Method for optimally adjusting give error bounds or for optimally computing the variances of residuals of IGP points of an ionospheric grid for correcting an SBAS system and SBAS system for implementing said method

Abstract

A method for optimally fitting GIVE ionospheric correction error bounds and/or a method for computing variances of residuals of IGP points of an ionospheric grid for correcting an SBAS system each comprise a step of inverse interpolation implemented on a set of observation pierce points IPPi. In the method for optimally fitting the GIVEs, the step of inverse interpolation scatters for each observation pierce point IPPi concerned a variance increment .sub.UIVE.sub.i.sup.2 over the IGP points of the mesh cell of the IPPi by using a least squares scheme. In the computation of the variances of residuals, the step of inverse interpolation scatters for each observation pierce point IPPi concerned a residual Res.sup.2 over the IGP points of the mesh cell of the IPPi by using a least squares scheme.

Claims

1. A method for optimally fitting GIVE ionospheric correction error bounds of a first set of IGP points of an ionospheric correction grid for a service area of a satellite-based augmentation system SBAS, the ionospheric correction grid being structured as a meshed network of cells of predetermined polygonal shape, the cells of the meshed network corresponding projectively to the SBAS service area and having as vertices IGP points of the first set, the method for optimally fitting the error bounds comprising the steps of: computing by at least one electronic computer, on the basis of predetermined information in respect of ionospheric error corrections of the IGP points of the first set, and of measurements of pseudo-distances of a second set of control and observation pierce points IPP which are contained in the cells of the ionospheric grid, for each observation pierce point IPPi of the second set, an innovation designated by stdUIVDerror.sub.i, according to the expression:
stdUIVDerror.sub.i=|VTEC.sub.iUIVD.sub.i|/{square root over (.sub.VTEC.sub.i.sup.2+.sub.UIVE.sub.i.sup.2)} in which: VTEC.sub.i designates the vertical ionospheric delay measured at the IPPi, UIVD.sub.i designates the vertical ionospheric delay interpolated on the basis of the GIVDj of the IGPj of the mesh cell of rank m surrounding the IPPi concerned; VTEC.sub.i designates the standard deviation of the measurement noise at the IPPi, .sub.UIVE.sub.i designates the standard deviation arising from the GIVEs of the IGPj of the mesh cell of rank m having participated in the interpolation of the UIVDi of the IPPi concerned; and then when the innovation of the IPPi scanned in the current mesh cell of rank m is strictly greater than a theoretical threshold MaxThd corresponding to predetermined confidence and integrity level required by the SBAS service, computing a variance increment .sub.UIVE.sub.i.sup.2 that would need to be added to the .sub.UIVE.sub.i.sup.2 on the IPPi considered in order for it to cover the integrity level required according to the equation:
.sub.UIVE.sub.i.sup.2=(+.sub.UIVE.sub.i.sup.2)(K.sub.fact.sup.21) in which: .sub.UIVE.sub.i designates the standard deviation arising from the GIVEs of the IGPj of the mesh cell of rank m having participated in the interpolation of the UIVDi of the IPPi concerned; and K.sub.fact.sup.2 designate respectively a first term and a second term, the first term being determined according to the equation:
=.sub.VTEC.sub.i.sup.2 where VTEC.sub.i designates the vertical ionospheric delay measured at the IPPi considered, and the second term K.sub.fact.sup.2 being determined according to the equation: $K_{\mathrm{fact}}^2=\frac{{\mathrm{stdUIVDerror}}_i^2}{{\left(\mathrm{SafMarg}\mathrm{MaxThd}\right)}^2}$ SafMarg designating the integrity margin as a percentage of the tolerated maximum threshold that one wishes to generate, greater than zero and strictly less than 1, and configured as a function of an integrity guarantee margin as a predetermined relative value, denoted X and expressed as a percentage, according to the expression: SafMarg=(1X); the method of optimal fitting further comprising the steps of, when the innovation of the IPPi scanned in the current mesh cell of rank m is strictly greater than a theoretical threshold MaxThd: determining (220) values of variance increments .sub.GIVE.sub.k.sup.2 to be allocated respectively to the IGPk of the mesh cell of the IPPi considered by an inverse interpolation scheme using a Least Squares scheme so as to distribute the variance increment .sub.UIVE.sub.i.sup.2 of the IPPi according to the relation: ${}_{{\mathrm{UIVE}}_i^2}=\underset{k=1}{\overset{N_{\mathrm{IGP}}}{.Math.}}{w}_k.Math.{}_{{\mathrm{GIVE}}_k}^2$ in which N.sub.IGP is the number of IGPs of the mesh cell of predetermined shape that are used in the computation of the UIVDi and UIVEi of the IPPi considered; k designates a numbering index in the mesh cell containing the IPPi of the IGPs of the said mesh cell, w.sub.k designate the respective weights of the IGPk, k varying from 1 to N.sub.IGP, computed by applying the GNSS standard according to a function of the GNSS standard which depends on the distance between the IPPi and the IGPk, the sum of the weights w.sub.k being equal to one; and then for each IGPk of the mesh cell m to which the IPPi considered belongs, updating the variance .sub.GIVE.sub.k of the said IGPk by replacing the current value .sub.GIVE.sub.k of the GIVEk with a new value equal to
{square root over (.sub.GIVE.sub.k.sup.2+.sub.GIVE.sub.k.sup.2)}.

2. The method for optimally fitting GIVE ionospheric correction error bounds according to claim 1, wherein the determination step of determining the values of variance increments .sub.GIVE.sub.k.sup.2 to be allocated respectively to the IGPk of the mesh cell of the IPPi considered is implemented by a Conventional Least Squares scheme in which a vector Yi of distribution of the .sub.UIVE.sub.i.sup.2 of the IPPi considered over the associated IGPk is computed according to the equation:
Yi=Hi.sup.t.Math.(Hi.Math.Hi.sup.t).sup.1.Math..sub.UIVE.sub.i.sup.2 in which Hi=[w.sub.1 w.sub.2 . . . W.sub.NIGP] designates a row vector with N.sub.IGP components for carrying out the interpolation of the IPPi considered, each component w.sub.k, k varying from 1 to N.sub.IGP, corresponding to the weight of an IGP.sub.k obtained with the direct interpolation computation scheme defined by the standard for the IPPi considered; $\mathrm{Yi}=\left[\begin{array}{c}{}_{{\mathrm{GIVE}}_1}^2\\ {}_{{\mathrm{GIVE}}_2}^2\\ \mathrm{.Math.}\\ {}_{{\mathrm{GIVE}}_{\mathrm{NIGP}}}^2\end{array}\right]$ designates a column vector with N.sub.IGP components of the distribution of the variance increment .sub.UIVE.sub.i.sup.2 to be distributed over the NI.sub.GP IGPk when the mesh cell of the IPPi considered comprises N.sub.IGP IGPs, as result of solving the equation; .sub.UIVE.sub.i.sup.2 designates the variance increment to be distributed.

3. The method for optimally fitting GIVE ionospheric correction error bounds according to claim 1, wherein the determination step of determining the values of variance increments .sub.GIVE.sub.k.sup.2 to be allocated respectively to the IGPk of the mesh cell of the IPPi considered is implemented by a least squares scheme fitted through a confidence level 1-p in which a vector Yi of distribution of the .sub.UIVE.sub.i.sup.2 of the IPPi considered over the associated IGPk is computed according to the equation:
Yi=T.sub.i.sup.CALSQ.Math.Hi.sup.t.Math.(Hi.Math.Hi.sup.t).sup.1.Math..sub.UIVE.sub.i.sup.2 in which $\mathrm{Yi}=\left[\begin{array}{c}{}_{{\mathrm{GIVE}}_1}^2\\ {}_{{\mathrm{GIVE}}_2}^2\\ \mathrm{.Math.}\\ {}_{{\mathrm{GIVE}}_{\mathrm{NIGP}}}^2\end{array}\right]$ designates a column vector with N.sub.IGP components of the distribution of the variance increment .sub.UIVE.sub.i.sup.2 to be distributed over the NI.sub.GP IGPk when the mesh cell of the IPPi considered comprises N.sub.IGP IGP, as result of solving the equation; Hi=[w.sub.1 w.sub.2 . . . w.sub.NIGP] designates a row vector with N.sub.IGP components for carrying out the interpolation of the IPPi considered, each component w.sub.k, k varying from 1 to N.sub.IGP, corresponding to the weight of an IGP.sub.k obtained with the direct interpolation computation scheme defined by the standard for the IPPi considered; and T.sub.i.sup.CALSQ is a square inflation matrix of rank NIGP, defined by: $T_i^{\mathrm{CALSQ}}=\frac{1}{{G\left(p\right)}^2}\left[\begin{array}{cccc}{t}_{v_1,}^2& 0& \mathrm{.Math.}& 0\\ 0& t_{v_2,}^2& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ 0& 0& \mathrm{.Math.}& t_{v_4,}^2\end{array}\right]$ with t.sub.v.sub.k.sub., designating the associated Student's factor the 1GPk of rank k dependent on v.sub.k the degree of freedom and dependent on the confidence probability , the said Student's factor t.sub.v.sub.k.sub., making it possible to bound an error with a predetermined confidence level (1-p) required by the SBAS service, the confidence probability being related to the confidence level by the relation $=1-\frac{1}{2}.Math.p,$ and the degree or freedom v.sub.k being equal here to the number of IPP having generated a residual for the IGPk concerned minus one; and G(p) designating the value obtained when the Gaussian assumption is applied for the same confidence probability (1-p) as that used for the computation of , that is to say the limit of the Student's factor t.sub.v.sub.k.sub., when the degree of freedom v.sub.k tends to infinity; and .sub.UIVE.sub.i.sup.2 designates the variance increment to be distributed.

