Method and system for determining protection limits with integrated extrapolation over a given time horizon

1. Method for determining protection limits at a future moment associated with navigation states of a carrier comprising:

measuring data on navigation states of the carrier through sensors of the carrier;

based on said measured data,

estimating, with an estimating filter, navigation states of the carrier at the present moment,

producing a statistical model of estimation errors of navigation states of the carrier at the present moment in the form of a covariance matrix,

extrapolating the statistical model of estimation errors to a future moment, wherein said extrapolating comprising a multiplication of:

a transition matrix, with constant and positive coefficients, with

a standard deviation vector constructed from the square roots of the elements of the diagonal of the covariance matrix of the estimating filter, in order to propagate standard deviations of the navigation states produced at the present moment, to a future moment, the propagation of standard deviations of navigation states being independent from previous dynamics of the carrier, and

calculating a protection limit at the future moment using the extrapolated statistical model.

2. Method according to claim 1 , in which the coefficients of the transition matrix are determined based on assumptions of the maximum dynamics of the carrier considered over a time horizon.

3. Method according to claim 2 , in which the assumptions of the maximum dynamics of the carrier include at least assumption of the maximum values of the ground speed, the vertical speed, rotation rate, horizontal and vertical load factors.

4. Method according to one of claims 1 to 3 , wherein:

the covariance matrix of the estimating filter has a validity which is delayed with respect to the estimate of the navigation states, which causes, in the absence of the transition matrix, a validity delay of the protection limit, and

the coefficients of the transition matrix are computed so that the protection limit, calculated at the future moment using the extrapolated statistical model which comprises the transition matrix, does not comprise this validity delay.

5. Method according to claim 4 , in which the coefficients of the transition matrix are determined as a function of the maximum dynamics of the carrier over a time horizon corresponding to one calculation cycle of estimates of navigation states.

6. Method according to one of claims 1 to 3 ,

wherein:

the carrier comprises navigation systems which are not synchronized, which causes, in the absence of the transition matrix, a validity delay of the protection limit, and

the coefficients of the transition matrix are computed so that the protection limit, calculated at the future moment using the extrapolated statistical model which comprises the transition matrix, does not comprise said validity delay.

7. Method according to claim 6 , in which the coefficients of the transition matrix are determined as a function of the maximum dynamics of the carrier over a time horizon corresponding to the maximum emission period of the protection limits.

8. Method according to claim 6 , in which the extrapolation is made to compensate for the validity delay related to asynchronism between the different navigation systems based on standard deviations previously propagated to the future moment to compensate for the validity delay of the protection limit for estimates of navigation states.

9. Method according to claim 8 , wherein:

the covariance matrix of the estimating filter has a validity which is delayed with respect to the estimate of the navigation states, which causes, in the absence of the transition matrix, a validity delay of the protection limit, and

the coefficients of the transition matrix are computed so that the protection limit, calculated at the future moment using the extrapolated statistical model which comprises the transition matrix, does not comprise this validity delay.

10. Method according to one of claims 1 to 3 , in which the coefficients of the transition matrix are determined as a function of specific dynamics of the carrier during a mission, over a time horizon corresponding to the duration of the mission.

11. Carrier navigation system comprising:

an estimation module providing navigation state estimates of the carrier at the present moment and a statistical model for estimation errors of the carrier navigation states at the present moment in the form of a covariance matrix,

a protection limits calculation module to calculate protection limits providing protection limits starting from estimates of navigation states and the statistical estimation errors model, and

an extrapolation module to extrapolate the statistical model of estimation errors configured to multiply a transition matrix with constant and positive coefficients to a vector of standard deviations constructed from the square roots of the elements of the diagonal of the covariance matrix, in order to propagate standard deviations of navigation states produced at the present moment to a future moment, the propagation of standard deviations of navigation states being independent from previous dynamics of the carrier,

such that the protection limits calculation module calculates the protection limits at the future moment starting from the extrapolated statistical model.