of the carrier frequency
• By measuring different carrier frequencies it is
possible to calculate linear combinations of the
distances between nodes and infer position
THEOREMS OF THE RIPS METHODS
THEOREM 1
• The RSSI signal is the power of the incoming radio signal measured in dBm
after it is mixed down to an intermediate frequency fIF
• It is then low pass filtered with filter cutoff frequency fcut, where fcut << fIF
• Let r(t) denote this filtered signal
• Theorem 1: Let f2 < f1 be two close carrier frequencies with δ = (f1 − f2)/2, δ
<< f2, and 2δ < fcut. Furthermore, assume that a node receives the radio
signal
s(t) = a1 cos(2πf1t + φ 1) + a2 cos(2 π f2t + φ 2) + n(t),
where n(t) is Gaussian noise. Then the filtered RSSI signal r(t) is periodic with
fundamental frequency f1 − f2 and absolute phase offset φ1 − φ 2
THEOREMS OF THE RIPS METHODS
THEOREM 2
• Theorem 2: Assume that two nodes A and B transmit pure sine waves
at two close frequencies f > f such that f − f < f , and two other nodes
C and D measure the filtered RSSI signal. Then the relative phase offset
of r (t) and r (t) is
A
C
B
A
B
cut
D
2π[(2d − d ) / (c/f ) + (d − d ) / (c/f )]
AD
AC
A
BC
BD
B
(mod 2π).
THEOREMS OF THE RIPS METHODS
THEOREM 3
• Theorem 3: Assume that two nodes A and B transmit pure sine waves
at two close frequencies f > f , and two other nodes C and D measure
the filtered RSSI signal. If f −f < 2 kHz, and d , d , d , d 1 km, then the
relative phase offset of r (t) and r (t) is
A
A
C
2π[(d − d + d − d )/(c/f)]
AD
BD
BC
AC
where f = (f + f )/2
A
B
•d =d −d +d −d
ABCD
AD
BD
BC
AC
B
B
AC
D
(mod 2π)
AD
BC
BD
THEOREMS OF THE RIPS METHODS
THEOREM 4
• Theorem 4: In a network of n nodes there are at most [(3/2)*(n−2)(n−3)]
independent interference measurements that can be made
• The solution to the system of equations is invariant under translation, rotation,
and reflection
• The number of unknowns is (2n - 3) in a 2D network and (3n – 6) in 3D
• At least 8 nodes in 3D are needed to get more measurements (20) than the
number of unknowns (18)
SOURCES OF ERROR (1)
• Carrier Frequency Inaccuracy – The difference between
the nominal and actual carrier frequency of the
transmitted signal.
• Carrier Frequency Drift and Noise – The phase noise and
drift of the actual carrier frequency of the transmitted
signal during the measurement. Any noise of drift will be
directly observable. This error can be minimized by
shortening the length of a single phase measurement
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955408,4/stock-photo-error-icon61313860.jpg
• Multipath Effects – Anytime the RF signal bounces off
anything rather than traveling directly to the receiver. It is
expected higher level algorithms can filter this error out
SOURCES OF ERROR (2)
• Antennae Orientation – Time of Flight can change if the antennae are not
pointed directly at the receivers
• RSSI Measurement Delay Jitter – The jitter of the delay between the
antennae receiving the radio signal and the RF chip delivering the RSSI signal
to the signal processing unit
• RSSI Signal-to-Noise Ratio – The signal strength relative to the noise of the rC(t)
signal. SNR mainly depends on the distance between transmitters and
receivers as the amplitudes of the signal decrease exponentially in space
• Signal Processing Error – Error introduced by the signal processing algorithm
that calculates the phase offset
• Time synchronization Error – Error of the time instance when the receivers
measure their absolute phase offset of the received signal strength
IMPLEMENTATION
• Selecting a pair of transmitters from a group of motes participating in the
localization and scheduling their transmission time
• Fine-grain calibration of the radios of senders to transmit at close frequencies
• Transmission of a pure sine wave by the two senders at multiple frequencies
• Analysis of the RSSI samples of the interference signal at each of the
receivers to estimate the frequency and phase offset of the signal
• Calculation of the actual dABCD range from the measured relative phase
offsets for each pair of receivers
• The Localization Algorithm
• Selection and scheduling of transmitting pairs, distance calculations, freq.
