Joint Navigation and Synchronization using SOOP in GPS ... · [] joint work with François Quitin, Chi Cheng, and Wee Peng Tay, Sirajudeen Gulam Razul, and Chong Meng Samson See LENG

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


3 Algorithm


5 Conclusion


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


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.


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


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


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?


Measurements

Outline

1 Introduction


3 Algorithm


5 Conclusion


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


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)]


Algorithm

Outline

1 Introduction


3 Algorithm


5 Conclusion


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.


Experiment

Outline

1 Introduction


3 Algorithm


5 Conclusion


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.


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


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


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


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 .


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.


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.


Thank you!


IntroductionMeasurementsmeasurement typemeasurement model

AlgorithmExperimentexperiment setupresults

Conclusion

Documents

Joint Navigation and Synchronization using SOOP in GPS ... · [] joint work with François Quitin, Chi Cheng, and Wee Peng Tay, Sirajudeen Gulam Razul, and Chong Meng Samson See LENG