4. The method for optimally fitting GIVE ionospheric correction error bounds according to claim 1, wherein the determination step f determining the values of variance increments .sub.GIVE.sub.k.sup.2 to be allocated respectively to the IGPk of the mesh cell of the IPPi considered is implemented by a least squares scheme weighted by a confidence level niv_conf, in which a vector Yi of distribution of the .sub.UIVE.sub.i.sup.2 of the IPPi considered over the associated IGPk is computed according to the equation:
Yi=Pi.Math.Hi.sup.t.Math.(Hi.Math.Pi.Math.Hi.sup.t).sup.1.Math..sub.UIVE.sub.i.sup.2 in which $\mathrm{Yi}=\left[\begin{array}{c}{}_{{\mathrm{GIVE}}_1}^2\\ {}_{{\mathrm{GIVE}}_2}^2\\ \mathrm{.Math.}\\ {}_{{\mathrm{GIVE}}_{\mathrm{NIGP}}}^2\end{array}\right]$ designates a column vector with N.sub.IGP components of the distribution of the variance increment .sub.UIVE.sub.i.sup.2 to be distributed over the Map IGPk when the mesh cell of the IPPi considered comprises NIGP IGP, as result of solving the equation; Hi=[w.sub.1 w.sub.2 . . . w.sub.NIGP] designates a row vector with N.sub.IGP components for carrying out the interpolation of the IPPi considered, each component w.sub.k, k varying from 1 to N.sub.IGP, corresponding to the weight of an IGP.sub.k obtained with the direct interpolation computation scheme defined by the standard for the IPPi considered; and Pi is a diagonal square weighting matrix of rank N.sub.IGP, defined by: $\mathrm{Pi}=\left[\begin{array}{cccc}{q}_1& 0& \mathrm{.Math.}& 0\\ 0& q_2& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ 0& 0& \mathrm{.Math.}& q_{\mathrm{NIGP}}\end{array}\right]$ with $q_k={\left(\frac{t_{v_k,}}{G\left(p\right)}\right)}^2$ associated with the IGPk, k varying from 1 to N.sub.IGP, t.sub.v.sub.k.sub., designating the associated Student's factor the 1GPk of rank k dependent on v.sub.k the degree of freedom and dependent on the confidence probability , the said Student's factor t.sub.v.sub.k.sub., making it possible to bound an error with a predetermined confidence level (1-p) required by the SBAS service, the confidence probability being related to the confidence level by the relation $=1-\frac{1}{2}.Math.p,$ and the degree of freedom v.sub.k being equal here to the number of IPP having generated a residual for the IGPk concerned minus one; and G(p) designating the value obtained when the Gaussian assumption is applied for the same confidence probability (1-p) as that used for the computation of , that is to say the limit of the Student's factor t.sub.v.sub.k.sub., when the degree of freedom v.sub.k tends to infinity; and .sub.UIVE.sub.i.sup.2 designates the variance increment to be distributed.

5. The method for optimally fitting GIVE ionospheric correction error bounds of the IGPs according to claim 1, wherein the determination step of determining the values of variance increments .sub.GIVE.sub.k.sup.2 to be allocated respectively to the IGPk of the mesh cell of the IPPi considered is implemented by a least squares scheme weighted by a confidence level 1-p in which a vector Yi of distribution of the .sub.UIVE.sub.i.sup.2 of the IPPi considered over the associated IGPk is computed according to the equation: $\mathrm{Yi}={\mathrm{Hi}}^t.Math.{\left(\mathrm{Hi}.Math.{\mathrm{Hi}}^t\right)}^{-1}.Math.\left[{}_{{\mathrm{UIVE}}_i}^2.Math.{\left(\frac{t_{{\mathrm{Nb}}_{\mathrm{IPP}\mathrm{MEAN}},}}{G\left(p\right)}\right)}^2\right]$ in which $\mathrm{Yi}=\left[\begin{array}{c}{}_{{\mathrm{GIVE}}_1}^2\\ {}_{{\mathrm{GIVE}}_2}^2\\ \mathrm{.Math.}\\ {}_{{\mathrm{GIVE}}_{\mathrm{NIGP}}}^2\end{array}\right]$ designates a column vector with N.sub.IGP components of the distribution of the variance increment .sub.UIVE.sub.i.sup.2 to be distributed over the NIGP IGPk when the mesh cell of the IPPi considered comprises NIGP IGP, as result of solving the equation; Hi=[w.sub.1 w.sub.2 . . . w.sub.NIGP] designates a row vector with N.sub.IGP components for carrying out the interpolation of the IPPi considered, each component w.sub.k, k varying from 1 to N.sub.IGP, corresponding to the weight of an IGP.sub.k obtained with the direct interpolation computation scheme defined by the standard for the IPPi considered; and t.sub.Nb.sub.IPP MEAN.sub., designating a Student's factor dependent on the confidence probability , the said Student's factor t.sub.Nb.sub.IPP MEAN.sub., making it possible to bound an error with a predetermined confidence level (1-p) required by the SBAS service, the confidence probability being related to the confidence level by the relation $=1-\frac{1}{2}.Math.p,$ and the degree of freedom Nb.sub.IPP MEAN being a number computed on the basis of the weighted sum of the number of IPP in the neighbourhood of the IGPk having served in obtaining the UIVDi and UIVEi of the IPPi tested, according to the formula: ${\mathrm{Nb}}_{\mathrm{IPP}\mathrm{MEAN}}=\frac{\underset{k=1}{\overset{N_{\mathrm{IGP}}}{.Math.}}{w}_k.Math.\left({\mathrm{Nb}}_{\mathrm{IPPk}}-1\right)}{\underset{k=1}{\overset{N_{\mathrm{IGP}}}{.Math.}}{w}_k}$ with: w.sub.k, the weight of the IGPk obtained by applying the interpolation scheme defined by the RTCA DO-229D standard to the IPPi concerned to obtain its UIVDi and UIVEi; Nb.sub.IPP k corresponds to the number of IPP situated around the IGPk in the neighbourhood consisting of the union of all the cells containing this IGPk; and G(p) designating the value obtained when the Gaussian assumption is applied for the same confidence probability (1-p) as that used for the computation of , that is to say the limit of the Student's factor t.sub.v.sub.k.sub., when the degree of freedom v.sub.k tends to infinity; and .sub.UIVE.sub.i.sup.2 designates the variance increment to be distributed.

6. The method for optimally fitting GIVE ionospheric correction error bounds according to claim 1, wherein the shape of each mesh cell is a triangular shape and the number N.sub.IGP of vertex IGPs of each mesh cell is equal to 3, or the shape of each mesh cell is the shape of a quadrilateral, preferably comprised from among the shapes of a rectangle, of a square and of a lozenge, and the number N.sub.IGP of vertex IGPs of each mesh cell is equal to 4.