calibration, and localization are all done on the base station
PHYSICAL ATTRIBUTES
• Uses the MICA2 mote platform with
TinyOS operating System
• Chipcon CC1000 radio
• Allows pure sine wave transmission at a
specific frequency
• Radio engine component that
coordinates and synchs the particular
nodes and handles the interference
signal
• A signal processing component estimates
the phase and freq. of the sample signal
• Transmits at different power levels and a
wide freq. band
• Time required to calibrate has a large 5
ms jitter
http://deliveryimages.acm.org/10.114
5/1000000/990705/figs/f2.jpg
TIME SYNCHRONIZATION
• Measuring the relative phase offset of the
interference signal at the receivers requires
measuring the absolute phase offset relative
to a common time instant
• After getting the absolute phase offsets from
each node the relative phase offset is
achieved by subtracting them from each
other
• Only the 4 nodes participating are time
synched and only for the duration of the
synching
• The master node sends out a packet with a
precise timestamp to all participating nodes
who then use that timestamp to calibrate to
their local time
• This message specifies when the calibration
or tuning will take place in the future and at
what powers to do them at
TUNING
• The CC1000 chip needs to perform internal calibration
of the internal frequency synthesizer PLL (phase locked
loop)
• Calibration is required to compensate for supply
voltage and temperature variations
• Channel 0 is at 430 MHz and each channel is a .526
MHz step up
• PLL on C1000 chip can get up to 65 Hz freq. resolution
• Due to time and sampling rate constraints the
difference between the broadcast frequencies is from
200 – 100 Hz
• Freq. tuning algorithm determines settings for
transmitters of the same frequency
• f = 430.1 + 0.526 · channel + 65 · 10−6 · tuning.
PEAK DETECTION AND FILTERING
• Samples are processed on nodes
• Signal Processing Algorithm estimates the frequency and phase of RSSI signal
• Some of the data is processed online, but it is limited and more extensive
data is processed later post-processing
FREQUENCY AND PHASE
ESTIMATION
• Raw samples are filtered in a way to enhance SNR
• Max and Min peaks are acquired from the leading 24 samples for the
adaptive peak detection algorithm
• The acquired amplitude serves as quality indicator
• Peaks are discarded if they do not cross the low threshold in order to get rid
of false positives
• Post-processing works on peak indexes and determines the period and freq.
is the reciprocal of the period
• Phase is estimated by the average phase of the filtered peaks
SCHEDULING
High-Level
Low-Level
• Responsible for selecting the pair of
transmitters
• Coordinates the activities of the two
transmitters and multiple receivers
• Minimizes the number of
interference measurements while
still allowing enough to acquire a
3D localization
• Frequency tuning algorithm and
phase offset estimation require
proper freq. calibration and timing
• Base selects all possible pairs of
transmitters while all nodes within
range act as receivers
• Has different transmitters use
different powers to account for
differing distance from the receivers
RANGE CALCULATION
• dABCD = λini + γi = λjnj + γj ,
• A set of wavelengths is needed so that their least common multiple is larger
than the domain of the distance
• The equations become invalid due to noise and are reduced to similar
inequalities
• Solving for the inequalities gives the average di value
• The answer with minimum value to its error function becomes the final
estimate
LOCALIZATION
• RIPS does NOT provide ranging between nodes but
rather a combination of distances between the 4
nodes
• Remember dABCD = dAD − dBD + dBC − dAC
• A Genetic Algorithm (GA) is used to determine the
relative position of the nodes
• The algorithm uses all the given ranges and tries to
minimize the difference between the input range
and the range in the solution
• The solution with the least amount of error is selected
http://upload.wikimedia.org/wikipedi
a/commons/f/ff/St_5-xbandantenna.jpg
EFFECTIVE RANGE
• Determining range is not straightforward because it is not direct pairwise
• The maximum distance between a transmitter and receiver is the related to
the radio range
• The interference signal can be “heard” almost twice as far away as the
radio range this is called the Interferometric Radio Range (IRR) (r)
• No constraint on distance between two transmitters or receivers, however
they need to be in twice the IRR
• Signals need to be tuned so one signal is not much stronger than the other
transmitter’s
• Possible values of the distance : − 2r < dABCD < 2r.
