# US 2014/0152497 A1 · Method and system for determining an error in the estimation of the time taken to cross the ionosphere

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- Number: US 2014/0152497 A1
- Document ID: US20140152497A1
- Status: Published application
- Kind: A1
- Application number: 14/093,362
- Filed: 2013-11-29
- Published: 2014-06-05
- Earliest claimed: 2012-11-30
- Assignees: Thales
- Applicants: Thales
- Inventors: Sebastien TRILLES
- Web page: https://patentgrep.com/patent/US20140152497A1

## CPC

- G01S 19/13: Receivers
- G01S 19/02: Details of the space or ground control segments
- G01S 19/072: {Ionosphere corrections}
- G01S 19/21: Interference related issues {; Issues related to cross-correlation, spoofing or other methods of denial of service}
- G01S 19/40: Correcting position, velocity or attitude
- G01S: RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES

## Abstract

A method for determining an error in the estimation of time taken to cross the ionosphere by a signal along a vertical sight axis associated with a receiver, the vertical sight axis cutting the ionosphere at a point of interest, the vertical sight axis being an axis passing through the receiver and a satellite of interest, comprises: determining at least two points of cutting of the ionosphere by two sight axes between a satellite and at least two ground stations; determining at least one angle formed by segments going from the point of interest to two of the cutting points; and determining the spatial dispersion of the cutting points with respect to the point of interest on the basis of the angle, by finding the difference with a predetermined angle and taking the average of the difference or differences.

## Claims

### Claim 1

A method for determining an error in the estimation of the time taken to cross the ionosphere by a signal along a vertical sight axis associated with a receiver, the said vertical sight axis cutting the ionosphere at a point of interest, the vertical sight axis being an axis passing through the receiver and a satellite of interest, the method comprising:
a first step of determining at least two points of cutting of the ionosphere by two sight axes between a satellite and at least two ground stations or a ground station and at least two satellites;
a second step of determining at least one angle formed by a segment going from the said point of interest to one of the said cutting points and by a segment going from the said point of interest to another of the said cutting points;
a third step of determining the spatial dispersion of the said cutting points with respect to the said point of interest on the basis of the said angle, by finding the difference with a predetermined angle and taking the average of the said difference or of the said differences;
a fourth step of determining an error in the estimation of the ionosphere crossing time by addition:
of a first error in the estimation of the crossing time dependent on a variance calculated by interpolation on the basis of a TRIN model,
to a second error in the estimation of the crossing time dependent on the said spatial dispersion.

### Claim 2 (depends on 1)

The determining method according to claim 1, in which the said fourth determining step uses the relation:
GIVE=TGIVE+t(n)2( UIVE+k.σp2)
where GIVE is the said error in the estimation of the ionosphere crossing time,
TGIVE is the said first error,
t(n)2( UIVE+k.σp2) is the said second error and is composed of:
σp2 which is the said spatial dispersion,
t(n)2 which is the standard deviation of a Student's distribution with n degree of freedom,
n being the number of the said cutting points that are used for the calculation of σp2,
UIVE which represents the average of the error in calculating the delay of the crossing of the ionosphere by a signal along the said two sight axes and
k which is a coefficient making it possible to normalize σp2.

### Claim 3 (depends on 1)

The determining method according to claim 1, further comprising:
a fourth step of determining a first distance between the said point of interest and one of the said cutting points and a second distance between the said point of interest and another of the said cutting points and in which the said third step is adapted for determining the said spatial dispersion on the basis furthermore of the said first and second distances, by comparison with a predetermined distance and by taking the average of the said comparison or of the said comparisons.

### Claim 4 (depends on 1)

The determining method according to claim 1, further comprising:
a fifth step of determining a first inclination of a first sight axis associated with one of the said cutting points with respect to a vertical axis and a second inclination of a second sight axis associated with another of the said cutting points, and
the said second step is adapted for determining the said spatial dispersion on the basis furthermore of the said first and second inclinations.

### Claim 5 (depends on 3)

The determining method according to claim 3, in which the said predetermined angle is obtained as being an angle minimizing the error in the estimation of the crossing time.

### Claim 6 (depends on 1)

The determining method according to claim 1, in which the said predetermined angle is
2

π
n
with n the number of the said ionosphere cutting points.

### Claim 7 (depends on 1)

The determining method according to claim 1, in which the said predetermined distance is obtained as being a distance minimizing the error in the estimation of the crossing time.

### Claim 8 (depends on 1)

A system comprising a satellite and at least two ground stations implementing the method according to claim 1.