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Multilateration (Hyperbolic Location Technique, TDOA)

Multilateration (Hyperbolic Location Technique, TDOA). Zafer Hasim TELLIOGLU August, 2010 www.zhtellioglu.com. Multilateration is time difference of arrival based position estimation algorithm A receiver can estimate its location by using a few synchronous transmitters

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Multilateration (Hyperbolic Location Technique, TDOA)

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  1. Multilateration(Hyperbolic Location Technique, TDOA) Zafer Hasim TELLIOGLU August, 2010 www.zhtellioglu.com

  2. Multilateration is time difference of arrival based position estimation algorithm • A receiver can estimate its location by using a few synchronous transmitters • 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] Location of the F-16 is estimated by using 4 receivers. Emitters [1] Era VERA-E ELINT and Passive Surveillance System Document

  5. 2-D Localization Algorithm

  6. 2 Receivers Case Emitter d2 d1 Passive Receiver The same pulse has not been received! Passive Receiver The same pulse is received!

  7. 2 Receivers Case Emitter d2 d1 Passive Receiver The same pulse has not been received! Passive Receiver The same pulse is received! There is a time difference of arrival for the same pulse in different receivers due to distance difference between d1 and d2!

  8. 2 Receivers Case y E(xe,ye) The distance between 2 points: d1 d0 y R1(x1,y1) x x R0(x0,y0) Reference receiver & Reference point (x0=0, y0=0)

  9. 2 Receivers Case y E(xe,ye) The distance between 2 points: d1 d0 y R1(x1,y1) x x R0(x0,y0) Reference receiver & Reference point (x0=0, y0=0)

  10. 2 Receivers Case y E(xe,ye) The distance between 2 points: d1 d0 y R1(x1,y1) x x R0(x0,y0) Reference receiver & Reference point (x0=0, y0=0) Note That; Receivers can not measure the distance (di) to the emitter! There is no any RADAR transmitter! If the receivers are synchronous, the difference can be measured!

  11. 2 Receivers Case y E(xe,ye) d1 d0 R1(x1,y1) Position of the receivers are known! x R0(x0,y0)

  12. 2 Receivers Case y E(xe,ye) d1 d0 R1(x1,y1) 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! x R0(x0,y0) Another emitter provides the same TDOA and d Any (xe, ye) 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 dequations! • 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 (xe, ye) can be solved! • Using more receivers is better way in applications.

  14. AOA in 2 Receivers Case • 2 receivers can provide Angle of Arrival! () Emitter [3] 2 receivers! y Emitter   AOA Finder L 2 receivers! x L R0(x0,y0) R1(x1,y1) [3] www.eslkidstuff.com\BodyTour.htm

  15. 3 Receivers Case • 2D location of the emitter can be solved. E(xe,ye) R2(x2,y2) y d2 d0 d12 d1 R1(x1,y1) x R0(x0,y0) d10

  16. 3-D Localization Algorithm

  17. 4 Receivers Case • N receivers provides N-1 curves and dequations! • xe,ye,ze are unknowns in 3-D space. • At least 4 receivers are required! • 4 receivers  3 equations  3 unknowns (xe, ye, ze) can be solved! • Using more receivers is better way in applications.

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

  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.

  21. Application & Implementation • TDOA measurement error changes the algorithm implementation. [4] [5]. Measurement uncertainty should be handle in the system. y y TDOA uncertainty converts the curve to an area in 2-D space. Area Curve R1(x1,y1) R1(x1,y1) x x R0(x0,y0) R0(x0,y0) [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

  22. Application & Implementation • Statistical methods can be used to estimate location of the emitter with minimum error. [5, 6, 7] [5] Emitter location estimation using noisy TDOA data [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

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