EXPERIMENTAL SETUP
• 16 nodes in a
4x4 grid
• 3 anchor
points
randomly
chosen
• 18x18 meters
• This is only
testing 2D
• Testing on flat
grassy field
FREQUENCY ACCURACY
• Results comparable to high resolution
discrete Fourier transforms were
achieved
• One of the senders changed its carrier
freq. in small increments
• Ideal V-shaped curve appears
matching tuning parameters
• Phase difference (bottom) have more
noise as expected
PHASE ACCURACY
• One pair of motes were fixed as
transmitters
• Frequency tuning around 0 Hz
interference
• Repeated 30 times
• Median phase and average deviation
at each frequency
• Calculated average of the deviations
• Used amplitude as a quality of
measurement indicator
RANGING ACCURACY
• The error distribution of the calculated dABCD ranges can be approximated by the
superposition of a set of Gaussian distributions
• Filtering is used to improve the number of 0 error peaks while keeping enough
information to use
• Amplitude of the signal shows strong correlation with error in ranging
• Interference signal is measured by all modes in range
• Bad frequency measurements lead to bad range measurements and are filtered out
LOCALIZATION ACCURACY
• Localization was run using the filtered data
• Genetic optimization was run for 2 minutes
with the results in the above right figure
• Average accuracy was 5 cm
• Largest error was under 10 cm
• RIPS is pretty accurate in 2D
LATENCY
• Because so many measurements are required to take place between
different arrangements, different algorithms, freq. tuning, and actual
measurements the process takes about 80 minutes
• The tuning algorithm, range calculations, and localization are done on the
base station
• Using less combinations would drastically reduce the time to get results
without sacrificing accuracy
• If the tuning algorithm is implemented on the motes the time can also be cut
down by shortening message routes
• Its possible to decrease the number of tuning steps required as well
• The network is easily scalable since each section can be divided up by radio
range
CONCLUSION
• RIPS achieves high accuracy and long range simultaneously
• Supports 3D localization
• Does not require extra hardware or calibration
• Two transmitters create an interference signal whose phase offset is
measured by receivers
• This phase offset can be used to determine the range related to all 4 nodes
involved in the measurement
• From all the relative measurements the map of the 3D network can be
determined
RF ANGLE OF ARRIVALBASED NODE LOCATION
OUTLINE
• Introduction
• Technique
• Analysis of Technique
• Implementation
• Experimental Results
• Conclusion
http://images.tutorvista.com/cms/im
ages/102/hyperbola.png
INTRODUCTION
• In comparison to other localization methods which
use large infrastructure, extensive processing, and/or
long latencies TRIPLOC is a rapid localization
distribution method that uses radio interferometry like
RIPS but improves upon it
• TRIPLOC gathers it’s four nodes into a group of three
orthogonal nodes and one or more receiver farther
away
• On the anchor antennae array two of the nodes are
transmitters and one is a receiver
• The measured phase difference between the
receiver on the TRIPLOC array and the other receiver
constrains the location of the latter to the hyperbola
SOME TERMINOLOGY
• Node position is usually
determined by ranging or bearing
• Ranging- node estimates its
difference to different
reference points
• Bearing- the angle between
forward facing direction and
direction to object
• Triangulation is the process of
determining the position of an
object from the bearings of
known reference points
• TRIPLOC employs Bearing from
multiple nodes to determine
location
https://engineering.purdue.edu/~as
m215/topics/brngdir.gif
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RADIO INTERFEROMETRY (RI)
http://chezsez.files.wordpress.com/2010/06/
600px-doppler_effect_svg.png
• Bearing estimates are useful when anchor positions
are known
• Several acoustic beamforming techniques have
been proposed to find the angle of incidence if a
signal at an array of sensors
• There have been several improvements on the RIPS
system to track mobile devices and improve latency
• Mobile nodes have their RF signals undergo a Doppler
shift
• From the Doppler shift the motion and position can
be determined
• TRIPLOC cannot do localization for mobile nodes, but
it performs the calculations so fast that it can do it for
slowly moving nodes
RI MEASUREMENTS
• TRIPLOC array midpoint is assumed known as well as distance between antennae
