Temasek Laboratories@NTU
Joint Navigation and Synchronization using SOOP inGPS-denied environments: Algorithm and Empirical
Study
Leng Mei
2015-09-09
[] joint work with François Quitin, Chi Cheng, and Wee Peng Tay, Sirajudeen Gulam Razul, and Chong Meng Samson SeeLENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 1 / 24
Outline
1 Introduction
2 Measurementsmeasurement typemeasurement model
3 Algorithm
4 Experimentexperiment setupresults
5 Conclusion
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 2 / 24
Introduction
Outline
1 Introduction
2 Measurementsmeasurement typemeasurement model
3 Algorithm
4 Experimentexperiment setupresults
5 Conclusion
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 3 / 24
Introduction
Motivation
Figure: environment underinvestigation
GPS-denied:I requires dedicated GPS receiverI requires open sky viewI weak GPS signal close to noise levelI deliberately disabled by adversaries
singal-of-opportunity (SOOP):I widely available from existing
infrastructureI relatively high SNRI requires certain prior knowledgeI synchronization issue
F oscillators with poor qualityF passive beacon
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 4 / 24
Introduction
Goal
Figure: environment underinvestigation
Scenarios:I two receivers, mobile & unsynchronisedI two receivers cooperate with each otherI capture SOOP in an “eavesdropping” wayI minimum prior knowledge:
F unknown signal structureF unknown transmit timeF unknown transmit powerF knowns: beacon states (position,
velocity)
Goal: with two cooperative receivers, to jointly track a target receiver’sstate and its clock drifting with respect to its cooperative peer.
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 5 / 24
Introduction
Navigation Scheme
target receiver: Ganchor receiver: Acooperation:
I two receivers see a common set of beaconsI A shares with G its received signal or beacon information derived from
its received signalI A shares with G its own state information
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 6 / 24
Introduction
Navigation Scheme
1 spectrum scanning: identify near-by available beacons2 handshaking: agree on the beacon to receive from and the time to
receive3 information exchanging: A shared its received information and its
state information with G4 tracking: G perform self-localization and self-synchronization with
information from A and its own received signal.
SOOP are ad hocbursts from beacons are received in a sequential way
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 7 / 24
Introduction
Questions to answer
1 MeasurementsI what types of measurements to use?I how does clock drifting affect the measurement? → proper
measurement model2 Tracking algorithm:
I can we adapt extended Kalman filter for this problem?I how does the nonlinearily and uncertainty affect the performance?
3 Field experiment:I how well does our measurement model fit in real life?I how well does our algorithm perform in real life?
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 8 / 24
Measurements
Outline
1 Introduction
2 Measurementsmeasurement typemeasurement model
3 Algorithm
4 Experimentexperiment setupresults
5 Conclusion
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 9 / 24
Measurements measurement type
Measurement Type
RSS? TOA? AOA?TDOA/FDOA ← unknown waveform & signal characteristicsmethods to obtain measurements: cross-correlation
0.372 0.374 0.376 0.378 0.38 0.382 0.384 0.386 0.388 0.390
10
20
30
Time (second)
Ampl
itude
received signal after lowpass filtering
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
x 104
0
2
4
6
x 105
Frequency (Hz)
Pow
er
Figure: received packets fromIridium
Figure: complex ambiguity functionbetween raw signals
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 10 / 24
Measurements measurement model
Measurement Model
at the l-th time slot
τ(l)b ≈
∥∥∥p(l)1 − s(l)b ∥∥∥− ∥∥∥p(l)2 − s(l)b ∥∥∥+ T (l)e α(l) + θ(l) +$τb , (1a)ξ
(l)b ≈ (v
(l)1 − v
(l)b )
T u(l)1,b − (v(l)2 − v
(l)b )
T u(l)2,b + α(l) +$ξb. (1b)
TDOA/FDOA measurement : [τ (l)b , ξ(l)b ]
I θ(l): clock offset up to the l-th time slot→ θ(l) ≈ θ(l−1) + (t(l)b − t
(l−1)b )α(l−1)
I α(l): c(β(l)2 − β(l)1 ) approximately
I $τb and $ξb : measurement noise, assumed Gaussian.
