Multilateration (Hyperbolic Location Technique, TDOA) Zafer Hasim TELLIOGLU August, 2010 .
-
Upload
lesley-jennings -
Category
Documents
-
view
236 -
download
10
Transcript of Multilateration (Hyperbolic Location Technique, TDOA) Zafer Hasim TELLIOGLU August, 2010 .
MultilaterationMultilateration(Hyperbolic Location Technique, TDOA)(Hyperbolic Location Technique, TDOA)
Zafer Hasim TELLIOGLUZafer Hasim TELLIOGLU
August, 2010August, 2010
www.zhtellioglu.comwww.zhtellioglu.com
22
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
33
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
55
2-D Localization Algorithm2-D Localization Algorithm
66
2 Receivers Case2 Receivers Case
PassiveReceiver
PassiveReceiver
d1
d2
Emitter
The same pulse is received!
The same pulse has not been received!
77
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 !
88
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
99
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
1313
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.
1414
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
1515
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
1717
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
2323
EndEnd