A METHOD AND SYSTEM FOR 3D POSITION ESTIMATION OF AN OBJECT USING TIME OF ARRIVAL MEASUREMENTS

• US 20160247392A1
• Filed: 10/27/2014
• Published: 08/25/2016
• Est. Priority Date: 10/27/2014
• Status: Abandoned Application

• Current Assignee: Umm Al-Qura University
• Original Assignee: Umm Al-Qura University
• Inventors: KHALAF-ALLAH, Mohamed
• Application Number:
  US14/435,942
• Publication Number:
  US 20160247392A1
• Time in Patent Office: Days
• US Class Current: 1/1
• CPC Class Codes: G01S 13/74 Systems using reradiation of radio waves, e.g. secondary radar systems; Analogous systems
• CPC Class Codes: G01S 13/878 Combination of several spaced transmitters or receivers of known location for determining the position of a transponder or a reflector G01S13/874 takes precedence
• CPC Class Codes: G01S 19/28 Satellite selection
• CPC Class Codes: G01S 19/40 Correcting position, velocity or attitude
• CPC Class Codes: G01S 19/42 Determining position
• CPC Class Codes: G01S 5/14 Determining absolute distances from a plurality of spaced points of known location
• CPC Class Codes: G01S 5/30 Determining absolute distances from a plurality of spaced points of known location
• CPC Class Codes: G08C 21/00 Systems for transmitting the position of an object with respect to a predetermined reference system, e.g. tele-autographic system
• CPC Class Codes: H04B 10/071 using a reflected signal, e.g. using optical time domain reflectometers [OTDR]
• CPC Class Codes: H04W 4/02 Services making use of location information
• CPC Class Codes: H04W 56/002 Mutual synchronization

Abstract

A system and associated methodology determines the 3D position of an object using time of arrival measurements. In one embodiment, the system uses four stations to receive a transmitted or reflected signal from the object. The system finds the required coordinate component while minimizing the computational requirement.

Claims

1. A method for determining a 3D position of an object, the method comprising:

receiving, from a first station, a first time of arrival of a signal;

receiving, from a second station, a second time of arrival of the signal;

receiving, from a third station, a third time of arrival of the signal;

receiving, from a fourth station, a fourth time of arrival of the signal;

calculating a first range measurement based on the first time of arrival and a signal propagation speed in a media;

calculating a second range measurement based on the second time of arrival and the signal propagation speed in the media;

calculating a third range measurement based on the third time of arrival and the signal propagation speed in the media;

calculating a fourth range measurement based on the fourth time of arrival and the signal propagation speed in the media;

determining, using processing circuitry and with reduced computation time, the 3D position of the object as a function of the first range measurement, the second range measurement, the third range measurement, the fourth range measurement, and positions of the first, second, third and fourth stations; and

sending the 3D position of the object to an external device to provide enhanced accurate position data to host applications.

2. The method of claim 1, wherein the 3D position of the object is defined by x, y and z coordinates.

3. The method of claim 1, further comprising:

calculating the x coordinate as a function of I₁, I₂, I₃, I₄, I₅ and I₆

where

I₁=(z₃−

z₁)(x₂−

x₁)−

(z₂−

z₁)(x₃−

x₁),

I₂=(z₄−

z₁)(x₂−

x₁)−

(z₂−

z₁)(x₄−

x₁),

I₃=(z₃−

z₁)A₁−

(z₂−

z₁)A₂,

I₄=(z₄−

z₁)A₁−

(z₂−

z₁)A₃,

I₅=(z₃−

z₁)(y₂−

y₁)−

(z₂−

z₁)(y₃−

y₁),

I₆=(z₄−

z₁)(y₂−

y₁)−

(z₂−

z₁)(y₄−

y₁),

A₁=(r₁²−

r₂²)+(x₂²−

x₁²)+(y₂²−

y₁²)+(z₂²−

z₁²),

A₂=(r₁²−

r₃²)+(x₃² x₁²)+(y₃² y₁²)+(z₃²−

z₁²),

A₃=(r₁²−

r₄²)+(x₄²−

x₁²)+(y₄²−

y₁²)+(z₄²−

z₁²),

r₁ is the first range measurement, r₂ is the second range measurement, r₃ is the third range, measurement and r₄ is the fourth range measurement,

x₁, y₁, z₁ are coordinates defining the 3D position of the first station,

x₂, y₂, z₂ are the coordinates defining the 3D position of the second station,

x₃, y₃, z₃ are the coordinates defining the 3D position of the third station, and

x₄ y₄, z₄ are the coordinates defining the 3D position of the fourth station.

4. The method of claim 3, wherein calculating the x coordinate includes applying

5. The method of claim 3, further comprising:

calculating the y coordinate as a function of I₁, I₂, I₃, I₄, I₅ and I₆.