7. An SBAS satellite-based augmentation system for augmenting the performance of a global navigation satellite system GNSS, the SBAS system comprising SBAS service(s) user terminals, one or more satellites for augmenting the satellites of the GNSS system and for broadcasting information messages to the user terminals, one or more RIMS observation stations furnished with GNSS receivers, and one or more computers, the SBAS system configured to fit in an optimal manner ionospheric correction error bounds, called final GIVEs, of a first set of IGP points of an ionospheric correction grid for a service area of the SBAS system, the ionospheric correction grid being structured as a meshed network of cells of predetermined polygonal shape, the cells of the meshed network corresponding projectively to the SBAS service area and having as vertices IGP points of the first set, and the SBAS system wherein the electronic computer or computers are configured to: on the basis of predetermined information in respect of ionospheric error correction of the IGP points of the first set, and of measurements of pseudo-distances of a second set of control and observation pierce points IPP which are contained in the cells of the ionospheric grid, for each observation pierce point IPPi of the second set, an innovation designated by stdUIVDerror.sub.i, according to the expression: ${\mathrm{stdUIVDerror}}_i=\frac{.Math.{\mathrm{VTEC}}_i-{\mathrm{UIVD}}_i.Math.}{\sqrt{{}_{{\mathrm{VTEC}}_i}^2+{}_{{\mathrm{UIVE}}_i}^2}}$ in which: VTEC.sub.i designates the vertical ionospheric delay measured at the IPP i, *UIVD.sub.i designates the vertical ionospheric delay interpolated on the basis of the GIVDj of the IGPj of the mesh cell of rank m surrounding the IPPi concerned; .sub.VTEC.sub.i designates the standard deviation of the measurement noise at the IPPi, .sub.UIVE.sub.i designates the standard deviation arising from the GIVEs of the IGPj of the mesh cell of rank m having participated in the interpolation of the UIVDi of the IPPi concerned; and then when the innovation of the IPPi scanned in the current mesh cell of rank m is strictly greater than a theoretical threshold MaxThd corresponding to a predetermined confidence or integrity level (1-p) required by the SBAS service, compute a variance increment .sub.UIVE.sub.i.sup.2 that would need to be added to the .sub.UIVE.sub.i.sup.2 on the IPPi considered in order for it to cover the integrity level required according to the equation:
.sub.UIVE.sub.i.sup.2=(+.sub.UIVE.sub.i.sup.2)(K.sub.fact.sup.21) in which: .sub.UIVE.sub.i designates the standard deviation arising from the GIVEs of the IGPj of the mesh cell of rank m having participated in the interpolation of the UIVDi of the IPPi concerned; and K.sub.fact.sup.2 designate respectively a first term and a second term, the first term being determined according to the equation:
=.sub.VTEC.sub.i.sup.2 where VTEC.sub.i designates the vertical ionospheric delay measured at the IPPi considered, and the second term K.sub.fact.sup.2 being determined according to the equation: $K_{\mathrm{fact}}^2=\frac{{{\mathrm{stdUIVDerror}}_i}^2}{{\left(\mathrm{SafMarg}\mathrm{MaxThd}\right)}^2}$ SafMarg designating the integrity margin as a percentage of the tolerated maximum threshold that one wishes to generate, greater than zero and strictly less than 1, and configured as a function of an integrity guarantee margin as a predetermined relative value, denoted X and expressed as a percentage, according to the expression: SafMarg=(1X); and then when the innovation of the IPPi scanned in the current mesh cell of rank m is strictly greater than a theoretical threshold MaxThd: determine values of variance increments .sub.GIVE.sub.k.sup.2 to be allocated respectively to the IGPk of the mesh cell of the IPPi considered by an inverse interpolation scheme using a Least Squares scheme so as to distribute the variance increment .sub.UIVE.sub.i.sup.2 of the IPPi according to the relation: ${}_{{\mathrm{UIVE}}_i}^2=\underset{k=1}{\overset{N_{\mathrm{IGP}}}{.Math.}}{w}_k.Math.{}_{{\mathrm{GIVE}}_k}^2$ in which N.sub.IGP the number of IGPs of the mesh cell of predetermined shape that are used in the computation of the UIVDi and UIVEi of the IPPi considered; k designates a numbering index in the mesh cell containing the IPPi of the IGPs of the said mesh cell, w.sub.k designate the respective weights of the IGPk, k varying from 1 to N.sub.IGP, computed by applying the GNSS standard according to a function of the GNSS standard which depends on the distance between the IPPi and the IGPk, the sum of the weights w.sub.k being equal to one; and then for each IGPk of the mesh cell m to which the IPPi considered belongs, update the variance GIVE.sub.k of the said IGPk by replacing the current value .sub.GIVE.sub.k of the GIVEk with a new value equal to {square root over (.sub.GIVE.sub.k.sup.2+.sub.GIVE.sub.k.sup.2)}.

8. A method for optimally computing the variances of the residuals of a first set of IGP points of an ionospheric correction grid for a service area of an SBAS system, the ionospheric correction grid being structured as a meshed network of cells of predetermined polygonal shape, the cells of the meshed network corresponding projectively to the SBAS service area and having as vertices IGP points of the first set, the method for optimally computing the variances of the residuals of the IGPs comprising the steps of: computing by at least one electronic computer, on the basis of predetermined information in respect of ionospheric error correction of the IGP points of the first set, and of measurements of pseudo-distances of a second set of control and observation pierce points IPP which are contained in the cells of the ionospheric grid, for each observation pierce point IPPi of the second set, a residual, designated by Res.sub.i, referred to the vertical, according to the equation: ${\mathrm{Res}}_i=\frac{{\mathrm{STEC}}_i-{\mathrm{UISD}}_i}{F_{\mathrm{pp}\mathrm{standard}}}$ in which: STECi designates the ionospheric delay, measured by an observation station, of the real line of sight and which is dependent on the elevation of the said line of sight; UISDi designates the vertical ionospheric delay interpolated according to the standard of the user terminal on the basis of the GIVDk of the IGPk of the mesh cell surrounding the IPPi; F.sub.pp standard designates the standard rabattement function for mapping the ionospheric delay as a function of the elevation of the line of sight, and then the square Res.sub.i.sup.2; of the residual Res.sub.i; the method for optimally computing the variances of the residuals of the IGPs further comprising the steps of, for each observation pierce point IPPi of the second set, determining values of variance increments .sub.Resk.sup.2 to be allocated respectively to the IGPk of the mesh cell m of the IPPi considered by an inverse interpolation scheme using a Least Squares scheme in which a vector Yi of distribution of the square Res.sub.i.sup.2 of the residual Res.sub.i of the IPPi considered is computed according to the equation:
Yi=Hi.sup.t.Math.(Hi.Math.Hi.sup.t).sup.1.Math.Res.sub.i.sup.2 in which H=[w.sub.1 w.sub.2 . . . w.sub.NIGP] designates a row vector with NIGP components for carrying out the interpolation of the IPPi considered, each component w.sub.k, k varying from 1 to N.sub.IGP, corresponding to the weight of an IGP.sub.k obtained with the direct interpolation computation scheme defined by the standard for the IPPi considered; ${}^{*}\mathrm{Yi}=\left[\begin{array}{c}{}_{\mathrm{Res}1}^2\\ {}_{\mathrm{Res}2}^2\\ \mathrm{.Math.}\\ {}_{\mathrm{ResNIGP}}^2\end{array}\right]$ designates a column vector with NIGP components of the distribution of the square Res.sub.i.sup.2 of the residual Res.sub.i to be distributed over the NIGP IGPk when the mesh cell of the IPPi considered comprises N.sub.IGP IGP, as result of solving the equation; Res.sub.i.sup.2 designates the square of the residual Res.sub.i to be distributed, and then determining a weighting coefficient pi as inverse of a weight, this weighting coefficient being representative of the quality of the measurement of the STECi rectified into VTECi by dividing by the rabattement function for mapping the IPPi considered, and expressed according to the following formula: $p_i=\frac{{}_{{\mathrm{VTEC}}_i}^2}{{}_{\mathrm{VTEC}\mathrm{NOMINAL}}^2}$ in which .sub.VTEC.sub.i.sup.2 designates the measurement noise in respect of the pseudo-distance measured by the measurement terminal for the IPPi considered, and .sub.VTEC.sub.i.sub.NOMINAL.sup.2 designates a nominal reference measurement noise of the measurement terminal; thereafter, after having computed all the Yi and pi corresponding to the first set of the pierce points IPPi observed, for each IGP, computing an unexpanded-residual variance according to the equation: ${}_{\mathrm{MOPS}}=\sqrt{\frac{1}{\mathrm{Ps}}\underset{i=1}{\overset{\mathrm{Nipp}}{.Math.}}\frac{1}{p_i}{}_{{\mathrm{Res}}_{\mathrm{ippi}}}^2}$ with: Ps, the sum of the normalized weights 1/p.sub.i of each residual that are available for the following IGP considered: $\mathrm{Ps}=\underset{i=1}{\overset{N_{\mathrm{ipp}}}{.Math.}}\frac{1}{p_i}$ N.sub.ipp being the number of IPPs having generated a residual for the IGP concerned, .sub.Res.sub.ippi.sup.2 the residual interpolated as inverse at the IGP considered for the IPPi forming part of the IPPs having generated a residual for the IGP concerned.

9. The method for optimally computing the variances of the residuals of a first set of IGP points of an ionospheric correction grid for a service area of an SBAS system according to claim 8, wherein the weighting coefficient p.sub.i is modulated by the inverse of the weight w.sub.i of the IPPi according to the IGP such as defined by the MOPS DO-229 standard and may be written according to the expression: $p_i=\frac{1}{w_i}\frac{{}_{{\mathrm{VTEC}}_i}^2}{{}_{\mathrm{VTEC}\mathrm{NOMINAL}}^2},$ and the standard deviation .sub.MOPS of the IGP considered is computed according to the expression
.sub.MOPS={square root over ((K.Math.P.Math.K.sup.t).sup.1.Math.K.Math.P.Math.X.sup.t)} in which: K designates the unit row vector of dimension Nipp: K=[1 1 . . . 1], P designates the diagonal matrix of weights and $P=\left[\begin{array}{ccc}\frac{1}{p_1}& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& & \mathrm{.Math.}\\ 0& \mathrm{.Math.}& \frac{1}{p_{\mathrm{Nipp}}}\end{array}\right],$ X designates the column vector of residuals: $X=\left[\begin{array}{c}{}_{{\mathrm{Res}}_1}^2\\ \mathrm{.Math.}\\ {}_{{\mathrm{Res}}_{\mathrm{Nipp}}}^2\end{array}\right].$