• At predetermined time P and A_1 transmit a pure sinusoidal signal at slightly different
frequencies
• A_2 and the receiver node (R) measure the low-frequency beat interference
pattern created by P and A_1
• This is termed a Radio Interferometric Measurement (RIM)
• The maximum distance difference will occur when the receiver node is collinear with
the transmitters this removes the 2pi modulo ambiguity
• dA_1PR =ДΦλ/2π
BEARING APPROXIMATION 1
• dA_1PR defines the arm of the hyperbola
that intersects the position of node R
and whose asymptote passes through
the midpoint of the line A_1 and P
• The distance between the hyperbola
center and the intersection point H is
defined as a
• The length of the line segment
perpendicular to the axis containing
the foci that extends from the H to the
asymptote is called b
• In order to solve for β the values of a
and b must be determined
𝑑𝐴_1𝑃𝑅
• β = 𝑐𝑜𝑠 −1 (
𝑑𝐴_1𝑃
)
BEARING APPROXIMATION 2
• β could be +/- because if the symmetry of the
hyperbola
• In essence each RIM gives two possible β
measurements
• To solve for this the assistant nodes switch roles
and perform a second RIM
• Due to the fact that the center of the
hyperbolas are not the same for each RIM
there is an allowed error threshold
• The average of the two βs that have error
under the error threshold is the bearing
estimate βhat
• R must be farther away from the node
because the error in beta will be larger if it is
close due to the hyperbolic shape
TRIANGULATION
• When the approximate bearing of R is determined (β) its position
can be determine using triangulation
• Using two known angles and a known side the distance to R from
either anchor node can be determined
• If R is ambiguous then three have to be used, but if a β is slightly
off then there will be error
• The triangulation technique used was Least Squares Orthogonal
Error Vector Solutions which basically uses linear algebra to
come up with Rhat the position estimate with noising bearing
measurements
BEARING ESTIMATION ERROR
• Because computing distance differences can be computationally intensive
several assumptions are made by the TRIPLOC system
• Measurements noise
• Asymptotic approximation
• Translation of bearing candidates
• The analysis of array position and orientation errors are purposefully omitted
• These assumptions are made instead
• The antenna configurations are known
• Transmitter location is known
• Relative bearings are known
MEASUREMENT NOISE ERROR
• Distance Differences can contain error in the form of
measurement error
• This error can come from non-ideal signal propagation,
noise from circuitry, sampling error, or other sources
• Estimating the amount of error in βhat is done by taking
the partial derivative with respect to distance
• To see what amplification effect an error in a given
distance difference d produces on the bearing
estimate, evaluate the partial derivative at d
• When the absolute value of the measured distance
difference is close to the antenna separation, the
computed bearing candidates are very sensitive to
measurement noise
ASYMPTOTE APPROXIMATION
• For a pair of transmitters the bearing of the
receiver is approximated with angles of the
asymptote of the receiver
• It is assumed that the receiver lies on the
hyperbolic asymptote, rather than on the
hyperbola itself
• For close receivers errors of this type are not
negligible
• This error is βhat minus β and is given the
symbol ε
• The error of the approximation decreases as
the distance of the receiver from the
transmitter array increases
TRANSLATION OF BEARING
CANDIDATES
• At least two transmitter anchors are needed
because for each transmitter pair there are two
possible βs
• Bearing candidates are treated as vectors from
the center of the hyperbola
• These vectors need their coordinates translated
from the hyperbolic to the system coordinates
• A vector translated this way will not point directly
at the bearing anymore but slightly off
• If the receiver is far enough away it won’t be off
enough to matter
COMPOUND BEARING
ESTIMATION ERROR
• Two transmitter pairs each report two bearing
candidates for a total of four bearing estimates
• Its likely only two should be close to each other
(The correct ones)
• In order to figure out which ones they are all
possible pairs of one from each transmitter are
taken
• The pair with the least pairwise angular distance
is selected and the average is taken to give βhat
• In the diagram over 500 simulations are run with
an added Gaussian noise
• Errors peak where expected where the individual
transmitter pairs exhibit high error sensitivity
