Joint Navigation and Synchronization using SOOP in GPS-denied … · 2016-03-15 · Introduction...

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) +$τ

b , (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) +$ξ

b. (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.


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−1HT

l , (6b)

Pl|l =(P−1

l|l−1 + FTl Rl

−1Fl)−1

, (6c)

ml|l = ml|l−1 + Kl(y(l) − f (ml|l−1)), (6d)


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!


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Joint Navigation and Synchronization using SOOP in GPS-denied … · 2016-03-15 · Introduction...

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