MultilaterationMultilateration(Hyperbolic Location Technique, TDOA)(Hyperbolic Location Technique, TDOA)

Zafer Hasim TELLIOGLUZafer Hasim TELLIOGLU

August, 2010August, 2010

www.zhtellioglu.comwww.zhtellioglu.com

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Multilateration is time difference of arrival Multilateration is time difference of arrival based position estimation algorithmbased position estimation algorithm

A receiver can estimate its location by using a A receiver can estimate its location by using a few few synchronoussynchronous transmitters transmitters

An emitter can be located by using a few An emitter can be located by using a few synchronoussynchronous receivers receivers

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Location Estimation Location Estimation oof f a a Receiver Receiver (Navigation)(Navigation)

LORANLORAN ( (LOLOng ng RARAnge nge NNavigation) and avigation) and CHAYKACHAYKA are the most famous systems are the most famous systems

44

Location Estimation of an EmitterLocation Estimation of an Emitter

Cell-Phone (GSM) Tracking, Passive Radars etc…Cell-Phone (GSM) Tracking, Passive Radars etc…

Kopáč, Ramona, Tamara and VERA are the famous Kopáč, Ramona, Tamara and VERA are the famous Electronic Warfare Support Measurement Systems.Electronic Warfare Support Measurement Systems.

[1]

[1] Era VERA-E ELINT and Passive Surveillance System Document

Location of theF-16 is estimated byusing 4 receivers.Emitters

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2-D Localization Algorithm2-D Localization Algorithm

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2 Receivers Case2 Receivers Case

PassiveReceiver

PassiveReceiver

d1

d2

Emitter

The same pulse is received!

The same pulse has not been received!

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2 Receivers Case2 Receivers Case

PassiveReceiver

PassiveReceiver

d1

d2

Emitter

The same pulse is received!

The same pulse has not been received!

There is a time difference of arrival for the same pulse in different receivers due to distance difference between d1 and d2 !

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2 Receivers Case2 Receivers Case

x

y

d0

d1

Reference receiver &Reference point (x0=0, y0=0)

E(xe,ye)

R1(x1,y1)

R0(x0,y0)

The distance between 2 points:

y

x

noreceiveriyxERd ii :22

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2 Receivers Case2 Receivers Case

x

y

d0

d1

Reference receiver &Reference point (x0=0, y0=0)

E(xe,ye)

R1(x1,y1)

R0(x0,y0)

The distance between 2 points:

noreceiveriyyxxERd eieiii :22

y

x

noreceiveriyxERd ii :22

21

2111 ee yyxxERd

20

2000 ee yyxxERd

1010

2 Receivers Case2 Receivers Case

x

y

d0

d1

Reference receiver &Reference point (x0=0, y0=0)

E(xe,ye)

R1(x1,y1)

R0(x0,y0)

The distance between 2 points:

noreceiveriyyxxERd eieiii :22

y

x

noreceiveriyxERd ii :22

21

2111 ee yyxxERd

20

2000 ee yyxxERd

Note That; Receivers can not measurethe distance (di) to the emitter!There is no any RADAR transmitter!

If the receivers are synchronous, the difference can be measured!

1111

2 Receivers Case2 Receivers Case

x

y

d0

d1

E(xe,ye)

R1(x1,y1)

R0(x0,y0)

Position of the receivers are known!

!calculated becan known! is andTDOA

(TDOA) difference timethemeasurecan receivers ssynchronou

:differencearrivalsoftime

21

21

20

201010

dv

waveofspeedvv

dTDOATOA

yyxxyyxxddd eeee

1212

2 Receivers Case2 Receivers Case

x

y

d0

d1

E(xe,ye)

R1(x1,y1)

R0(x0,y0)

!calculated becan known! is andTDOA

(TDOA) difference timethemeasurecan receivers ssynchronou

:differencearrivalsoftime

21

21

20

201010

dv

waveofspeedvv

dTDOATOA

yyxxyyxxddd eeee

Another emitterprovides the sameTDOA and d

d, x0,y0,x1,y1 are known. xe, ye are unknowns!1 equation and 2 unknowns!There is no unique solution of the equation.Indeed, d is a hyperbolic curve equation!

Any (xe, ye) pair on the curve gives the same d

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2 Receivers Case2 Receivers Case

2 receiver points provide one curve!2 receiver points provide one curve!