knowns: s(l)b , v(l)b , p
(l)2 , v
(l)2
unknowns: [p(l)1 ,v(l)1 , θ
(l), α(l)]
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 11 / 24
Algorithm
Outline
1 Introduction
2 Measurementsmeasurement typemeasurement model
3 Algorithm
4 Experimentexperiment setupresults
5 Conclusion
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 12 / 24
Algorithm
Dynamic Model
∆l , t(l)b − t(l−1)b
clock: [θ(l)
α(l)
]=[1 ∆l0 1
] [θ(l−1)
α(l−1)
]+ ν(l)c , (2)
receiver movement:[p(l)v(l)
]=[1 1 1 ∆l ∆l ∆l0 0 0 1 1 1
] [p(l−1)v(l−1)
]+ ν(l−1)s , (3)
important parameters: covariance of ν(l)c and ν(l)sI ν
(l)c : depends on intensity of the diffusion process of clock components.
I ν(l)s : depends on acceleration.
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 13 / 24
Algorithm
Extended Kalman Filter
dynamics: x(l) = Hlx(l−1) + ν(l), (4)measurements: y(l) = f (x(l)) +$(l). (5)
Gaussian assumption:I ν(l) ∼ N
(0,Q(l)
): prior knowledge
I $(l) ∼ N(0,R(l)
): measurement accuracy → CRLB
linearisation: Fl = ∇xf (x)|x=x(l)ml|l−1 = Hlml−1|l−1, (6a)Pl|l−1 = Ql + HlPl−1|l−1HTl , (6b)
Pl|l =(P−1l|l−1 + F
Tl Rl−1Fl
)−1, (6c)
ml|l = ml|l−1 + Kl(y(l) − f (ml|l−1)), (6d)
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 14 / 24
Experiment
Outline
1 Introduction
2 Measurementsmeasurement typemeasurement model
3 Algorithm
4 Experimentexperiment setupresults
5 Conclusion
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 15 / 24
Experiment experiment setup
Experiment
Figure: one set of receiver
103.7 103.75 103.8 103.85 103.9 103.95 104
1.25
1.3
1.35
1.4
1.45
longitude
latitude
A
B
C
receiver: USRP N210+WBXbeacon: Iridium satellitesoff-line processing:
I spectrum scanning, handshaking, andinformation exchanging are correctlycarried out.
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 16 / 24
Experiment results
TDOA/FDOA measurement
−2 −1 0 1 2x 10−6
0
10
20
30
40
50
60between A and B
num
ber o
f bin
serror in TDOA (second)
−6 −4 −2 0 2 4 6x 10−6
0
20
40
60
80
100
120between A and C
num
ber o
f bin
s
error in TDOA (second)
−4 −2 0 2 40
10
20
30
40between A and B
num
ber o
f bin
s
error in FDOA (Hz)−200 −100 0 100 2000
10
20
30
40between A and C
num
ber o
f bin
s
error in FDOA (Hz)
Figure: histogram for TDOA/FDOA estimation error
mean: close to zerostandard deviation:
I TDOA: 2.73 µs for A-B, 1.73 µs for A-CI FDOA: 2.19 Hz for A-B, 36.8 Hz for A-C
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 17 / 24
Experiment results
Measurement Model Correctness
0 5 10 15 20 25 30 35 40 45 50−100
−50
0
50
time (minute)di
stan
ce (k
m)
(13a): θ1 = −0.012872, θ0 = −27.36
0 5 10 15 20 25 30 35 40 45 50−0.1
−0.05
0
0.05
0.1
time (minute)
velo
city
(km
/s)
(13b): θ1 = −0.012895
True TDOAEstimatebias
True FDOAEstimatebias
Figure: values of TDOA/FDOA v.s its true value
from TDOA bias θ(l) = θ(0) + Tα(l): empirical value for α -0.012872from FDOA bias α(l): empirical value for α -0.012895
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 18 / 24
Experiment results
Localizing static receiver - 1
0 500 1000 1500 2000 2500
−2
−1.8
−1.6
−1.4
−1.2
−1
x 105
Time (second)
bias
in ti
me
(ns)
observed bias in timelinefitted bias in timeestimate offset
0 500 1000 1500 2000 2500
−4000
−2000
0
2000
4000
6000
Time (second)bi
as in
tim
e (n
s)
estimation error (esimate − observed)estimation error (estimate − linefitted)
0 500 1000 1500 2000 2500
−65
−60
−55
−50
−45
−40
−35
Time (second)
bias
in fr
eque
ncy
(ns/
s)
observed bias in freqlinefitted bias in freqestimate skew
0 500 1000 1500 2000 2500−8
−6
−4
−2
0
2
4
6
Time (second)
bias
in fr
eque
ncy
(ns/
s)
estimation error (estimate − observed)estimation error (estimate − linefitted)
(a) Tracking clock drifting parameters
−1544−1543
−1542−1541 6186.5 6186.66186.76186.86186.9
6187 6187.16187.2
153
153.2
153.4
153.6
153.8
154
154.2
154.4
154.6
154.8
155
y−axis (km)
tracking trace for receivers
x−axis (km)
initial guess
(b) Trace for estimating the receiver lo-cation
Figure: jointly estimating static receiver B’s location and clock parameters.
