METHOD AND APPARATUS FOR SATELLITE ORBIT INTERPOLATION USING PIECEWISE HERMITE INTERPOLATING POLYNOMIALS
First Claim
1. A method for determining the position of a satellite at any instant of time between two sampling instants, based on information in at least one navigation message provided by the satellite, the information allowing the computation of the satellite positions at the two sampling instants, the method comprising the steps of:
- a) setting the first sampling instant;
b) computing the satellite position at the first sampling instant using parameters provided in a navigation message with a suitable time of validity;
c) setting a next sampling instant later than the first sampling instant;
d) computing the satellite position at the second sampling instant again using parameters provided in a navigation message with a suitable time of validity; and
e) for each of the three dimensions of motion, constructing a polynomial of at least third degree by choosing the coefficients of the polynomial so that the polynomial interpolates the satellite position at each of the sampling instants.
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Abstract
A method and corresponding apparatus and system for determining the position of a satellite at any instant of time between two sampling instants, based on information in at least one ephemeris message provided by the satellite, the information allowing the computation of the satellite positions at the two sampling instants. The method includes the steps of: computing the satellite positions at two sampling instants using parameters provided in one or more ephemeris messages with suitable times of ephemeris; and for each of the three dimensions of motion, constructing a polynomial of at least third degree by choosing the coefficients of the polynomial so that it interpolates the satellite position at each of the two sampling instants. Typically, the method also calls for computing the satellite velocities at each of the sampling instants, and choosing the coefficients of the polynomial for each of the three dimensions of motion so as to provide a polynomial that not only interpolates the satellite position at the two sampling instants, but has a first derivative that interpolates the satellite velocity at the two sampling instants. The polynomial and its derivative can then be evaluated at any desired time between the sampling instants to determine the spacecraft position and velocity, respectively, at the desired time. The method also provides for determining at least a fifth degree polynomial by using values of the spacecraft acceleration, at each of the sampling instants, calculated from the ephemeris information. The polynomial is typically a Hermite interpolating polynomial.
11 Citations
26 Claims
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1. A method for determining the position of a satellite at any instant of time between two sampling instants, based on information in at least one navigation message provided by the satellite, the information allowing the computation of the satellite positions at the two sampling instants, the method comprising the steps of:
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a) setting the first sampling instant;
b) computing the satellite position at the first sampling instant using parameters provided in a navigation message with a suitable time of validity;
c) setting a next sampling instant later than the first sampling instant;
d) computing the satellite position at the second sampling instant again using parameters provided in a navigation message with a suitable time of validity; and
e) for each of the three dimensions of motion, constructing a polynomial of at least third degree by choosing the coefficients of the polynomial so that the polynomial interpolates the satellite position at each of the sampling instants. - View Dependent Claims (2, 3, 4, 5, 6, 7, 24)
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8. An apparatus for determining the position of a satellite at any instant of time between two sampling instants, based on information in at least one navigation message provided by the satellite, the information allowing the computation of the satellite positions at the two sampling instants, the method comprising the steps of:
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a) means for setting the first sampling instant;
b) means for computing the satellite position at the first sampling instant using parameters provided in a navigation message with a suitable time of validity;
c) means for setting a next sampling instant later than the first sampling instant;
d) means for computing the satellite position at the second sampling instant again using parameters provided in a navigation message with a suitable time of validity; and
e) means, for each of the three dimensions of motion, for constructing a polynomial of at least third degree by choosing the coefficients of the polynomial so that the polynomial interpolates the satellite position at each of the sampling instants. - View Dependent Claims (9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26)
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15. A system for determining the position of a satellite at any instant of time between two sampling instants, based on information in at least one navigation message provided by the satellite, the information allowing the computation of the satellite positions at the two sampling instants, the method comprising the steps of:
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a) the satellite, for providing the ephemeris message;
b) a receiver, for receiving the ephemeris message;
c) means for setting the first sampling instant;
d) means for computing the satellite position at the first sampling instant using parameters provided in a navigation message with a suitable time of validity;
e) means for setting a next sampling instant later than the first sampling instant;
f) means for computing the satellite position at the second sampling instant again using parameters provided in a navigation message with a suitable time of validity; and
g) means, for each of the three dimensions of motion, for constructing a polynomial of at least third degree by choosing the coefficients of the polynomial so that the polynomial interpolates the satellite position at each of the sampling instants.
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Specification