10. The method for optimally computing the variances of the residuals of a first set of IGP points of an ionospheric correction grid for a service area of an SBAS system according to claim 8, wherein the weighting coefficient p.sub.i is modulated by the inverse of the weight w.sub.i centre norm of the IPPi according to the IGP the expression: $p_i=\frac{1}{w_i\mathrm{centre}\mathrm{norm}}\frac{{}_{{\mathrm{VTEC}}_i}^2}{{}_{\mathrm{VTEC}\mathrm{NOMINAL}}^2}$ in which the weight w.sub.i centre norm is computed according to the equation: if w.sub.i=0, then the IPP is not used for the computation of the .sub.MOPS of the IGP considered if $0<w_i<\frac{1}{N_{\mathrm{IGP}}},\mathrm{then}{w}_{i\mathrm{center}\mathrm{norm}}=w_i$ otherwise, $w_{i\mathrm{center}\mathrm{norm}}=1-\frac{w_{i\mathrm{center}\mathrm{ini}}}{\underset{i=1}{\overset{N_{\mathrm{IGP}}}{.Math.}}{w}_{i\mathrm{center}\mathrm{ini}}},$ N.sub.IGP corresponding to the number of IGP having served in the interpolation of the ionospheric delay at the IPPi and the term w.sub.i center ini being written $w_{i\mathrm{center}\mathrm{ini}}=.Math.w_i-\frac{1}{N_{\mathrm{IGP}}}.Math.,$ the weight w.sub.i being defined by the MOPS DO-229 standard, and the standard deviation .sub.MOPS of the IGP considered is computed according to the expression
.sub.MOPS={square root over ((K.Math.P.Math.K.sup.t).sup.1.Math.K.Math.P.Math.X.sup.t)} in which: K designates the unit row vector of dimension Nipp: K=[1 1 . . . 1], P designates the diagonal matrix of weights $P=\left[\begin{array}{ccc}\frac{1}{p_1}& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& & \mathrm{.Math.}\\ 0& \mathrm{.Math.}& \frac{1}{p_{\mathrm{Nipp}}}\end{array}\right],$ and X designates the column vector of residuals: $X=\left[\begin{array}{c}{}_{{\mathrm{Res}}_1}^2\\ \mathrm{.Math.}\\ {}_{{\mathrm{Res}}_{\mathrm{Nipp}}}^2\end{array}\right].$

11. The method for optimally computing the variances of the residuals of a first set of IGP points of an ionospheric correction grid for a service area of an SBAS system according to claim 8, comprising an additional step of: for each 1GPk of the second set, computing an expanded-residual variance .sub.MOPS.sup.d on the basis of the unexpanded-residual variance .sub.MOPS according to the equation: ${}_{\mathrm{MOPS}}^d=\left(\frac{t_{v_k,}}{G\left(p\right)}\right).Math.{}_{\mathrm{MOPS}}$ with $d_k=\left(\frac{t_{v_k},}{G\left(p\right)}\right)$ the expansion coefficient associated with the IGPk, k varying from 1 to N.sub.IGP, t.sub.v.sub.k.sup., designating the associated Student's factor the 1GPk of rank k dependent on v.sub.k the degree of freedom and dependent on the confidence probability , the said Student's factor t.sub.v.sub.k.sub., making it possible to bound an error with a predetermined confidence level (1-p) required by the SBAS service, the confidence probability being related to the confidence level by the relation $=1-\frac{1}{2}.Math.p,$ and the degree of freedom v.sub.k being equal here to the number of IPP having generated a residual for the IGPk concerned minus one; and G(p) designating the value obtained when the Gaussian assumption is applied for the same confidence probability , that is to say the limit of the Student's factor t.sub.v.sub.k.sub., when the degree of freedom v.sub.k tends to infinity.

12. A simplified method for optimally computing the variances of the residuals of a first set of IGP points of an ionospheric correction grid for a service area of an SBAS system, the ionospheric correction grid being structured as a meshed network of cells of predetermined polygonal shape, the cells of the meshed network corresponding projectively to the SBAS service area and having as vertices IGP points of the first set, the method for optimally computing the variances of the residuals of the IGPs comprising the steps of: computing with at least one electronic computer, on the basis of predetermined information in respect of ionospheric error correction of the IGP points of the first set, and of measurements of pseudo-distances of a second set of control and observation pierce points IPP which are contained in the cells of the ionospheric grid, for each observation pierce point IPPi of the second set, a residual, designated by Res.sub.i, referred to the vertical, according to the equation: ${\mathrm{Res}}_i=\frac{{\mathrm{STEC}}_i-{\mathrm{UISD}}_i}{F_{\mathrm{pp}\mathrm{standard}}}$ in which: STECi designates the ionospheric delay, measured by an observation station, of the real line of sight and which is dependent on the elevation of the said line of sight; UISDi designates the vertical ionospheric delay interpolated according to the standard of the user terminal on the basis of the GIVDk of the IGPk of the mesh cell surrounding the IPPi; F.sub.pp standard designates the standard rabattement function for mapping the ionospheric delay as a function of the elevation of the line of sight, and then the square Res.sub.i.sup.2 of the residual Res.sub.i; the method for optimally computing the variances of the residuals of the IGPs further comprising the steps of, for each observation pierce point IPPi of the second set, determining values of variance increments .sub.Resk.sup.2 to be allocated respectively to the IGPk of the mesh cell m of the IPPi considered by an inverse interpolation scheme using a Least Squares scheme in which a vector Yi of distribution of the square Res.sub.i.sup.2 of the residual Res.sub.i of the IPPi considered is computed according to the equation:
Yi=Hi.sup.t.Math.(Hi.Math.Hi.sup.t).sup.1.Math.Res.sub.i.sup.2 in which H=[w.sub.1 w.sub.2 . . . w.sub.NIGP] designates a row vector with N.sub.IGP components for carrying out the interpolation of the IPPi considered, each component wk, k varying from 1 to N.sub.IGP, corresponding to the weight of an IGPk obtained with the direct interpolation computation scheme defined by the standard for the IPPi considered; $*\mathrm{Yi}=\left[\begin{array}{c}{}_{\mathrm{Res}1}^2\\ {}_{\mathrm{Res}2}^2\\ \mathrm{.Math.}\\ {}_{\mathrm{REesNIGP}}^2\end{array}\right]$ designates a column vector with N.sub.IGP components of the distribution of the square Res.sub.i.sup.2 of the residual Res.sub.i to be distributed over the N.sub.IGP IGPk when the mesh cell of the IPPi considered comprises N.sub.IGP IGP, as result of solving the equation; Res.sub.i.sup.2 designates the square of the residual Res.sub.i to be distributed, and then determining a weighting coefficient pi as inverse of a weight, this weighting coefficient being representative of the quality of the measurement of the STECi rectified into VTECi by dividing by the rabattement function for mapping the IPPi considered, and expressed according to the following formula: $p_i=\frac{1}{w_i}\frac{{{}_{\mathrm{VTEC}}^2}_i}{{}_{\mathrm{VTEC}\mathrm{NOMINAL}}^2}$ in which .sub.VTEC.sub.i.sup.2 designates the measurement noise in respect of the pseudo-distance measured by the measurement terminal for the IPPi considered, w.sub.i designates the weight of the IPPi according to the IGP such as defined by the DO-229 standard; and .sub.VTEC.sub.i.sub.NOMINAL.sup.2 designates a nominal reference measurement noise of the measurement terminal; thereafter, after having computed all the Yi and pi corresponding to the first set of the pierce points IPPi observed, for each IGP, sorting the residuals computed by the inverse interpolation scheme by removing the residuals computed on the basis of those IPPi whose measurement qualities are insufficient with respect to a predetermined quality threshold, and retaining the N.sub.ipp_fil computed residuals, and then computing an unexpanded simplified residual variance according to the equation: ${}_{\mathrm{MOPS}\_\mathrm{simp}}=\sqrt{\frac{1}{N_{\mathrm{ipp}\_\mathrm{fil}}}\underset{i=1}{\overset{N\mathrm{ipp}\_\mathrm{fil}}{.Math.}}{}_{{\mathrm{Res}}_{\mathrm{ippi}}}^2}$ with: N.sub.ipp_fil the number of IPPs having generated a residual for the 1GP concerned and whose measurement quality is sufficient; .sub.Res.sub.ippi.sup.2 is the residual interpolated as inverse at the IGP considered for the IPPi forming part of the sorted IPPs having generated a residual for the IGP concerned.

13. The simplified method for optimally computing the variances of the residuals of a first set of IGP points of an ionospheric correction grid for a service area of an SBAS system according to claim 12, wherein for each 1GPk of the second set, compute an expanded simple residual variance .sub.MOPS_simp.sup.d on the basis of the unexpanded simple residual variance .sub.MOPS_simp according to the equation: ${}_{\mathrm{MOPS}\_\mathrm{simp}}^d=\left(\frac{t_{v_k,}}{G\left(p\right)}\right).Math.{}_{\mathrm{MOPS}\_\mathrm{simp}}$ with $d_k=\left(\frac{t_{v_k,}}{G\left(p\right)}\right)$ associated with the IGPk, k varying from 1 to N.sub.IGP, t.sub.v.sub.k.sub., designating the associated Student's factor the 1GPk of rank k dependent on v.sub.k the degree of freedom and dependent on the confidence probability , the said Student's factor t.sub.v.sub.k.sub., making it possible to bound an error with a predetermined confidence level (1-p) required by the SBAS service, the confidence probability being related to the confidence level by the relation $=1-\frac{1}{2}.Math.p,$ and the degree of freedom v.sub.k being equal here to the number of IPP having generated a residual for the IGPk concerned minus one; and G(p) designating the value obtained when the Gaussian assumption is applied for the same confidence probability , that is to say the limit of the Student's factor t.sub.v.sub.k.sub., when the degree of freedom v.sub.k tends to infinity.

14. The method for optimally computing the variances of the residuals of a first set of IGP points of an ionospheric correction grid for a service area of an SBAS system according to claim 8, wherein the shape of each mesh cell is a triangular shape and the number N.sub.IGP of vertex IGPs of each mesh cell is equal to 3, or the shape of each mesh cell is the shape of a quadrilateral, preferably comprised from among the shapes of a rectangle, of a square and of a lozenge, and the number N.sub.IGP of vertex IGPs of each mesh cell is equal to 4.