slightly increasing clock skewLENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 19 / 24
Experiment results
Localizing static receiver - 2
0 500 1000 1500 2000 2500 30000
500
1000
1500
2000
2500
3000
Time (second)
erro
r (ns
)
Clock Offset
CRBEstimation
0 500 1000 1500 2000 2500 30000
5
10
15
20
Time (second)
erro
r (ns
/s)
Clock Skew
CRBEstimation
(a) clock parameters
0 500 1000 1500 2000 2500 30000
0.5
1
1.5
Time (second)
erro
r (km
)
Position
CRBEstimation
0 500 1000 1500 2000 2500 30000
0.05
0.1
0.15
Time (second)
erro
r (km
)
Position
X−axis: CRBX−axis: EstimationY−axis: CRBY−axis: EstimationZ−axis: CRBZ−axis: Estimation
(b) position
RMSE smaller than 50 m within 5 minutesclock skew model mismatch in CRLB
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 20 / 24
Experiment results
Tracking manoeuvring receiver
0 500 1000 1500 2000 2500
−6.05
−6
−5.95
−5.9
−5.85
x 105
Time (second)
bias
in ti
me
(ns)
observed bias in timelinefitted bias in timeestimate offset
0 500 1000 1500 2000 2500
−6000
−4000
−2000
0
2000
4000
6000
8000
Time (second)
bias
in ti
me
(ns)
estimation error (esimate − observed)estimation error (estimate − linefitted)
0 500 1000 1500 2000 2500
−40
−20
0
20
40
60
80
Time (second)
bias
in fr
eque
ncy
(ns/
s)
observed bias in freqlinefitted bias in freqestimate skew
0 500 1000 1500 2000 2500−60
−40
−20
0
20
40
60
Time (second)
bias
in fr
eque
ncy
(ns/
s)
estimation error (estimate − observed)estimation error (estimate − linefitted)
(c) Tracking clock drifting parameters
−1560−1540
−1520−1500
6186618861906192619461966198
140
142
144
146
148
150
y−axis (km)
tracking trace for receiver C
x−axis (km)
initial guess
tracking trajectory
true trajectory
(d) Tracking the receiver state
Figure: The proposed algorithm for tracking the manoeuvring receiver C .
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 21 / 24
Conclusion
Summary
1 bias caused by clock drifting:I in TDOA: time-varying and linearly depends on clock skewI in FDOA: device dependent, roughly constant or slowly time-varying
2 sequential tracking algorithm:I dynamic model matters:
F correctly tracking the state and the clock parameters when the modelfits well
F problematic when tracking manoeuvring receiver with insufficientmeasurements or incorrect model information
I initial guess matters:F the clock biases and the receiver states are correlated.
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 22 / 24
Conclusion
Future Work
incorporate IMU to improve accuracy for tracking manoeuvringtarget.
I to compensate for insufficient measurements due to long observationintervals
I must deal with the accumulating error in IMUextend to scenarios with multiple targets.explore alternative beacons, including UAV, planes, and FM stations.
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 23 / 24
Thank you!
LENG Mei Joint Navigation and Synchronization using SOOP in GPS-denied environments: Algorithm and Empirical Study2015-09-09 24 / 24
IntroductionMeasurementsmeasurement typemeasurement model
AlgorithmExperimentexperiment setupresults
Conclusion