Satellite ephemeris error
View Patent ↗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 ( 42 a to 42 d ) 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.
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
]
=
[
a
1
a
2
a
3
a
4
a
5
a
6
]
=
[
∂
TDOA
(
t
1
)
∂
x
…
∂
TDOA
(
t
1
)
∂
z
⋮
⋮
∂
TDOA
(
t
N
)
∂
x
…
∂
TDOA
(
t
N
)
∂
z
∂
FDOA
(
t
1
)
∂
x
…
∂
FDOA
(
t
1
)
∂
z
⋮
⋮
∂
FDOA
(
t
N
)
∂
x
…
∂
FDOA
(
t
N
)
∂
z
]
-
1
(
[
TDOA
1
⋮
TDOA
N
FDOA
1
⋮
FDOA
N
]
-
[
〈
TDOA
〉
1
⋮
〈
TDOA
〉
N
〈
FDOA
〉
1
⋮
〈
FDOA
〉
N
]
)
,
wherein TDOA is the measured time difference, FDOA is the measured frequency difference, <TDOA> is the expected time difference, and <FDOA> is the expected frequency difference—and the a 1 . . . a 6 are the elements of the ephemeris correction vector A.
2. The non-transitory tangible computer readable storage medium of claim 1 , further comprising executable instructions that cause the computer to
repeat the propagation of the initial satellite ephemeris elements by slightly adjusting the initial satellite ephemeris elements before the propagation.
3. The non-transitory tangible computer readable storage medium of claim 2 , wherein the executable instructions that cause the computer to repeat the propagation comprises executable instructions that cause the computer to
iteratively perform the propagation until the first difference is within a prearranged iteration number limit.
4. An apparatus for correcting satellite ephemeris error comprising:
a) a plurality of means for calibration transmitting of known but different geographical locations;
b) means for determining at least one of measured time difference and measured frequency difference associated with signal replicas received via different satellites from the plurality of calibration transmitting means comprising a reference transmitter at a known geographical location and at least one ephemeris calibration transmitter at a substantially different known geographical locations;
c) means for calculating at least one of expected time difference and expected frequency difference by propagating initial satellite ephemeris elements including position and velocity vectors to corresponding times of the at least one of time difference and frequency difference; and
d) means for determining changes to the satellite ephemeris elements for correcting satellite ephemeris error by calculating a first difference between the 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 means for determining changes to the satellite ephemeris elements for correcting satellite ephemeris error comprises
means for calculating 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
]
=
[
a
1
a
2
a
3
a
4
a
5
a
6
]
=
[
∂
TDOA
(
t
1
)
∂
x
…
∂
TDOA
(
t
1
)
∂
z
⋮
⋮
∂
TDOA
(
t
N
)
∂
x
…
∂
TDOA
(
t
N
)
∂
z
∂
FDOA
(
t
1
)
∂
x
…
∂
FDOA
(
t
1
)
∂
z
⋮
⋮
∂
FDOA
(
t
N
)
∂
x
…
∂
FDOA
(
t
N
)
∂
z
]
-
1
(
[
TDOA
1
⋮
TDOA
N
FDOA
1
⋮
FDOA
N
]
-
[
〈
TDOA
〉
1
⋮
〈
TDOA
〉
N
〈
FDOA
〉
1
⋮
〈
FDOA
〉
N
]
)
,
wherein TDOA is the measured time difference, FDOA is the measured frequency difference, <TDOA> is the expected time difference, and <FDOA> is the expected frequency difference—and the a 1 . . . a 6 are the elements of the ephemeris correction vector A.
5. The apparatus of claim 4 , further comprising
means for repeating the propagation of the initial satellite ephemeris elements by slightly adjusting the initial satellite ephemeris elements before the propagation.
6. The apparatus of claim 5 , wherein the means for repeating the propagation comprises
means for iteratively performing the propagation until the first difference is within a prearranged iteration number limit.