Localization of Mobile Nodes in an UnderwaterDistributed Antenna System

Patrick Carroll, Katherine Domrese, Hao Zhou, Shengli Zhou, andPeter Willett

Presented By: Zheng Peng

Dept. of Electrical and Computer EngineeringUniversity of Connecticut

November 12, 2014

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Distributed Antenna System (DAS) networks are a commonfeature in current underwater networksKey features:

◮ Secondary communication link.◮ Multiple acoustic nodes at different locations.◮ Centralized Processing

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Modem Advancements

Current acoustic OFDM modem technology has advanced beyondwhat initially was available for localization.

Any message sent, regardless of content, can accurately estimatethe relative Doppler speed of the transmitter and receiver

With stationary receivers, such as DAS network antennas, theDoppler speed of any mobile node can be accurately estimated.

With the additional Doppler information, position and instantaneousvelocity can both be estimated. With one message from N antennas,we obtain:

N time-of arrivals

N Doppler speed estimates.

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Localization Algorithm DerivationFirst, we form the time-difference of arrival (TDOA) estimate:

∆tn,1(k) = tsn(k) − ts1(k) (1)

which is equivalently:

∆tn,1(k) =1

cdsn(k) +Os(k) + wrn(k)−

1

cds1(k) +Os(k) + wr1(k) (2)

=1

c[dsn(k)− ds1(k)] + wrn(k)− wr1(k) (3)

With the timing offset eliminated, and assuming that our noises arezero-mean additive Gaussian, the ML estimator for the position wouldbe:

[x(k), y(k), z(k)] = argmin(x(k),y(k),z(k))

N∑

n=2

[(c∆tn,1(k) − dsn(k)− ds1(k)]2 (4)

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Doppler InformationThe Doppler shift measured at each node can be represented as:

vn(k) = |vn(k)|(cos(α(k)) + tan(γ(k))) (5)

where

|vn(k)| =√

xs(k)2 + ys(k)2 + zs(k)2 (6)

The total angle between an antenna and the active node isdenoted as:

cos(α(k)) =xs(k) − xn

rn(k)+

ys(k)− yn

rn(k)(7)

tan(γ(k)) =zs(k)− zn

rn(k)(8)

where

rn(k) =√

(xs(k)− xn)2 + (ys(k)− yn)2 + (zs(k)− zn)2 (9)

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Localization Algorithm DerivationWe define the complete state vector:

Θ(k) = [x(k), y(k), z(k), x(k), y(k), z(k)] (10)

Again assuming zero-mean additive Gaussian noise the joint likelihoodfor the active node s is:

Θ(k) = argminΘ(k)

1

2(cσt)2

N∑

n=2

[(c∆tn,1(k)− (dsn(k) − ds1(k))]2

+1

σ2v

N∑

n=1

(vn(k)− vn(k))2 (11)

where σv is the Doppler speed measurement noise standard deviationin m/s.

Solved by first using a coarse search grid for initial point, thengradient-descent search to for solution.

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Tracking

Tracking filters in this scenario serves two purposes:

TDOA only measurements can only estimate velocity with filtering;this acts as a baseline for comparison

Most mobile elements will employ basic filtering; examine ifDoppler information can improve tracking.

We use a Kalman Filter (KF) and Probabilistic Data Association Filter(PDAF) for approximate straight-line motion.

The state for the Doppler-aided KF and PDAF are provided a6-state measurement and track 9 states (3D position, velocity andacceleration).

We present only the KF results here and in the short paper. Fullpaper will have both.

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Simulations

Four antenna nodes located on the same z-plane defined as z = 0arranged in a square separated by 300m.

Active node begins positioned in this grid at (x, y, z) = (75, 25, 10)in meters

Node has constant velocity defined as (x, y, z) = (−.5, .7, .4) inmeters/second.

There are 20 total measurements during the scenario.

1000 Monte-Carlo runs.

The simulated noise level is σr = 0.825m and σv = .07m/s.

Messaging intervals of 5 s.

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Simulated Position Error for Mobile Node

0 2 4 6 8 10 12 14 16 181

2

3

4

5

6

7

Measurement Cycle (k)

RM

S P

ositio

n E

rro

r (m

ete

rs)

Doppler MLPosition MLDoppler KFDoppler PDAF

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Simulated Velocity Error for Mobile Node

0 2 4 6 8 10 12 14 16 180.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Measurement Cycle (k)

RM

S V

elo

city E

rro

r (m

ete

rs/s

eco

nd

)

Doppler MLDoppler KFDoppler PDAF

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Pool Testing

Pool testing was performed at the UCONN Brundage Pool onJune 24th, 2014.

The pool is approximate 24 meters by 13 meters, and the fourantenna nodes were deployed at the corner edges.

The active node was moved along the entire length of the pool ata constant velocity, 7.5m away from the side.

Active node transmits a message every 4 seconds, approximately20 times total.

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Node Layout During Pool Test

−25 −20 −15 −10 −5 0 50

2

4

6

8

10

12

14

X−position (m)

Y−

posi

tion

(m)

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Position Error for Mobile Node During Pool Test

0 5 10 15 200

5

10

15

20

25

30

Measurement Cycle (k)

RM

S P

ositio

n E

rror

(mete

rs)

Doppler MLPosition MLDoppler KFPosition KF

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Velocity Error for Mobile Node During Pool Test

0 5 10 15 200

1

2

3

4

5

6

Measurement Cycle (k)

RM

S V

elo

city E

rro

r (m

ete

rs/s

eco

nd

)

Doppler MLDoppler KFPosition KF

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Summary

Derived a mobility oriented localization algorithm that exploitsadvances and trends in underwater acoustic networking.

Presented algorithms and simulations of the solution.

Tested the algorithm in a controlled environment and performedanalysis of the sources of error present in results.

Future work includes examining additional tracking algorithms andinvestigating possible larger scale testing.

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