Satellite navigation method with satellite failure detection by statistical processing of cross-innovation

1 . A method for navigation on the basis of a plurality of pseudo-measurements obtained from satellite positioning signals each originating from a satellite, using a Kalman filter bank comprising a main filter calculating a main navigation solution from pseudo-measurements obtained from satellites and sub-filters each calculating:

a secondary navigation solution on the basis of pseudo-measurements obtained from satellites, excluding therefrom the pseudo-measurements obtained from at least one satellite, and at least

a pseudo-measurement innovation for each remaining satellite,

a cross-innovation reflecting the difference between an observation corresponding to the pseudo-measurement excluded by the sub-filter and an a posteriori estimate of said observation obtained from the secondary navigation solution produced by the sub-filter,

wherein the method comprises the steps of:

determining a sensitivity equation reflecting a sensitivity of the cross-innovation to non-excluded pseudo-measurement innovations;

extracting coefficients for the sensitivity (Cs i ) of each sub-filter to pseudo-measurements for each satellite (i) from the sensitivity equation;

forming a satellite failure indicator on the basis of the sensitivity coefficients (Cs i ) for each sub-filter to the pseudo-measurements for each satellite (i) and comparing the satellite failure indicator with a threshold in order to determine whether the satellite has failed.

2 . The method as claimed in claim 1 , in which the sensitivity equation is as follows:

X

+

=

∏

n

1

(

I

-

K

i

*

H

i

)

*

X

-

+

∑

i

=

1

n

-

1

(

∏

n

k

=

i

+

1

(

I

-

K

k

*

H

k

)

)

*

K

i

*

y

i

+

K

n

*

y

n

in which:

i is a sequence number of a reset carried out on the basis of data from satellite i among a set of n resets carried out by a sub-filter, i varying from 1 to n;

n is the number of pseudo-distance measurements used by the sub-filters and therefore the number of resets made by each sub-filter;

I is the identity matrix;

K i is a column vector for reset gains of reset i of the pseudo-distances by the sub-filter;

H i is a row vector for an observation equation corresponding to the pseudo-distance measurement of satellite i;

y i is the pseudo-distance measurement for satellite i;

X − is the state vector before carrying out the n resets;

X + is the state vector after carrying out the n resets.

3 . The method as claimed in claim 2 , in which the sensitivity coefficient Cs i for each satellite of rank i is equal to

∏

k

=

n

k

=

i

+

1

⁢

(

I

-

K

k

*

H

k

)

*

K

i

and the sensitivity coefficient Cs i =K n for the satellite with rank n.

4 . The method as claimed in claim 3 , in which the calculation of the indicator comprises the step for calculating for each sub-filter (j) a row vector (S ij ) associating the sensitivity coefficient for each satellite (i) and the measurements (H j ) used in the sub-filter, i.e. S ij =H j *Cs i for i≠j and assuming that S ij =1 for i=j.

5 . The method as claimed in claim 4 , in which the row vectors are aggregated to form the matrix SS such that:

SS

=

[

S

11

=

1

…

S

1

⁢

n

=

H

n

□

*

∏

k

=

n

k

=

2

(

I

-

K

k

*

H

k

)

*

K

1

⋮

⋱

⋮

S

n

⁢

1

=

H

1

*

K

n

…

S

nn

=

1

]

.

6 . The method as claimed in claim 5 , in which the indicator is defined as follows:

(

∑

i

=

1

n

⁢

S

i

⁢

j

⁢

y

i

)

2

(

∑

i

=

1

n

⁢

❘

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S

i

⁢

j

⁢

σ

i

❘

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)

2

+

∑

i

=

1

n

⁢

(

S

i

⁢

j

2

⁢

r

i

2

)

in which

j is the index for the sub-filter concerned,

σ i is the standard deviation in the absence of failure of the pseudo-distance measurement innovation excluding satellite i,

r i 2 is the variance for the noise measurement.

7 . The method as claimed in claim 1 , in which the threshold is identical for all of the satellites.

8 . The method as claimed in claim 1 , in which the threshold can be adjusted as a function of a desired probability of false detection in the absence of failure.

9 . The method as claimed in claim 1 , in which the threshold is calculated as a function of a desired probability of false detection based on a centered Gaussian distribution assumption in the absence of a failure.

10 . A navigation system comprising an electronic navigation calculation unit and a satellite navigation device connected to the electronic navigation calculation unit, the electronic navigation calculation unit using a bank of Kalman filters and being configured to carry out the method as claimed in claim 1 .

11 . A vehicle with the on-board navigation system as claimed in claim 10 .