Multilateration (Hyperbolic Location Technique, TDOA) Zafer Hasim TELLIOGLU August,

2 Multilateration is time difference of arrival based position estimation algorithm A receiver can estimate its location by using a few synchronous transmitters A receiver can estimate its location by using a few synchronous transmitters An emitter can be located by using a few synchronous receivers An emitter can be located by using a few synchronous receivers

3 Location Estimation of a Receiver (Navigation) LORAN (LOng RAnge Navigation) and CHAYKA are the most famous systems

4 Location Estimation of an Emitter Cell-Phone (GSM) Tracking, Passive Radars etc… Kopáč, Ramona, Tamara and VERA are the famous Electronic Warfare Support Measurement Systems. [1] [1] Era VERA-E ELINT and Passive Surveillance System Document Location of the F-16 is estimated by using 4 receivers. Emitters

5 2-D Localization Algorithm

6 2 Receivers Case Passive Receiver Passive Receiver d1d1 d2d2 Emitter The same pulse is received! The same pulse has not been received!

7 2 Receivers Case Passive Receiver Passive Receiver d1d1 d2d2 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 d 1 and d 2 !

8 2 Receivers Case x y d0d0 d1d1 Reference receiver & Reference point (x 0 =0, y 0 =0) E(x e,y e ) R 1 (x 1,y 1 ) R 0 (x 0,y 0 ) The distance between 2 points: yy xx

9 2 Receivers Case x y d0d0 d1d1 Reference receiver & Reference point (x 0 =0, y 0 =0) E(x e,y e ) R 1 (x 1,y 1 ) R 0 (x 0,y 0 ) The distance between 2 points: yy xx

10 2 Receivers Case x y d0d0 d1d1 Reference receiver & Reference point (x 0 =0, y 0 =0) E(x e,y e ) R 1 (x 1,y 1 ) R 0 (x 0,y 0 ) The distance between 2 points: yy xx Note That; Receivers can not measure the distance (d i ) to the emitter! There is no any RADAR transmitter! If the receivers are synchronous, the difference can be measured!

11 2 Receivers Case x y d0d0 d1d1 E(x e,y e ) R 1 (x 1,y 1 ) R 0 (x 0,y 0 ) Position of the receivers are known!

12 2 Receivers Case x y d0d0 d1d1 E(x e,y e ) R 1 (x 1,y 1 ) R 0 (x 0,y 0 ) Another emitter provides the same TDOA and  d  d, x 0,y 0,x 1,y 1 are known. x e, y e are unknowns! 1 equation and 2 unknowns! There is no unique solution of the equation. Indeed,  d is a hyperbolic curve equation! Any (x e, y e ) pair on the curve gives the same  d

13 2 Receivers Case 2 receiver points provide one curve! N receivers provides N-1 curves and equations! N receivers provides N-1 curves and  d equations! 2 receivers can not provide location of the emitter in 2-D space. At least 3 receivers are required! 3 receivers  2 equations  2 unknowns () can be solved! 3 receivers  2 equations  2 unknowns ( x e, y e ) can be solved! Using more receivers is better way in applications.

14 AOA in 2 Receivers Case 2 receivers can provide Angle of Arrival! () 2 receivers can provide Angle of Arrival! (  ) x y  R 1 (x 1,y 1 )R 0 (x 0,y 0 )  Emitter L 2 receivers! L AOA Finder 2 receivers! [3][3] [3]

15 3 Receivers Case 2D location of the emitter can be solved. x y d0d0 d1d1 E(x e,y e ) R 1 (x 1,y 1 ) R 0 (x 0,y 0 )  d 10 R 2 (x 2,y 2 ) d2d2  d 12

16 3-D Localization Algorithm

17 4 Receivers Case N receivers provides N-1 curves and equations! N receivers provides N-1 curves and  d equations! x e, y e, z e are unknowns in 3-D space. At least 4 receivers are required! 4 receivers  3 equations  3 unknowns () can be solved! 4 receivers  3 equations  3 unknowns ( x e, y e, z e ) can be solved! Using more receivers is better way in applications.

18 4 Receivers Case [2] Era VERA-E ELINT and Passive Surveillance System Document [2][2]

19 Application

20 Application & Implementation Receivers or received signals must be synchronous to provide exact time of difference. The measurement error should be handled in the algorithm. The more receivers the better result! Over-determined system provides more accurate location estimation in erroneous measurements. Over-determined system provides more accurate location estimation in erroneous measurements.

21 Application & Implementation TDOA measurement error changes the algorithm implementation. [4] [5]. Measurement 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 R 1 (x 1,y 1 ) R 0 (x 0,y 0 ) x y R 1 (x 1,y 1 ) R 0 (x 0,y 0 ) TDOA uncertainty converts the curve to an area in 2-D space. Area Curve

22 Application & Implementation Statistical methods can be used to estimate location of the emitter with minimum error. [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 , March [7] Muhammad Aatique. Evaluation Of Tdoa Techniques For Position Location In Cdma Systems. Master Thesis. Virginia Polytechnic Institute And State University [5] Emitter location estimation using noisy TDOA data

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