System and method for model-base compression of GPS ephemeris

• US 7,679,550 B2
• Filed: 02/21/2007
• Issued: 03/16/2010
• Est. Priority Date: 02/21/2006
• Status: Expired due to Fees

• Current Assignee: Purdue Research Foundation (Purdue University)
• Original Assignee: Purdue Research Foundation (Purdue University)
• Inventors: Eichel, Brenda E., Garrison, James L.
• Primary Examiner(s): PHAN, DAO LINDA
• Application Number:
  US11/709,309
• Publication Number:
  US 20070273581A1
• Time in Patent Office: 1,119 Days
• Field of Search: 342/352, 342/357.01, 342/357.06, 342/357.09, 342/357.1, 701/207, 701/213, 701/226
• US Class Current: 342/357.29
• CPC Class Codes: G01S 19/05 providing aiding data

Abstract

A method for propagating ephemeris data for a satellite in Earth orbit is provided. The method includes the steps of receiving orbital positional data for a first time period of a satellite'"'"'s Earth orbit, propagating orbital positional data for the satellite'"'"'s Earth orbit during a second time period extending beyond the first time period, fitting a Keplerian ephemeris model to the propagated orbital positional data to estimate model coefficients, and sending the estimated model coefficients to receivers for determination of receiver position at a time during the second time period.

Claims

1. A method for propagating ephemeris data for a satellite in Earth orbit comprising:

receiving orbital positional data for a first time period of a satellite'"'"'s Earth orbit;

propagating the received orbital positional data to generate propagated orbital positional data for the satellite'"'"'s Earth orbit during a second time period extending beyond the first time period;

fitting a Keplerian ephemeris model to the propagated orbital positional data to estimate model coefficients; and

sending the estimated model coefficients to receivers for determination of receiver position at a time during the second time period.

2. The method of claim 1, wherein the model fitting step comprises the steps of:

generating velocity vectors for satellite positions in the first and the second time period; and

generating arguments of latitude for the satellite positions from the orbital positional data for the satellite positions and the generated velocity vectors for the satellite positions.

3. The method of claim 1, wherein the reception of orbital positional data step comprises receiving orbital positional data for a satellite from International Global Positioning System Service.

4. The method of claim 2 further comprising the step of determining a dominant frequency for a long time series of the generated arguments of latitude.

5. The method of claim 4, wherein the dominant frequency determination comprises applying sinusoidal estimation to the long time series of generated arguments of latitude to identify the dominant frequency.

6. The method of claim 4, wherein the step of applying sinusoidal estimation comprises applying a Fourier transform to the long time series of generated arguments of latitude to identify the dominant frequency.

7. The method of claim 4 further comprising the step of fitting a Keplerian model to the propagated orbital positional data to determine estimates for the model coefficients.

8. The method of claim 6, wherein the model coefficient estimation step comprises iteratively adjusting a state vector for the set of Keplerian elements comprised of argument of latitude, true anomaly, argument of perigee, semi-major axis, eccentricity, inclination, and right ascension of the ascending node until an error term is less than a threshold.

9. The method of claim 8, wherein the sending of the model coefficients step comprises the steps of:

sending a mean value, secular rate, and periodic terms of harmonic frequencies for each of the argument of latitude, true anomaly, argument of perigee, semi-major axis, eccentricity, inclination, and right ascension of the ascending node;

sending a constant mean value for the argument of perigee; and

sending the secular rate and the periodic terms for the argument of latitude for an expansion of true anomaly.

10. The method of claim 7 further comprising the steps of:

computing fit residuals between the Keplerian model and the propagated orbital positional data in an Earth centered reference frame; and

transforming the fit residuals to a satellite centered reference frame.

11. The method of claim 10 further comprising the steps of:

applying a sinusoidal estimation to a set of computed fit residuals to determine dominant frequencies for the set of computed fit residuals; and

sending the dominant frequencies for the computed fit residuals with the estimated coefficients for the periodic positional model and the model coefficients for the Keplerian model.

12. The method of claim 11, wherein the step of applying sinusoidal estimation comprises applying a Fourier transform.

13. The method of claim 12 further comprising:

fitting a periodic positional model to the computed fit residuals to determine estimates for coefficients of the periodic positional model; and

sending the estimated coefficients for the periodic positional model with the model coefficients for the Keplerian model.

14. The method of claim 12 further comprising:

sending an ephemeris reference time and a sidereal time at the reference time with the dominant frequencies for the computed residuals, the estimated coefficients for the periodic positional model, and the Keplerian model coefficients.