N receivers provides N-1 curves and N receivers provides N-1 curves and d equations!equations!

2 receivers can not provide location of the emitter in 2 receivers can not provide location of the emitter in 2-D space.2-D space.

At leastAt least 3 receivers are required! 3 receivers are required! 3 receivers 3 receivers 2 equations 2 equations 2 unknowns ( 2 unknowns (xe, ye) can be ) can be

solved!solved!

Using Using moremore receivers is better way in applications. receivers is better way in applications.

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AOA in AOA in 2 Receivers Case2 Receivers Case

2 receivers can provide Angle of Arrival!2 receivers can provide Angle of Arrival! ( ())

x

y

R1(x1,y1)R0(x0,y0)

Emitter

L

L

vTDOA

vL

TDOA)(

/sin

Emitter

2 receivers!

L

AOAFinder

2 receivers!

[3]

[3] www.eslkidstuff.com\BodyTour.htm

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33 Receivers Case Receivers Case

2D location of the emitter can be solved.2D location of the emitter can be solved.

x

y

d0 d1

E(xe,ye)

R1(x1,y1)

R0(x0,y0)

d10

R2(x2,y2)

d2

equations. two theusingby calculated becan and

known! are and , TDOA,

(TDOA) difference timethemeasurecan receivers ssynchronou

:differencearrivalsoftime

receivers! threeusingby equations Two

1210

21

21

22

221212

21

21

20

201010

ee

eeee

eeee

yx

ddv

waveofspeedvv

dTDOATOA

yyxxyyxxddd

yyxxyyxxddd

d12

1616

33-D Localization Algorithm-D Localization Algorithm

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44 Receivers Case Receivers Case

N receivers provides N-1 curves and N receivers provides N-1 curves and d equations!equations!

xxee,, yyee,, zzee are unknowns in 3-D space. are unknowns in 3-D space.

At leastAt least 4 receivers are required! 4 receivers are required! 4 receivers 4 receivers 3 equations 3 equations 3 unknowns ( 3 unknowns (xe, ye, ze) can be ) can be

solved!solved!

Using Using moremore receivers is better way in applications. receivers is better way in applications.

21

21

21

20

20

201010

222

222

)()()()()()(

)()()(

eeeeee

bababaab

ab

zzyyxxzzyyxxddd

zzyyxxd

zyxd

1818

44 Receivers Case Receivers Case

[2] Era VERA-E ELINT and Passive Surveillance System Document

[2]

1919

ApplicationApplication

2020

Application & ImplementationApplication & Implementation

Receivers or received signals must be Receivers or received signals must be synchronous to provide exact time of synchronous to provide exact time of difference.difference.The measurement error should be The measurement error should be handled in the algorithm.handled in the algorithm.The more receivers the better result!The more receivers the better result! Over-determined system provides more Over-determined system provides more

accurate location estimation in erroneous accurate location estimation in erroneous measurements.measurements.

2121

Application & ImplementationApplication & Implementation

TDOA measurement error changes the TDOA measurement error changes the algorithm implementation. algorithm implementation. [4] [5]. [4] [5]. Measurement Measurement uncertainty should be handle in the system.uncertainty should be handle in the system.

[4] Edward Dickerson, Dickey Arndt, Jianjun Ni. UWB Tracking System Design with TDOA Algorithm for Space Applications[5] Fredrik Gustafsson and Fredrik Gunnarsson. Positioning Using Time-difference Of Arrival Measurements

x

y

R1(x1,y1)

R0(x0,y0)x

y

R1(x1,y1)

R0(x0,y0)

TDOA uncertainty convertsthe curve to an area in 2-D space.

Area

Curve

2222

Application & ImplementationApplication & Implementation

Statistical methods can be used to Statistical methods can be used to estimate location of the emitter with estimate location of the emitter with minimum error.minimum error. [5, 6, 7] [5, 6, 7]

[5] Fredrik Gustafsson and Fredrik Gunnarsson. Positioning Using Time-difference Of Arrival Measurements[6] D. J. Torrieri. Statistical theory of passive location systems. IEEE Trans. Aerosp. Electron. Syst., vol. AES-20, no. 2, pp. 183-198, March 1984.[7] Muhammad Aatique. Evaluation Of Tdoa Techniques For Position Location In Cdma Systems. Master Thesis. Virginia Polytechnic Institute And State University

[5]Emitter location estimationusing noisy TDOA data

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