Underwater Localization with Time- Synchronization and Propagation Speed Uncertainties Roee Diamant, Lutz Lampe.

Underwater Localization with Time-Synchronization and Propagation Speed Uncertainties

Roee Diamant, Lutz Lampe

Brief overview on underwater communication

Localization in the underwater acoustic channel

Suggested localization protocol

Future work

Outline

Motivations Most underwater activities require underwater communications [1]

Cables are heavy, deployment is expensive. Solution: wireless information transmission through the ocean

Wireless communication: Radio (30Hz-300Hz, very high attenuation) Optical (short distances, pointing precision)

Large body of relevant applications [2]: Ocean exploration warning systems, pollution control Military underwater surveillance Underwater oil exploration

Challenges of UWAC Fast time-varying frequency-selective channel

Large Doppler shift and Doppler spread

Power attenuation increase with frequency

Ambient noise decreases with frequency

Half duplex communication

Slow propagation speed

Limited signal bandwidth

[3]

Example of measured channel responses

Sea trial

Challenges of UWAC

Character RF UWAC Effect

Propagation delay T

low throughputTransmission

rate ~1MB ~1Kb

Error

probabilities~10-7 ~10^-4

Low reliability

SNR high low Substantial multiple access interference

~10^5 T

Localization in UWAC Networks: GPS is only used by surface nodes [4] Accurate attenuation models are hard to find [3]

Propagation speed is an unknown parameter [5]

Network nodes are not time-synchronized

Nodes permanently move in the channel

Joint time-synchronization and location estimation where the propagation speed is an unknown variable

Brief overview on underwater communication

Localization in the underwater acoustic channel

Suggested localization protocol

Future work

Outline

System Model Network of L anchor nodes at known time-varying locations

At least one unlocalized node at time-varying location

Nodes are not time-synchronized such that

Unlocalized node has INS system to self evaluate its location

Self-evaluated locations are not accurate but are used to accurately measure movements for a short period of time

ypi

xpi ll ,, ,

Anchor node index

Location index yn

xn jj ,

lllm ostt

Node’s m time

Node’s l time SkewOffset

2'

2

'',yn

yn

xn

xnnn jjjjd x

nxn

yn

yn

nn jj

jj

'

'',tan

Location index

m

System Model (2) Propagation delay is

where is the unknown propagation speed within

The objective is to estimate at the end of a localization window with duration

c

22pd,

1 yp

yn

xp

xnpn ljlj

cT

sec15601420 mc

yN

xN jj ,

W

Available MeasurementsaplT ,

anR

bnT '

bplR ',

We assume that time-of-arrival (ToA) measurements are affected by i.i.d white Gaussian noise

time

Unlocalized node

Anchor node

Problem Formulation

xn

xn

yn

yn

nn

yn

yn

xn

xnnn

lpn

yp

yn

xp

xnpnl

jj

jj

jj

jjjjd

ljljc

TyN

xN

'

'',

2

'

2

'',

l2pd

p',n'l,bp'l,l

bn'

l1pd

pn,l,apl,l

an

,,

22pd,,

,

tan)4(

)3(

o+)-T+(Rs=T)2(

o+)+T+(Ts=R)1(

1560c1420:s.t

1min

Given pnl ,,R,R,T,T,l,l bpl,

an

bpl,

apl,

yp

xp

Time-Synchronization Followed by Localization

Eq. (1) and (2) can be rearranged in a matrix form

where depend on the skew and offset of the unlocalized node relative to the anchor node

Using separate LS estimators we estimate the clock skew and offset of the unlocalized node relative to all anchor nodes

Next, we obtain the propagation delay at all points,

llllB +b=

l

pdpn,l,T

l

Localization Motion vectors can be represented as

We get the following Eq.

)(tan1

d=

n'n,2

n'n,n'n,

)tan(= n'n,n'n,n'n,

','

','

2

''

2

''pd

',',

22pd,,

)4(

)3(

1ˆ)2(

1ˆ)1(

nnyn

yn

nnxn

xn

yp

yn

xp

xnpnl

yp

yn

xp

xnpnl

jj

jj

ljljc

T

ljljc

T

Localization (2) Using simple manipulation we represent the localization

problem in the matrix form

where depends on the elements of

Following [6], we use the rough estimator to construct vector and its covariance matrix,

Next, we refine the rough estimator to get a weighted LS estimator

ekA W

W

kWT-1T AAA=

~

e

eQ

kW1-e

T-11-e

T QAAQA=

e

-11-e

T AQAˆ WLSQ

Localization (3)

Finally, we represent the inner connection between the variables of (related by the motion vectors) in

to estimate

Refinement step: use to construct Then, is used instead of the rough LS estimator

y=jG N

y1-WLS

T-11-WLS

TN QGGQG=j

W

Nj

W

W W~

Flow ChartOnline measurements:

ToA and INS

Initial processing:ToA noise mitigation, motion vectors

Time synchronization for each anchor : Estimate skew and offset

Estimate propagation delay

Localization :Rough LS estimatorConstruct error covariance matrixWLS estimatorUtilize inner connection, WLS estimator

Iterativerefinement

Simulation Results Simulations were performed using 2 anchor nodes and an

unlocalized node, moving at random speed and directions

To simulate errors, we added i.i.d Guassian noise to ToA measurements, and motion vectors

Anchor nodes offset and skew where generated as i.i.d Guassian noise

Results were compared to the simple multileteration method and a benchmark method (joint protocol) [6]. Reference methods are given nominal propagation speed of 1500m/sec

Localization Simulation Results

All nodes time-synchronizedSound speed known

All nodes are time-synchronizedSound speed is unknown

Localization Simulation Results (2)All nodes not time-synchronized, sound speed is unknown

Trial Sea

Sea Trial Four vessels: three anchors and one unlocalized node, each

deployed transceiver at 10m depth Vessels moved freely with ocean current Achieved localization accuracy ~10m (compared with GPS

positioning of the vessels)

Summary and future work We suggested a heuristic algorithm for UWAL

The algorithm compensates time-synchronization and sound-speed uncertainties

Extension of this work will include formalization of the Cramér–Rao bound for the considered problem, propagation speed estimation using localization and results from the sea trial

Follow-up research will be continuous tracking of already localized nodes

[1] M.Chitre, S.Shahabodeen, and M.Stojanovic, “Underwater acoustic communications and networking: Recent advances and future challenges,” in Marine Technology Society Journal, vol. 42, no. 1,2008, pp.103–116

[2 ]W. Burdic, Underwater Acoustic System Analysis. Los Altos, CA, USA: Peninsula Publishing, 2002.

[3 ]Stojanovic and J. G. Proakis, Acoustic (underwater) Communications in Encyclopedia of Telecommunications. Hoboken, NJ, USA: John Wiley and Sons, 2003

[4 ]Lee, P. Lee, S. Hong, and S. Kim, “Underwater navigation system based on inertial sensor and doppler velocity log using indirect feedback kalman filter,” in Journal of Offshore and Polar Engineering, vol. 15, no. 2, jun 2005, pp. 88–95

[5 ]Tan, R. Diamant, W. Seah, and M. Waldmeyer, “A survey of techniques and challenges in underwater localization,” Accepted for Publication in the ACM Journal of Ocean Engineering

[6 ]J. Zheng and Y. Wu, “Localization and time synchronization in wireless sensor networks: A unified approach,” in

IEEE Asia Pacific Conf. on Circuits and Sys., Macao, China, Nov. 2008

[7 ]S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ: Prentice-Hall, 1993.

Bibliography

Thank you!

Questions?

Roee Diamant, Lutz Lampe

[email protected]