Method and apparatus for clock synchronization that accounts for curvature in the space-time continuum

• US 7,426,156 B1
• Filed: 08/26/2004
• Issued: 09/16/2008
• Est. Priority Date: 08/26/2003
• Status: Expired due to Fees

• Current Assignee: The United States Of America As Represented By The Secretary Of The Army
• Original Assignee: The United States Of America As Represented By The Secretary Of The Army
• Inventors: Bahder, Thomas B.
• Primary Examiner(s): Miska; Vit W.
• Assistant Examiner(s): KAYES, SEAN PHILLIP
• Application Number:
  US10/926,065
• Time in Patent Office: 1,482 Days
• Field of Search: 368/47, 368/46, 368/48, 368 52- 61, 342/357.01, 342/357.02, 701/207, 701213-214
• US Class Current: 368/46
• CPC Class Codes: G04C 11/02 by radio time setting brought into action by radio G04C9/02
• CPC Class Codes: G04G 7/02 by radio
• CPC Class Codes: G04R 20/06 Decoding time data; Circuits therefor

Abstract

Methods and apparatuses for applying a correction that accounts for curvature in the space-time continuum in the context of clock synchronization are disclosed. A representative apparatus, among others, includes a memory having a curved space-time correction module and a processor. The processor is adapted to receive a reference message having a time-stamp from a master-clock and determine a correction to the time-stamp using the curved space-time correction module, wherein the correction accounts for curvature in space-time.

Claims

1. An apparatus for synchronization with a master-clock, the apparatus comprising:

a memory having a curved space-time correction module stored therein wherein the memory includes the current position (r_R) of the apparatus, and the correction is a function of both the apparatus (r_R) and a position (r_T) that is associated with the master clock; and

wherein the correction, Δ

(r_T, r_R), includes the term

$\frac{2<br><br><br><br>\mathrm{GM}}{c^2}<br><br>\left(\mathrm{\Lambda <br><br>}<br><br>\left(r_T,r_R\right)-\frac{<br><br>r_R-r_T<br><br>}{R_E}\right),$

where G is the universal gravitational constant, M is the mass of the Earth where c is the speed of light in a vacuum, where R_E is the Earth'"'"'s equatorial radius, and where Λ

(r_T, r_R) is a function of the position associated with the master clock, r_T, and the position of the apparatus, r_R, and which is given by the equation;

$\mathrm{\Lambda <br><br>}<br><br>\left(r_T,r_R\right)=\ln <br><br>\left(\frac{\tan <br><br>\left(\frac{{\mathrm{\theta <br><br>}}_T}{2}\right)}{\tan <br><br>\left(\frac{{\mathrm{\theta <br><br>}}_R}{2}\right)}\right),$

and θ

_T and θ

_T are defined by

$\cos <br><br><br><br>{\mathrm{\theta <br><br>}}_n=\frac{r_a·<br><br>\left(r_T-r_R\right)}{<br><br>r_a<br><br><br><br><br><br>r_T-r_R<br><br>},$

a=T, R; and

a processor in communication with the memory, the processor adapted to receive a reference message having a time-stamp from the master clock, wherein the processor determines a correction to the time-stamp using the curved space-time correction, and wherein the correction accounts for curvature in space time.

2. The apparatus of claim 1, wherein the correction, Δ

(r_T, r_R), further includes the term,

$\frac{{\mathrm{\Omega <br><br>}}^2<br><br>R_E^2}{c^2}<br><br><br><br>r_R-r_T<br><br>,$

where Ω

is the angular velocity of the Earth.

3. An apparatus for synchronization with a master-clock, the apparatus comprising:

means for receiving in a receiver a reference signal from a transmitter, the reference signal carrying a timestamp that is related to the time the reference signal was emitted from the transmitter, wherein the position of the transmitter at the time of emission of the reference signal is given by r_T, and wherein the position of the receiver at the time of reception of the reference signal is given by r_R; and

means for determining the time that the reference signal was received at the receiver using the reference signal, wherein the determination of the time includes applying a correction that accounts for curvature in the space-time continuum, wherein correction for curvature in the space-time continuum is a function of both r_R and r_T and wherein the correction includes a term which is

$\frac{2<br><br><br><br>\mathrm{GM}}{c^2}<br><br>\left(\mathrm{\Lambda <br><br>}<br><br>\left(r_T,r_R\right)-\frac{<br><br>r_R-r_T<br><br>}{R_E}\right),$

where G is the universal gravitational constant, M is the mass of the Earth where c is the speed of light in a vacuum, where R_E is the Earth'"'"'s equatorial radius, and where Λ

(r_T, r_R) is given by the equation;

$\mathrm{\Lambda <br><br>}<br><br>\left(r_T,r_R\right)=\ln <br><br>\left(\frac{\tan <br><br>\left(\frac{{\mathrm{\theta <br><br>}}_T}{2}\right)}{\tan <br><br>\left(\frac{{\mathrm{\theta <br><br>}}_R}{2}\right)}\right),$

and θ

_T and θ

_T are defined by

$\cos <br><br><br><br>{\mathrm{\theta <br><br>}}_n=\frac{r_a·<br><br>\left(r_T-r_R\right)}{<br><br>r_a<br><br><br><br><br><br>r_T-r_R<br><br>},$

a=T, R.

4. The apparatus of claim 3, wherein the correction includes a second term which is

$\frac{{\mathrm{\Omega \; <li></li>}}^2<br><br>R^2}{c^2}<br><br><br><br>r_R-r_T<br><br>,$

where Ω

is the angular velocity of the Earth.

5. The apparatus of claim 3, further including:

reference frame converting means for converting the position of the receiver at the time of reception (r_R) from a first reference frame to a second reference frame.

6. The apparatus of claim 3, wherein the first reference frame is Earth-Centered, Earth-Fixed (ECEF) reference frame, and the second reference frame is Earth-Centered-Inertial reference frame.