POSITION ESTIMATION ERROR
ANALYSIS
• Triangulation is used to compute the distance to the receiver from the
bearing measurement
• Simulation results are presented to demonstrate the effect of error from
different sources and reference real experiments
• Position error comes from three different sources:
• Position of the arrays
• Orientation of the arrays
• Bearing estimation error
POSITION ERROR OF THE ARRAYS
• T_2 is varied along the x axis and error is calculated for whether the
measurement of T_2 was off by .1, .2, or .3 m
ORIENTATION ERROR OF THE
ARRAYS
• To simulate orientation error a constant was added to the bearing reported
from T_2
• As expected R between the two Ts gives a large error estimate
BEARING ESTIMATION ERROR
• Assume location and orientation of the two antenna arrays are known
• Assume that the bearing estimates have added white noise in form of a
Gaussian random variable with σ being changed for each run
• Results suggest that as standard deviation of the bearing error is increased
the standard deviation of the location area increases as well
TRIPLOC SYSTEM SPECS
• Crossbow ExScal motes
• TI CC1000 radio chip
• Mutually orthogonal antennae to reduce parasitic effects (35.35 cm apart) and with
a wavelength greater than 70.7 cm to avoid 2pi modulo
• TinyOS operating system
• All operations run locally
• Initialization of localization process is required first
• Create and broadcast a schedule of when array anchors perform the RIMs
• All anchors keep track of when each anchor is performing the RIM so they know
when it is their turn
• Tuning is required. Two broadcast in increments and one monitors until it finds the
matching beat frequency lets the others know
• Calibration of the bearing system is requires. To calibrate place receivers at known
locations and run the estimation algorithm, the difference is the true orientation of
the arrays
MAKING RADIO INTERFEROMETRIC
MEASUREMENTS
• Because phase difference is used to calculate the bearing the signal must
be measured at the same instant
• TRIPLOC uses the same method as RIPS to synchronize clocks with a primary
node sending out a message with the time of its system in the message, a
receiver measures the time it received this message and calibrates the two
times
• After synchronization the radio needs to be acquired from the MAC layer
• Next the radio is calibrated
• Transmit and sample enough RSSI periods (about 6) to get a phase
difference
• Restore the radio to its original state so information can be shared by the
nodes
LATENCY ANALYSIS
• Latency is the amount of time it takes
from making the measurement to
getting the result, in this case the
position of the receivers
• Since TRIPLOC is intended for mobile
arrays it must perform very fast RIMs so
the sensor hasn’t had time to move far
• Each array performs two RIMs, one for
each P,A pair
• The bottom line is TRIPLOC allows its
receivers to calculate their position in
less than 1 s
EXPERIMENT 1
• Experiment 1 measures the bearing
accuracy of six receiver nodes
• The nodes are placed 60 degrees apart
10 m from the center anchor node A
• Performed 50 bearing estimates
• This experiment is consistent with the error
predictions for bearing estimations
EXPERIMENT 2
• Experiment 2 was measuring the accuracy of
14 receiver nodes from three arrays
• Outdoor, low-multipath environment
• More real world than other experiments
• 35 bearing estimates from each anchor to all
nodes so 1470 estimates total
• This experiment is also consistent with
expected results from the bearing error
estimate analysis
EXPERIMENT 3
• 20x20 m with 4 anchors in the corners
and 16 nodes in a slightly randomized
grid
• Each target node (one in grid)
periodically estimates its position
using the bearing estimation and
triangulation techniques presented in
the paper
• 100 estimations for each target
• Average overall position error was
found to be .78 m
CONCLUSION
• TRIPLOC is a method for rapidly distributed bearing estimation and localization
• The array anchor consists of three nodes arranged orthogonally to each other
• Two transmit slightly different frequencies and one measures the phase difference of
the beat frequency with another receiver a distance away
• The phase distance defines a hyperbola from which bearings can be estimated
• From these bearing estimations localization can be calculated
• Average bearing accuracy is 3.2 deg. and avg. position accuracy is .78 m
• All processing is done on nodes and avoids the 2pi modulo ambiguity
• TRIPLOC has a very fast localization time of about 1 second