15. An SBAS satellite-based augmentation system for augmenting the performance of a global navigation satellite system GNSS, the SBAS system comprising SBAS service(s) user terminals, one or more satellites for augmenting the satellites of the GNSS system and for broadcasting information messages to the user terminals, one or more RIMS observation stations furnished with GNSS receivers, and one or more computers, the SBAS system being configured to compute in an optimal manner variances of the residuals of a first set of IGP points of an ionospheric correction grid for a service area of an SBAS system, the ionospheric correction grid being structured as a meshed network of cells of predetermined polygonal shape, the cells of the meshed network corresponding projectively to the SBAS service area and having as vertices IGP points of the first set, the SBAS system wherein the electronic computer or computers are configured to: on the basis of predetermined information in respect of ionospheric error correction of the IGP points of the first set, and of measurements of pseudo-distances of a second set of control and observation pierce points IPP which are contained in the cells of the ionospheric grid, for each observation pierce point IPPi of the second set, a residual, designated by Res.sub.i, referred to the vertical, according to the equation: ${\mathrm{Res}}_i=\frac{{\mathrm{STEC}}_i-{\mathrm{UISD}}_i}{F_{\mathrm{pp}\mathrm{standard}}}$ in which: STECi designates the ionospheric delay, measured by an observation station, of the real line of sight and which is dependent on the elevation of the said line of sight; UISDi designates the vertical ionospheric delay interpolated according to the standard of the user terminal on the basis of the GIVDk of the IGPk of the mesh cell surrounding the IPPi; F.sub.pp standard designates the standard rabattement function for mapping the ionospheric delay as a function of the elevation of the line of sight, and then compute the square Res.sub.i.sup.2 of the residual Res.sub.i; and thereafter for each observation pierce point IPPi of the second set, determine values of variance increments .sub.Resk.sup.2 to be allocated respectively to the IGPk of the mesh cell m of the IPPi considered by an inverse interpolation scheme using a Least Squares scheme in which a vector Yi of distribution of the square Res.sub.i.sup.2 of the residual Res.sub.i of the IPPi considered is computed according to the equation:
Yi=Hi.sup.t.Math.(Hi.Math.Hi.sup.t).sup.1.Math.Res.sub.1.sup.2 in which H=[w.sub.1 w.sub.2 . . . w.sub.NIGP] designates a row vector with N.sub.IGP components for carrying out the interpolation of the IPPi considered, each component w.sub.k, k varying from 1 to N.sub.IGP, corresponding to the weight of an IGP.sub.k obtained with the direct interpolation computation scheme defined by the standard for the IPPi considered; $*\mathrm{Yi}=\left[\begin{array}{c}{}_{\mathrm{Res}1}^2\\ {}_{\mathrm{Res}2}^2\\ \mathrm{.Math.}\\ {}_{\mathrm{REesNIGP}}^2\end{array}\right]$ designates a column vector with NIGP components of the distribution of the square Res.sub.i.sup.2 of the residual Res.sub.i to be distributed over the NIGP IGPk when the mesh cell of the IPPi considered comprises NIGP IGP, as result of solving the equation; *Res.sub.i.sup.2 designates the square of the residual Res.sub.i to be distributed, and then determine a weighting coefficient pi as inverse of a weight, this weighting coefficient being representative of the quality of the measurement of the STECi rectified into VTECi by dividing by the rabattement function for mapping the IPPi considered, and expressed according to the following formula: $p_i=\frac{{}_{{\mathrm{VTEC}}_i^2}}{{}_{\mathrm{VTEC}\mathrm{NOMINAL}}^2}$ in which .sub.VTEC.sub.i.sup.2 designates the measurement noise in respect of the pseudo-distance measured by the measurement terminal for the IPPi considered, and .sub.VTEC.sub.i.sub.NOMINAL.sup.2 designates a nominal reference measurement noise of the measurement terminal; thereafter, after having computed all the Yi and pi corresponding to the first set of the pierce points IPPi observed, for each IGP, compute an unexpanded-residual variance according to the equation: ${}_{\mathrm{MOPS}}=\sqrt{\frac{1}{\mathrm{Ps}}\underset{i=1}{\overset{\mathrm{Nipp}}{.Math.}}\frac{1}{p_i}{}_{{\mathrm{Res}}_{\mathrm{ippi}}}^2}$ with: Ps, the sum of the normalized weights 1/p.sub.i of each residual that are available for the following IGP considered: $\mathrm{Ps}=\underset{i=1}{\overset{N_{\mathrm{ipp}}}{.Math.}}\frac{1}{p_i}$ N.sub.ipp being the number of IPPs having generated a residual for the IGP concerned, .sub.Res.sub.ippi.sup.2 the residual interpolated as inverse at the IGP considered for the IPPi forming part of the IPPs having generated a residual for the IGP concerned.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention will be better understood on reading the description of several embodiments which will follow and which is given solely by way of example while referring to the drawings in which:

(2) FIG. 1 is a first partial view according to the prior art of an SBAS system illustrating the ionospheric correction grid and the definition of a pierce point IPP;

(3) FIG. 2 is a second partial view according to the prior art of the SBAS system according to the invention illustrating the ionospheric correction grid and dual-frequency pseudo-distance measurements performed on the basis of a RIMS observation and control station FIG. 3 is a first partial view from above according to the prior art of an exemplary mesh of the IGPs of the ionospheric correction grid and of the IPPs contained in an area of influence allowing the computation of the GIVD of a given IGP interpolation point;

(4) FIG. 4 is a second partial view from above according to the prior art of an exemplary mesh of the IGPs of the ionospheric correction grid and of the configuration for computation of the UIVD for a given IPP;

(5) FIG. 5 is a third partial view from above according to the prior art of an exemplary mesh of the IGPs of the ionospheric correction grid and of the configuration for computation of the UIVE for a given IPP;

(6) FIG. 6 is a fourth partial view from above according to the prior art of an exemplary mesh of the IGPs of the ionospheric correction grid in which according to a known method for fitting the GIVEs, a first test loop for the IGPs is scanned, the testing of an IGP entailing the verification of the integrity on each IPP in which the calculation of its UIVD/UIVE has involved the tested IGP;

(7) FIG. 7 is a flowchart of a method of optimal fitting according to the invention of the error bounds of GIVE correction of a first set of IGP points of an ionospheric correction grid for a service area of an SBAS system;

(8) FIG. 8 is a partial view from above according to the invention of an exemplary mesh of the IGPs of the ionospheric correction grid in which the step of inverse interpolation according to the method for optimally fitting the GIVEs of FIG. 7 is implemented by scattering the UIVE.sup.2 as component GIVE.sup.2 over each impacted IGP;

(9) FIG. 9 is a view of an example of an area of coverage of the EGNOS European augmentation system;

(10) FIG. 10 is a view of an exemplary sweep according to the invention of the mesh cells of the service area of FIG. 9;

(11) FIG. 11 is a flowchart for optimal computation according to the invention of the variances .sub.MOPS.sup.2 of the residuals of a first set of IGP points of an ionospheric correction grid for a service area of an SBAS system

(12) FIG. 12 is a partial view from above according to the invention of an exemplary mesh of the IGPs of the ionospheric correction grid, in which the step of inverse interpolation according to the method for optimally computing the variances .sub.MOPS.sup.2 of the residuals of FIG. 11 is implemented by dispersing the residual of an IPP over the IGPs of the mesh cell of the said IPP.

DETAILED DESCRIPTION

(13) According to FIG. 7 and the first invention, a method 202 for optimally fitting error bounds, called final GIVEs and associated with a first set of points IGPj of an ionospheric correction grid for a service area of an SBAS system, is implemented by one or more computers, on the basis on the one hand of information in respect of ionospheric-error corrections calculated for the said points IGPj of the first set, j designating an integer index for identifying and scanning the said points IGPi of a portion of the ionospheric grid, structured as a meshed network of cells having a predetermined shape and corresponding to the SBAS service area, and on the basis on the other hand of information in respect of measurements of pseudo-distances of a second set of control pierce points IPPi which are contained in the cells of the service portion of the ionospheric grid, the measurements of pseudo-distances being performed by so-called RIMS control and telemetry stations.

(14) The points IGPj of the ionospheric grid portion corresponding to the coverage of the SBAS service area form a meshed network whose mesh cells have one and the same predetermined shape, and this shape is comprised from among triangular shapes and quadrilateral shapes, preferably rectangular, square or lozenge shapes.

(15) The provision of the information in respect of ionospheric-error corrections calculated for the said points IGPj of the first set and of the information in respect of measurements of pseudo-distances of the second set of control pierce points IPPi is implemented in the course of a prior step 204 of calculating and providing the said information forming a step of initializing the method 202 for optimally fitting the error bounds of final GIVEs.

(16) In contradistinction to what is done in the method of the prior art the method according to the invention does not perform any IGP-wise integrity verification tests by scanning through a scan loop for the IGPs on the first set, but performs IPP-wise integrity verification tests by scanning through a global scan loop 206 for the IPPi on the second set.

(17) The IPPi of the first set are partitioned into their membership cells or mesh cells and the global scan loop 206 for the IPPi comprises a first 208 loop for scanning the cells of the grid portion according to an order or a scan pattern which is predetermined, and comprises, nested in the first loop 208 for scanning the cells, a second local loop 209 for scanning the IPPi belonging to one and the same cell of the ionospheric grid portion.

(18) The method 202 for optimally fitting final-GIVE error bounds comprises a set of steps executed after the prior step 204.

(19) In a first step 210, a first commencing and initializing cell for first loop 208 is selected according to the initial rank that it occupies in the predetermined scan pattern for the cells. The scan index of the first loop being designated by m, the index m is set to 1 and corresponds to the initial rank 1 of the first cell of the pattern.

