System and method for efficient broadcast of satellite constellation ephemeris information
Approaches for efficient broadcast of satellite ephemeris information or data in NGSO satellite systems, based on Keplerian parametric models of the satellite orbits, are provided. Keplerian orbit parameters are utilized (e.g., parametric orbit models) for improved efficiency in broadcast of ephemeris data over use of point-wise vectors. The linear change and harmonic variations in Keplerian orbit parameters are accounted for, for example, based on the specification of the linear and harmonic terms, increasing accuracy and extending duration of validity of the orbit parameters. Data compression is employed by (i) differential encoding of orbital parameters, and (ii) exploiting the correlation between the harmonic (Fourier) coefficients model of the orbit parameters. An efficient transport mechanism entails classification of information in Classes with different repetition/update rates based on information types, significantly reducing required broadcast/update data rates while allowing for a wide variation in the orbit orientation.
1. A method for broadcasting satellite ephemeris data for a constellation of a plurality of satellites comprising:
characterizing each of a set of orbital parameters for each of the plurality of satellites as a function x(t) of a plurality of terms including a constant, a linear function of time and a number of harmonics, wherein each set of orbital parameters collectively reflects a position of the respective satellite as a function of time (t),
classifying each of the plurality of terms for each orbital parameter in one of a plurality of information classes, wherein each information class is subject to a respective update frequency for the respective terms classified therein, and wherein each of the plurality of terms for each orbital parameter is classified based on a rate of change over time (t) of the term;
determining an updated value for each of the terms of each frequency class based on the respective update frequency for the frequency class; and
broadcasting, by each of the plurality of satellites of the constellation, a current value for each of the terms of each frequency class at a frequency relative to the respective update frequency for the frequency class in order for a user terminal to determine a position of the respective satellite at a time (t).
2. The method according to claim 1 , wherein, for each of the plurality of satellites, the plurality of orbital parameters comprise the Radius r(t) of the orbit of the respective satellite, the inclination i(t) of the orbit of the respective satellite, the Argument of Latitude L(t) of the respective satellite, and the Longitude of Ascending Node Ω(t) of the respective satellite.
3. The method according to claim 2 , wherein the function x(t) for each orbital parameter is
x ( t )= A 0 x +A 1 x ×t+x 1,orbit ( t )+ x 2,orbit ( t ),
wherein
A 0 x is the constant which is an initial value at a reference time,
A 1 x ×t is the linear function of time which reflects a rate of linear change,
x 1,orbit (t) is a first harmonic which comprises an amplitude A 1,orbit x and a phase θ 1,orbit for the first harmonic for the orbit of the respective satellite, where
x 1,orbit (t) is a complex function of the amplitude A 1,orbit x and phase θ 1,orbit x for the first harmonic, and
x 2,orbit (t) is a second harmonic which comprises an amplitude A 2,orbit x and a phase θ 2, orbit x for the second harmonic for the orbit of the respective satellite, where
x 2,orbit (t) is a complex function of the amplitude A 2,orbit x and phase θ 2,orbit x for the second harmonic.
4. The method according to claim 3 , further comprising:
reducing the number of terms for each orbital parameter in each frequency class based on correlation and predictability factors of the orbital parameters comprising (i) orbital parameters that apply commonly for all of the plurality of satellites, (ii) orbital parameters that are common or highly correlated for the satellites of a common orbital plane (intra-plane satellites), (iii) orbital parameters for which time-variation follows a predictable temporal trajectory determined by Newtonian mechanics, and (iv) orbital parameters for which Fourier coefficients of the harmonic terms exhibit a high degree of correlation.
5. The method according to claim 4 , wherein the terms are classified based on their respective rates of change relative to the other terms.
6. The method according to claim 4 , wherein terms that exhibit higher rates of change relative to other terms are classified in an information class broadcast on a logical channel with a high periodicity, and terms that exhibit lower rates of change relative to other terms and near-constant terms are conveyed on transport channels of respective lower periodicities.
7. The method according to claim 4 , wherein there are three frequency classes Class A, Class B and Class C, wherein:
Class A is for terms reflecting relatively fast changing per-satellite information, which includes factor values reflecting delta changes in A 0 L , A 0 Ω , A 1 r , orbit, θ 1,orbit r , A 2,orbit r , θ 2,orbit r , for each orbital parameter, with a faster update frequency relative to Class B;
Class B is for relatively slow changing per-satellite information, which includes factor values reflecting values, relative to base values for terms that are common or highly correlated across the entire constellation, for the terms A 0 r , A 0hu i , A 0 L , A 0 Ω , A 1,orbit r , θ 1,orbit r A 2,orbit r , θ 2,orbit r for each orbital parameter; and
Class C is for the base values for the terms that are common or highly correlated across the entire constellation.
8. The method according to claim 1 , wherein the function x(t) for each orbital parameter is
x ( t )= A 0 x +A 1 x ×t+x 1,orbit ( t )+ x 2,orbit ( t ),
wherein
A 0 x is the constant which is an initial value at a reference time,
A 1 x ×t is the linear function of time which reflects a rate of linear change,
x 1,orbit (t) is a first harmonic which comprises an amplitude A 1,orbit x and a phase θ 1,orbit x for the first harmonic for the orbit of the respective satellite, where
x 1,orbit (t) is a complex function of the amplitude A 1,orbit x and phase θ 1,orbit x for the first harmonic, and
x 2,orbit (t) is a second harmonic which comprises an amplitude A 2,orbit x and a phase θ 2,orbit x for the second harmonic for the orbit of the respective satellite, where x 2,orbit (t) is a complex function of the amplitude A 2,orbit x and phase θ 2,orbit x for the second harmonic.
9. The method according to claim 8 , further comprising:
reducing the number of terms for each orbital parameter in each frequency class based on correlation and predictability factors of the orbital parameters comprising (i) orbital parameters that apply commonly for all of the plurality of satellites, (ii) orbital parameters that are common or highly correlated for the satellites of a common orbital plane (intra-plane satellites), (iii) orbital parameters for which time-variation follows a predictable temporal trajectory determined by Newtonian mechanics, and (iv) orbital parameters for which Fourier coefficients of the harmonic terms exhibit a high degree of correlation.
10. The method according to claim 9 , wherein the terms are classified based on their respective rates of change relative to the other terms.
11. The method according to claim 9 , wherein terms that exhibit higher rates of change relative to other terms are classified in an information class broadcast on a logical channel with a high periodicity, and terms that exhibit lower rates of change relative to other terms and near-constant terms are conveyed on transport channels of respective lower periodicities.
12. The method according to claim 9 , wherein there are three frequency classes Class A, Class B and Class C, wherein:
Class A is for terms reflecting relatively fast changing per-satellite information, which includes factor values reflecting delta changes in A L 0 , A 0 Ω , A 1,orbit r , A 2,orbit r , θ 2,orbit r for each orbital parameter, with a faster update frequency relative to Class B;
Class B is for relatively slow changing per-satellite information, which includes factor values reflecting values, relative to base values for terms that are common or highly correlated across the entire constellation, for the terms A 0 r , A 0 i , A 0 L , A 0 Ω , A 1,orbit r , θ 1,orbit r , A r 2,orbit , θ 2,orbit r for each orbital parameter; and
Class C is for the base values for the terms that are common or highly correlated across the entire constellation.