6. The method of claim 5, wherein calculating the y coordinate includes applying

7. The method of claim 1, further comprising:

calculating the z coordinate as a function of I₇, I₈, I₉, I₁₀, I₁₁ and I₁₂,

where

I₇=(y₃−

y₁)(x₂−

x₁)−

(y₂−

y₁)(x₃−

x₁),

I₈=(y₄−

y₁)(x₂−

x₁)−

(y₂−

y₁)(x₄−

x₁),

I₉=(y₃−

y₁)A₁−

(y₂−

y₁)A₂,

I₁₀=(y₄−

y₁)A₁−

(y₂−

y₁)A₃,

I₁₁=(y₃−

y₁)(z₂−

z₁)−

(y₂−

y₁)(z₃−

z₁), and

I₁₂=(y₄−

y₁)(z₂−

z₁)−

(y₂−

y₁)(z₄−

z₁).

8. The method of claim 7, wherein calculating the z coordinate includes applying

9. The method of claim 1, wherein the signal received at each station is transmitted from the object.

10. The method of claim 1, wherein the signal received at each station is reflected from the object.

11. A system for determining a 3D position of an object, the system comprising:

at least four stations;

a receiver configured to receive a first time of arrival from a first station, a second time of arrival from a second station, a third time of arrival from a third station, and a fourth time of arrival from a fourth station; and

processing circuitry configured to

calculate a first range measurement based on the first time of arrival and a signal propagation speed in a media,

calculate a second range measurement based on the second time of arrival and the signal propagation speed in the media,

calculate a third range measurement based on the third time of arrival and the signal propagation speed in the media,

calculate a fourth range measurement based on the fourth time of arrival and the signal propagation speed in the media,

determine the 3D position of the object as a function of the first range measurement, the second range measurement, the third range measurement, the fourth range measurement, and positions of the first, second, third and fourth stations, and

send the 3D position of the object to an external device to provide enhanced accurate position data to host applications.

12. The system of claim 11, wherein the 3D position of the object is defined by x, y and z coordinates.

13. The system of claim 11, wherein the processing circuitry is further configured to:

calculate the x coordinate as a function of I₁, I₂, I₃, I₄, I₅ and I₆

where

I₁=(z₃−

z₁)(x₂−

x₁)−

(z₂−

z₁)(x₃ x₁),

I₂=(z₄−

z₁)(x₂−

x₁) −

(z₂−

z₁)(x₄−

x₁),

I₃=(z₃−

z₁)A₁−

(z₂−

z₁)A₂,

I₄=(z₄−

z₁)A₁−

(z₂−

z₁)A₃,

I₅=(z₃−

z₁)(y₂−

y₁)−

(z₂−

z₁)(y₃−

y₁),

I₆=(z₄−

z₁)(y₂−

y₁)−

(z₂−

z₁)(y₄−

y₁),

A₁=(r₁²−

r₂²)+(x₂²−

x₁²)+(y₂²−

y₁²)+(z₂²−

z₁²),

A₂=(r₁²−

r₃²)+(x₃²−

x₁²)+(y₃²−

y₁²)+(z₃²−

z₁²),

A₃=(r₁²−

r₄²)+(x₄²−

x₁²)+(y₄²−

y₁²)+(z₄²−

z₁²),

r₁ is the first range measurement, r₂ is the second range measurement, r₃ is the third range, measurement and r₄ is the fourth range measurement,

x₁, y₁, z₁ are coordinates defining the 3D position of the first station,

x₂, y₂, z₂ are the coordinates defining the 3D position of the second station,

x₃, y₃, z₃ are the coordinates defining the 3D position of the third station, and

x₄, y₄, z₄ are the coordinates defining the 3D position of the fourth station.

14. The system of claim 11, wherein calculating the x coordinate includes applying

15. The system of claim 11, wherein the processing circuitry is further configured to:

calculate the y coordinate as a function of I₁, I₂, I₃, I₄, I₅ and I₆.

16. The system of claim 15, wherein calculating the y coordinate includes applying

17. The system of claim 11, wherein the processing circuitry is further configured to:

calculate the z coordinate as a function of I₇, I₈, I₉, I₁₀, I₁₁ and I₁₂,

where

I₇=(y₃−

y₁)(x₂−

x₁)−

(y₂−

y₁)(x₃−

x₁),

I₈=(y₄−

y₁)(x₂−

x₁)−

(y₂−

y₁)(x₄−

x₁),

I₉=(y₃−

y₁)A₁−

(y₂−

y₁)A₂,

I₁₀=(y₄−

y₁)A₁−

(y₂−

y₁)A₃,

I₁₁=(y₃−

y₁)(z₂−

z₁)−

(y₂−

y₁)(z₃ z₁), and

I₁₂=(y₄−

y₁)(z₂−

z₁)−

(y₂−

y₁)(y₂−

z₁).

18. The system of claim 17, wherein calculating the z coordinate includes applying

19. The system of claim 11, wherein the signal received at each station is transmitted from the object.

20. The system of claim 11, wherein the signal received at each station is reflected from the object.