(20) Next, for each IPPi contained in the cell of current rank m in the order of scanning of the first loop, the following steps are executed.

(21) In a second step 212, for the relevant IPPi of rank i contained in the cell of current rank m, the innovation, designated by stdUIVDerror.sub.i, of the relevant IPPi is computed according to the expression:

(22) $\begin{array}{cc}{\mathrm{stdUIVDerror}}_i=\frac{.Math.{\mathrm{VTEC}}_i-{\mathrm{UIVD}}_i.Math.}{\sqrt{{}_{{\mathrm{VTEC}}_i}^2+{}_{{\mathrm{UIVE}}_i}^2}}& \left(\mathrm{equation}\mathrm{\#11}\right)\end{array}$

(23) in which: VTEC.sub.i designates the vertical ionospheric delay measured at the IPP UIVD.sub.i designates the vertical ionospheric delay interpolated on the basis of the GIVDj of the IGPj of the mesh cell of rank m surrounding the IPPi concerned; .sub.VTEC.sub.i designates the standard deviation of the measurement noise at the IPPi, .sub.UIVE.sub.i designates the standard deviation arising from the GIVEs of the IGPj of the mesh cell of rank m having participated in the interpolation of the UIVDi of the IPPi concerned.

(24) Thereafter, in a third test step 214, it is verified whether the innovation of the current IPPi scanned in the current mesh cell of rank m is strictly greater than a predetermined theoretical threshold, designated by MaxThd, the test condition being written:
stdUIVDerror.sub.iMaxThd

(25) For example, MaxThd, is taken equal to 5.33 under assumptions of Gaussian distribution of the error, this corresponding to a confidence level required by the SBAS service equal to (1-10.sup.7), i.e. a confidence of 99.99999%. This theoretical threshold will be able to be modified if it is desired to modify the probability level required and will be denoted hereinafter G(p) with (p)=erf.sup.1(1p){square root over (2)}, erf.sup.1() designating the reciprocal function of the error function and (1-p) designating the required confidence level. It should be noted here that the permitted maximum threshold can be computed with a margin, thus avoiding cases judged to be too limiting.

(26) If this condition is not satisfied, that is to say if the innovation of the current IPPi is less than or equal to the predetermined theoretical threshold MaxThd, this means that the IGPj of the current mesh cell of rank m having served for the interpolation of the UIVDi of the IPPi considered have a GIVEj which is sufficient to guarantee the integrity level required. In this case, the GIVEj of the current mesh cell remain unchanged and a fourth step 216 of testing for the end of the second local scan loop for the IPPi contained in the mesh cell of current rank m is executed.

(27) If this condition is satisfied, that is to say if the innovation of the current IPPi exceeds the threshold MaxThd, then, the quantity .sub.UIVE.sub.i.sup.2 that would need to be added to the .sub.UIVE.sub.i.sup.2 on the IPPi considered in order for it to cover the integrity level required is computed in a fifth step 218 according to the equation:
.sub.UIVE.sub.i.sup.2=(+.sub.UIVE.sub.i.sup.2)(K.sub.fact.sup.21) (equation #12)

(28) in which:

(29) .sub.UIVE.sub.i designates the standard deviation arising from the GIVEs of the IGPj of the mesh cell of rank m having participated in the interpolation of the UIVDi of the IPPi concerned;

(30) and K.sub.fact.sup.2 designate respectively a first term and a second term.

(31) The first term may be written according to the equation:
=.sub.VTEC.sub.i.sup.2

(32) where VTEC.sub.i designates the vertical ionospheric delay measured at the IPPi considered.

(33) The second term K.sub.fact.sup.2 may be written according to the equation:

(34) $K_{\mathrm{fact}}^2=\frac{{\mathrm{stdUIVDerror}}_i^2}{{\left(\mathrm{SafMarg}\mathrm{MaxThd}\right)}^2}$

(35) in which: MaxThd designates the predetermined theoretical threshold, stdUIVDerror.sub.i designates the innovation of the IPPi concerned computed in the second step 212; SafMarg designates the integrity margin as a percentage of the tolerated maximum threshold that one wishes to generate, greater than 0 and strictly less than 1. Preferably, it will be desired to generate a margin lying between 10% and 50% at the maximum. This margin is therefore configured so as to generate an integrity guarantee margin as a relative value, denoted X and expressed as a percentage, according to the expression: SafMarg=(1X).

(36) The integrity guarantee margin as a relative value X is provided beforehand prior to the execution of the method 202 for optimally fitting the error bounds of the final GIVEs.

(37) The quantity .sub.UIVE.sub.i thus computed satisfies equation #13:

(38) $\mathrm{SafMarg}\mathrm{MaxTd}=\frac{.Math.{\mathrm{VTEC}}_i-{\mathrm{UIVD}}_i.Math.}{\sqrt{{}_{{\mathrm{UIVE}}_i}^2+{}_{{\mathrm{UIVE}}_i}^2+{}_{{\mathrm{VTEC}}_i}^2}}$

(39) and the square of this quantity .sub.UIVE.sub.i is exactly the value that needs to be added to the variance .sub.UIVE.sub.i.sup.2 in order for the integrity to be guaranteed with the configured margin X.

(40) Next, in a sixth step 220, the variance increment computed in the fifth step 218 is distributed or dispersed between the IGPj having served for the computation of the UIVEi of the IPPi considered.

(41) Given that the UIVDi and the UIVEi of an IPPi are obtained by interpolation, this interpolation being normalized according to a normalized function defined by the RTCA DO-229D standard, it is therefore necessary to invert this interpolation in order to redistribute in a perfectly compliant way the .sub.UIVE.sub.i.sup.2 computed previously in the fifth step 218.

(42) According to the aforementioned standard, it is recalled that the variance of the UIVEi of the IPPi is obtained through the following expression (equation #14):

(43) ${}_{{\mathrm{UIVE}}_i}^2=\underset{k=1}{\overset{N_{\mathrm{IGP}}}{.Math.}}{w}_k.Math.{}_{{\mathrm{GIVE}}_k}^2$

(44) in which N.sub.IGP is the number of IGPs of the mesh cell or cell of predetermined shape that are used in the computation of the UIVDi and UIVEi of the IPPi considered, this number possibly being 3 or 4, depending on the type of mesh cell used; k designates a numbering index in the mesh cell containing the IPPi of the IGPs of the said mesh cell, w.sub.k the weight of the IGPk computed by applying the standard according to a function which depends on the distance between the IPPi and the IGPk.

(45) This interpolation being a barycentric interpolation, the sum of the weights w.sub.k is equal to 1, that is to say satisfies the relation: .sub.k=1.sup.N.sup.IGP w.sub.k=.sub.1

(46) Consequently, the .sub.UIVE.sub.i.sup.2 is distributed in the same manner and satisfies the relation (equation #15):

(47) 0${}_{{\mathrm{UIVE}}_i}^2=\underset{k=1}{\overset{N_{\mathrm{IGP}}}{.Math.}}{w}_k.Math.{}_{{\mathrm{GIVE}}_k}^2$

(48) The sixth step 220 is a method for determining the values of .sub.GIVE.sub.k.sup.2 to be allocated respectively to the IGPk of the IPPi considered such as described in FIG. 8, which method uses the LS Least Squares scheme to ensure the realization of this partition whatever the conditions.

(49) An observation equation is defined by the expression:
Xi=Hi.Math.Yi

(50) in which

(51) Hi=[w.sub.1 w.sub.2 w.sub.3 w.sub.4] designates a row vector with four components when four IGPs have been used to carry out the interpolation of the IPPi considered, each w.sub.k corresponding to the weight of an IGP.sub.k obtained with the computation scheme defined by the RTCA DO-229D standard for the IPPi considered;

(52) $\mathrm{Yi}=\left[\begin{array}{c}{}_{{\mathrm{GIVE}}_1}^2\\ {}_{{\mathrm{GIVE}}_2}^2\\ {}_{{\mathrm{GIVE}}_3}^2\\ {}_{{\mathrm{GIVE}}_4}^2\end{array}\right]$
designates a column vector with four components of the distribution of the .sub.UIVE.sub.i.sup.2 to be distributed over the four IGPk when the mesh cell of the IPPi considered comprises four IGPs, as result of solving the equation; Xi=.sub.UIVE.sub.i.sup.2 designates the quantity to be distributed computed in the fifth step 218.

(53) It should be noted that the case where only three IGPs belonging to a triangular mesh cell are used for the computation of the UIVEi of the IPPi considered, it suffices to readapt the sizes of the vectors Hi and Yi, Hi then having a size [3,1] and Yi a size [1,3].

(54) According to a first embodiment of the sixth step 220 and a first computation scheme, the distributed inflation of the GIVEk is implemented by a Conventional Least Squares scheme (CLSQ, standing for Classical or Conventional Least Squares) in which the distribution Yi of the .sub.UIVE.sub.i.sup.2 of the IPPi considered over the associated IGPk is computed in a single sub-step with the aid of equation #16:
Yi=Hi.sup.t.Math.(Hi.Math.Hi.sup.t).sup.1.Math..sub.UIVE.sub.i.sup.2

(55) According to a second embodiment of the sixth step 220 and a second computation scheme, the distributed inflation of the GIVEk is implemented by a Conventional Least Squares scheme followed by a specific fitting of the GIVEk for each IGPk of the point IPPi considered, dependent on a confidence level associated with the said IGPk. This second computation scheme is referred to as least square scheme adjusted through a confidence level (CALSQ, standing for Confidence Adjusted Least Squares).