15. A reference station for providing compressed data to represent a propagated ephemeris comprising:

a receiver for receiving orbital positional data for a first epoch of a satellite ephemeris;

an orbit propagator for propagating orbital positional data for a second epoch of an ephemeris for the satellite corresponding to the received orbital positional data;

an ephemeris compressor for fitting an ephemeris format to the propagated orbital positional data of the second epoch to generate compressed data for representing the second epoch of the satellite ephemeris; and

a transmitter for sending the compressed data to satellite receivers for computing a receiver location from a satellite position represented by the compressed data.

16. The reference station of claim 15, wherein the ephemeris compressor comprises:

a Keplerian compressor for fitting a Keplerian ephemeris model to the propagated orbital positional data to generate estimated Keplerian model coefficients.

17. The reference station of claim 16, wherein the ephemeris compressor comprises:

a positional residual generator for computing fit residuals between the Keplerian ephemeris model and the propagated orbital positional data in an Earth centered reference frame;

a frame of reference transformer for transforming the computed fit residuals to a satellite reference frame; and

a positional residual compressor for fitting a periodic positional model to the computed fit residuals to generate estimates for coefficients of the periodic positional model.

18. The reference station of claim 15, wherein the receiver comprises access to a source providing orbital positional data received from the satellites.

19. The reference station of claim 18, wherein the source is International GNSS Service.

20. A method for receiving ephemeris data for a satellite in Earth orbit at a navigation receiver, comprising the steps of:

receiving estimated model coefficients of orbital positional data for a second time period of a satellite'"'"'s Earth orbit, the second time period extending beyond a first time period, the estimated model coefficients based on propagating orbital positional data for the first time period of a satellite'"'"'s Earth orbital positional data, the model coefficients obtained from fitting a Keplerian ephemeris model to the propagated orbital positional data to estimate the model coefficients; and

determining the receiver position at a time during the second time period, based at least partially on the estimated model coefficients.

21. The method of claim 20, wherein the estimated model coefficients are defined by the dominant frequencies in argument of latitude and time to compute the position of a GPS satellite at a requested time, t, in at least one of the ECI and the ECEF reference frame.

22. The method of claim 21, wherein computing of the position of the GPS satellite is based on using equations:

t_k=t−

t_oe 

 

(6.1)

θ

*=β

₁₉+β

₂₀t_k+β

₂₁ cos(2π

f_θ

*t_k)+β

₂₂ sin(2π

f_θ

*t_k)

ω

=β

₂₃

θ

=ω

+θ

*

a=β

₁+β

₂θ

+β

₃ cos(2θ

)+β

₄ sin(2θ

)

e=β

₅+β

₆θ

+β

₇ cos(θ

)+β

₈ sin(θ

)+β

₉ cos(3θ

)+β

₁₀ sin(3θ

)

i=β

₁₁+β

₁₂θ

+β

₁₃ cos(2θ

)+β

₁₄ sin(2θ

)

Ω

=β

₁₅+β

₁₆θ

+β

₁₇ cos(2θ

)+β

₁₈ sin(2θ

) 

 

(6.2)

$\begin{array}{cc}r=\frac{a<br><br>\left(1-e^2\right)}{1+e<br><br><br><br>\cos <br><br>\left({\mathrm{\theta <br><br>}}^{*}\right)}& \left(6.3\right)\end{array}$
δ

r=α

₁ cos(2π

t_kf_R1)+α

₂ sin(2π

t_kf_R1)+α

₃ cos(2π

t_kf_R2)+α

₄ sin(2t_kf_R2)

δ

_s=β

₅ cos(2π

t_kf_S1)+α

₆ sin(2π

t_kf_S1)+α

₇ cos(2π

t_kf_S2)+α

₈ sin(2π

t_kf_S2)

δ

ω

=α

₉ cos(2π

t_kf_W1)+α

₁₀ sin(2π

t_kf_W1) 

 

(6.4)

h_1,1=cos(Ω

)cos(θ

)−

sin(Ω

)cos(i)sin(θ

)

h_1,2=−

cos(Ω

)sin(θ

)−

sin(Ω

)cos(i)cos(θ

)

h_1,3=sin(Ω

)sin(i)

h_2,1=sin(Ω

)cos(θ

)+cos(Ω

)cos(i)sin(θ

)

h_2,2=−

sin(Ω

)sin(θ

)+cos(Ω

)cos(i)cos(θ

)

h_2,3=−

cos(Ω

)sin(i)

h_3,1=sin(i)sin(θ

)

h_3,2=sin(i)cos(θ

)

h_3,3=cos(i) 

 

(6.5)

X_ECI=(r+δ

r)h_1,1+δ

sh_1,2+∂

ω

h_1,3

Y_ECI=(r+δ

r)h_2,1+δ

sh_2,2+δ

ω

h_2,3

Z_ECI=(r+δ

r)h_3,1+δ

sh_3,2+δ

ω

h_3,3 

 

(6.6).