Satellite ephemeris error

摘要

A method of compensating for or correcting satellite ephemeris error involves measuring time difference of arrival (TDOA) and frequency difference of arrival (FDOA) for signal replicas received via two satellites (34, 46) from calibration transmitters (42a to 42d) at different geographical locations. An initial satellite ephemeris consisting of position and velocity vectors is used to calculate ephemeris changes yielding estimated TDOA and FDOA values providing a best fit to measured TDOA and FDOA values. This provides estimated changes required to compensate for or to correct errors in the initial satellite ephemeris. The method may be iterated to deal with large ephemeris changes: i.e. the changes obtained in one iteration may be used to correct ephemeris for use as a new initial ephemeris in a following iteration. The method may be used to correct ephemeris errors in one or both satellites, if so a greater number of calibration transmitters EphemCal 1 to EphemCal 10 may be used.

主权项

1. A non-transitory tangible computer readable storage medium storing a computer program for correcting satellite ephemeris error, the computer program comprising executable instructions that cause a computer to:
a) determine at least one of measured time difference and measured frequency difference associated with signal replicas received via at least two different satellites from a plurality of calibration transmitting means of known but different geographical locations; b) calculate at least one of expected time difference and expected frequency difference by propagating initial satellite ephemeris elements including position and velocity vectors of the at least two different satellites to corresponding times of the at least one of expected time difference and expected frequency difference; and c) determine changes to the satellite ephemeris elements for correcting satellite ephemeris error by calculating a first difference between said at least one of expected time difference and expected frequency difference with the at least one of measured time difference and measured frequency difference, wherein the executable instructions to determine changes to the satellite ephemeris elements for correcting satellite ephemeris error comprises executable instructions that cause the computer to calculate an ephemeris correction vector as a product of the first difference and the changes to the satellite ephemeris elements, wherein the ephemeris correction vector [A] is calculated as[A]=[a1a2a3a4a5a6]=[∂TDOA⁡(t1)∂x…∂TDOA⁡(t1)∂z⋮⋮∂TDOA⁡(tN)∂x…∂TDOA⁡(tN)∂z∂FDOA⁡(t1)∂x…∂FDOA⁡(t1)∂z⋮⋮∂FDOA⁡(tN)∂x…∂FDOA⁡(tN)∂z]-1⁢([TDOA1⋮TDOANFDOA1⋮FDOAN]-[⟨TDOA⟩1⋮⟨TDOA⟩N⟨FDOA⟩1⋮⟨FDOA⟩N]), wherein TDOA is the measured time difference, FDOA is the measured frequency difference, is the expected time difference, and is the expected frequency difference—and the a1 . . . a6 are the elements of the ephemeris correction vector A.