(56) In this second computation scheme, the same least squares computation scheme is firstly applied according to the same formulation as that used by the first computation scheme:
Yi=Hi.sup.t.Math.(Hi.Math.Hi.sup.t).sup.1.Math..sub.UIVE.sub.i.sup.2

(57) Thereafter, once this first series of .sub.GIVE.sub.k have been obtained, their value is refitted as a function of a confidence level allocated to each IGPk inheriting a .sub.GIVE.sub.k, according to a Student's factor whose degree of freedom is equal to the number of IPPs situated in a predetermined neighbourhood of the IGPk concerned minus one by using the expression:

(58) ${}_{{\mathrm{GIVE}}_k}^2{\left(\frac{t_{v_k,}}{G\left(p\right)}\right)}^2{}_{{\mathrm{GIVE}}_k}^2$

(59) in which:

(60) t.sub.v.sub.k.sub., designates the Student's factor which gives the confidence with a confidence probability given by a term , that we have with respect to the Gaussian criterion related to the fitting of the GIVEi of the IGPi concerned, and with v.sub.k the degree of freedom of the distribution corresponding here to the number of IPP around an IGP k minus 1; the term a is dependent on a predetermined confidence level (1-p) according to the expression

(61) $=1-\frac{1}{2}.Math.p,$
p designating the risk of error; for example if we seek to obtain a risk of error of 10.sup.7, that is to say a confidence level of 0.9999999,

(62) $=1-\frac{1}{2}.Math.{10}^{-7};$
and

(63) G(p) designating the value obtained when the assumption of Gaussian distribution of the error is applied for the same confidence probability (1-p) as that used for the computation of , that is to say the limit of the Student's factor t.sub.v.sub.k.sub., when the degree of freedom v.sub.k tends to infinity; for example if we seek to obtain a confidence level of (1-10.sup.7),

(64) $=1-\frac{1}{2}.Math.{10}^{-7}\mathrm{and}G\left(p\right)=5.33.$

(65) The predetermined neighbourhood of the IGPk can be defined by a predetermined radius.

(66) The implementation of the second computation scheme termed CALSQ can be formulated in a condensed manner, by putting:

(67) $T_i^{\mathrm{CALSQ}}=\frac{1}{{G\left(p\right)}^2}\left[\begin{array}{cccc}{t}_{v_1,}^2& 0& 0& 0\\ 0& t_{v_2,}^2& 0& 0\\ 0& 0& t_{v_3,}^2& 0\\ 0& 0& 0& t_{v_4,}^2\end{array}\right]$

(68) through the following formulation:
Yi=T.sub.i.sup.CALSQ.Math.Hi.sup.t.Math.(Hi.Math.Hi.sup.t).sup.1.Math..sub.UIVE.sub.i.sup.2 (equation #17)

(69) It should be noted that this scheme is considered to be conservative because of the fact that the smaller the number of IPPs around an IGP, the more the quantity which will be fitted .sub.GIVE.sub.k.sup.2 therein is increased.

(70) According to a third embodiment of the sixth step 220 and a third computation scheme, the distributed inflation of the GIVEk is implemented with a redistribution according to the confidence levels assigned to the IGPk associated with the IPPi considered. This third computation scheme is referred to as the least squares scheme weighted by the confidence levels (CWLSQ, standing for Confidence Weighted Least Squares).

(71) In this third computation scheme, we firstly compute the same Student's factors t.sub.v.sub.k.sub., as those computed in the second computation scheme, associated respectively with the IGPk of the IPPi considered.

(72) Next, on the basis of the Student's factors t.sub.v.sub.k.sub., computed, a diagonal matrix Pi is constructed by putting:

(73) $\mathrm{Pi}=\left[\begin{array}{cccc}{q}_1& 0& 0& 0\\ 0& q_2& 0& 0\\ 0& 0& q_3& 0\\ 0& 0& 0& q_4\end{array}\right]$

(74) with

(75) $q_k={\left(\frac{t_{v_k,}}{G\left(p\right)}\right)}^2$
associated with the IGPk, k varying from 1 to N.sub.IGP.

(76) It will be noted that this matrix Pi is of size 44 when four IGPk are used for the interpolation of the delay at the IPPi. If only three IGPk are used, it will be a 33 matrix.

(77) Thereafter, the vector Yi of distribution of the .sub.UIVE.sub.i.sup.2 of the IPPi considered over the associated IGPk is computed according to the following formulation of the CWLSQ:
Yi=Pi.Math.Hi.sup.t.Math.(Hi.Math.Pi.Math.Hi.sup.t).sup.1.Math..sub.UIVE.sub.i.sup.2 (equation #18)

(78) Here, with this third computation scheme, we obtain a slight redistribution of the .sub.UIVE.sub.i.sup.2 as a function of the confidence level that we have on each IGPk. Thus, if an IGPk is far distant from the IPPi but if the number of IPP in the neighbourhood of the said IGPk is small, its GIVEk will be increased in a more significant manner than in the CLSQ formulation of the first computation scheme to the detriment of the IGPk closest to the IPPi tested.

(79) According to a fourth embodiment of the sixth step 220 and a fourth computation scheme, the distributed inflation of the GIVEk is implemented with a fit of the confidence associated with the .sub.UIVE.sub.i.sup.2. This fourth scheme is referred to as the Least Squares scheme adjusted by residual confidence level ARCLSQ (standing for Adjusted Residual Confidence Least Squares).

(80) This fourth computation scheme entails evaluating a mean confidence level that will be applied directly to the .sub.UIVE.sub.i.sup.2 before redistributing it between the IGPk.

(81) In this fourth computation scheme, the degree of freedom of Student's distribution law is firstly estimated by a number Nb.sub.IPP MEAN, computed on the basis of the weighted sum of the number of IPP in the neighbourhood of the IGPk having served in obtaining the UIVDi and UIVEi of the IPPi tested, according to the formula:

(82) $\begin{array}{cc}{\mathrm{Nb}}_{\mathrm{IPP}\mathrm{MEAN}}=\frac{\underset{k=1}{\overset{N_{\mathrm{IGP}}}{.Math.}}{w}_k.Math.\left({\mathrm{Nb}}_{\mathrm{IPP}k}-1\right)}{\underset{k=1}{\overset{N_{\mathrm{IGP}}}{.Math.}}{w}_k}& \left(\mathrm{equation}\mathrm{\#19}\right)\end{array}$

(83) with: w.sub.k, the weight of the IGPk obtained by applying the interpolation scheme defined by the RTCA DO-229D standard to the IPPi concerned to obtain its UIVDi and UIVEi; Nb.sub.IPP k corresponds to the number of IPP situated around the IGPk in the neighbourhood consisting of the union of all the cells containing this IGPk.

(84) Next, the associated Student's factor t.sub.Nb.sub.IPP MEAN.sub., is computed.

(85) Thereafter, the vector Yi of distribution of the .sub.UIVE.sub.i.sup.2 of the IPPi considered over the associated IGPk is computed according to the following formulation of the ARCLSQ:

(86) 0$\begin{array}{cc}\mathrm{Yi}={\mathrm{Hi}}^t.Math.{\left(\mathrm{Hi}.Math.{\mathrm{Hi}}^t\right)}^{-1}.Math.\left[{}_{{\mathrm{UIVE}}_i}^2.Math.{\left(\frac{t_{{\mathrm{Nb}}_{\mathrm{IPP}\mathrm{MEAN}},}}{G\left(p\right)}\right)}^2\right]& \left(\mathrm{equation}\mathrm{\#20}\right)\end{array}$

(87) Thereafter, in a seventh step 222 subsequent to the sixth step 220, for each IGPk of the mesh cell to which the IPPi considered belongs, the variance of the GIVE.sub.k of the said IGPk is updated by replacing the current value .sub.GIVE.sub.k of the GIVEk with the expression {square root over (.sub.GIVE.sub.k.sup.2+.sub.GIVE.sub.k.sup.2)} for a new value of the GIVEk, which may also be written:
.sub.GIVE.sub.k{square root over (.sub.GIVE.sub.k.sup.2+.sub.GIVE.sub.k.sup.2)}

(88) Next, in an eighth step 224, for each IGPk of the tested IPPi concerned, the new value of the GIVEk is quantized according to a scale of tiers defined in the RTCA DO-229D standard, all versions up to and including the current version E, in which a maximum tier is fixed at the integer value 15.

(89) Thereafter, in a ninth test step 226, the quantized values of the GIVEk, associated respectively with the IGPk of the IPPi tested, are each compared with the integer threshold value equal to 14.

(90) When, among the quantized values of the GIVEk, there exists a GIVEk exceeding the threshold value of 14, in a tenth step 228, the quantized value or values of the GIVEk which exceed the threshold value of 14 are set to the integer end-stop value of 15, followed by a branch to the fourth step 216 of testing for the end of the second local scan loop for the IPPi contained in the mesh cell of rank m.

(91) When, among the quantized values of the GIVEk there does not exist any GIVEk exceeding the threshold value of 14, the quantized values of the GIVEk remain as is and a direct branch to the fourth step 216 is performed.

(92) In the course of the execution of the fourth step 216, it is verified whether all the IPPi contained in the cell of current rank m have been tested.

(93) If not all the IPPi of the cell of current rank m have been tested, an as yet untested IPPi of the cell of current rank m is tested in the second local scan loop, the index i of the untested IPPi becoming the new index of the IPPi to be tested, and the fifth, sixth, seventh, eighth, ninth steps are repeated.

(94) If all the IPPi of the cell of current rank m have been tested, an eleventh step 230 is executed in the course of which the scan rank m for scanning through the cells according to the predetermined pattern is incremented by one unit. After the eleventh step 230, a twelfth step 232 of testing for the end of the first loop is implemented in the course of which it is verified whether the incremented scan index m of the cells exceeds the rank of the last cell of the scan pattern.

(95) When the incremented scan index m of the cells does not exceed the rank of the last cell of the scan pattern, that is to say when the incremented scan index m is less than or equal to the scan index of the last cell of the pattern, i.e. the pattern's cell programmed to be swept last, the incremented scan index m of the first loop becomes the current scan index of the first loop, for each IPPi contained in the cell of current rank m in the order of scanning of the first loop, the steps of the second local loop are executed.

(96) When the incremented scan index m of the cells exceeds the rank of the last cell of the scan pattern, the method illustrated in FIG. 7 is terminated.

(97) The predetermined scan pattern for the cells is defined by a given sweep strategy for the grid portion corresponding to the SBAS service area.

(98) A sweep strategy defines a scheme making it possible to perform the looping over the set of IGPs of the portion according to the first loop, the ideal being to begin in an area inside which one is least liable to trigger an inflation of the GIVEs.

(99) According to FIG. 9, a map 252 represents the area of coverage 254 of the EGNOS system, with in particular the countries 256 shown hatched for which the EGNOS mission applies.

(100) According to a first sweep strategy, the cell with which the sweep process will begin is firstly determined in a central area, marked by a bold frame 258 in FIG. 9.

(101) This starting cell is defined, either as the most central cell with respect to the centre of the service area of the system which is generally a good indicator, or the cell containing the IGPs for which the sum of the GIVEs is smallest.

(102) Once this starting cell has been located, we iterate on the adjacent cells, always beginning with the cell containing the most IPP. When the number of IPP contained in two adjacent cells is the same, the cell situated most to the South is chosen if the latitude of the bottom-most IGP of the cell is less than 50, otherwise the northern-most cell is chosen.

(103) When the service area is situated in the southern hemisphere, the first strategy for defining a scan of the cells inverts in a complementary manner the directions considered and described previously when the service area is situated in the northern hemisphere.

(104) According to FIG. 10 and a second sweep strategy, which is simpler to implement than the first sweep strategy, the starting cell is determined in the same manner as in the first sweep strategy, and the order of scanning of the following cells is thereafter fixed by a spiral-shaped pattern 262 winding clockwise around the central cell. The direction of scan 264 of this spiraled cellular pattern is centrifugal. The scan pattern is illustrated partially in FIG. 10 by the commencement of a string of cells numbered from 1 to 11, starting from the central cell numbered with the number 1.

(105) The two iterative schemes illustrated in FIGS. 9 and 10 are merely two examples of cell sweep strategy, it being possible to envisage variants of these strategies. The very principle of doing a cell-wise sweep to control their integrity is considered to form part of the invention.

(106) The integrity control method defined hereinabove makes it possible not only to verify initially whether the integrity is adhered to but affords above all the capacity to steer the GIVEs of the IGPs at any time with an optimal value for each of them which considerably minimizes the risk of barring the use of an IGP if its GIVE does not make it possible to ensure integrity at the level of a line of sight at the time of control.

(107) An SBAS satellite-based augmentation system for augmenting the performance of a global navigation satellite system GNSS, configured to execute the first method 202 for optimally fitting the GIVEs of FIG. 7, comprises SBAS service(s) user terminals, one or more satellites for augmenting the satellites of the GNSS system and for broadcasting information messages to the user terminals, one or more RIMS observation stations furnished with GNSS receivers, and one or more computers.

(108) The SBAS system is configured to fit in an optimal manner ionospheric correction error bounds, called final GIVEs, of a first set of IGP points of an ionospheric correction grid for a service area of the SBAS system, the ionospheric correction grid being structured as a meshed network of cells of predetermined polygonal shape, the cells of the meshed network corresponding projectively to the SBAS service area and having as vertices IGP points of the first set.

(109) The electronic computer or computers of the SBAS system are configured to:

(110) on the basis of predetermined information in respect of ionospheric error correction of the IGP points of the first set, and of measurements of pseudo-distances of a second set of control and observation pierce points IPP which are contained in the cells of the ionospheric grid, for each observation pierce point IPPi of the second set, an innovation designated by stdUIVDerror.sub.i, according to the expression:

(111) ${\mathrm{stdUIVDerror}}_i=\frac{.Math.{\mathrm{VTEC}}_i-{\mathrm{UIVD}}_i.Math.}{\sqrt{{}_{{\mathrm{VTEC}}_i}^2+{}_{{\mathrm{UIVE}}_i}^2}}$
in which: VTEC.sub.i designates the vertical ionospheric delay measured at the IPP UIVD.sub.i designates the vertical ionospheric delay interpolated on the basis of the GIVDj of the IGPj of the mesh cell of rank m surrounding the IPPi concerned; .sub.VTEC.sub.i designates the standard deviation of the measurement noise at the IPPi, .sub.UIVE.sub.i designates the standard deviation arising from the GIVEs of the IGPj of the mesh cell of rank m having participated in the interpolation of the UIVDi of the IPPi concerned; and then

(112) when the innovation of the IPPi scanned in the current mesh cell of rank m is strictly greater than a theoretical threshold MaxThd corresponding to predetermined confidence or integrity level required by the SBAS service, compute a variance increment .sub.UIVE.sub.i.sup.2 that would need to be added to the .sub.UIVE.sub.i.sup.2 on the IPPi considered in order for it to cover the integrity level required according to the equation:
.sub.UIVE.sub.i.sup.2=(+.sub.UIVE.sub.i.sup.2)(K.sub.fact.sup.21)

(113) in which: .sub.UIVE.sub.i designates the standard deviation arising from the GIVEs of the IGPj of the mesh cell of rank m having participated in the interpolation of the UIVDi of the IPPi concerned; and K.sub.fact.sup.2 designate respectively a first term and a second term.

(114) The first term being determined according to the equation:
=.sub.VTEC.sub.i.sup.2

(115) where VTEC.sub.i designates the vertical ionospheric delay measured at the IPPi considered, and

(116) the second term K.sub.fact.sup.2 being determined according to the equation:

(117) $K_{\mathrm{fact}}^2=\frac{{\mathrm{stdUIVDerror}}_i^2}{{\left(\mathrm{SafMarg}\mathrm{MaxThd}\right)}^2}$

(118) SafMarg designating the integrity margin as a percentage value that one wishes to generate which is positive and strictly less than 1, and which is configured as a function of an integrity guarantee margin as a predetermined relative value, denoted X and expressed as a percentage, according to the expression: SafMarg=(1X) (for example, if it is desired to generate an integrity margin of 15%, then X=0.15 and .SafMarg=0.85); and then

(119) when the innovation of the IPPi scanned in the current mesh cell of rank m is strictly greater than a theoretical threshold MaxThd:

(120) determine values of variance increments .sub.GIVE.sub.k.sup.2 to be allocated respectively to the IGPk of the mesh cell of the IPPi considered by an inverse interpolation scheme using a Least Squares scheme so as to distribute the variance increment .sub.UIVE.sub.i.sup.2 of the IPPi according to the relation:

(121) ${}_{{\mathrm{UIVE}}_i}^2=\underset{k=1}{\overset{N_{\mathrm{IGP}}}{.Math.}}{w}_k.Math.{}_{{\mathrm{GIVE}}_k}^2$

(122) in which N.sub.IGP is the number of IGPs of the mesh cell of predetermined shape that are used in the computation of the UIVDi and UIVEi of the IPPi considered; k designates a numbering index in the mesh cell containing the IPPi of the IGPs of the said mesh cell, w.sub.k designate the respective weights of the IGPk, k varying from 1 to N.sub.IGP, computed by applying the GNSS standard according to a function of the GNSS standard which depends on the distance between the IPPi and the IGPk, the sum of the weights w.sub.k being equal to one; and then

(123) for each IGPk of the mesh cell m to which the IPPi considered belongs, update the variance GIVE.sub.k of the said IGPk by replacing the current value .sub.GIVE.sub.k of the GIVEk with a new value equal to {square root over (.sub.GIVE.sub.k.sup.2+.sub.GIVE.sub.k.sup.2)}.

(124) According to FIG. 11 and the second invention, a second method 302 for optimized computation of the standard deviations of residuals, called .sub.MOPS, or of the variances .sub.MOPS.sup.2 of residuals, in the particular case where the operating standard of the user terminal is the MOPS standard, which are associated with a first set of points IGPj of an ionospheric correction grid for a service area of an SBAS system, is now described.

(125) The standard deviations .sub.MOPS make it possible to model the error of interpolation carried out between the IGPs and the pierce point of the signal received by the user, and the error of the rabattement function for mapping the vertical delay to the slant delay fixed here by the MOPS standard, the said standard deviations .sub.MOPS being involved in the computation of the initial GIVEs, and as a consequence the final GIVEs of the IGPs, determined according to the first method. It is recalled that the IGPs ensure the integrity of a predetermined SBAS service and calculate the ionospheric error corrections serving in the interpolation computation in respect of the errors performed by the user terminals according to the standard defining the operating algorithms of the said user terminals.

(126) The computation of the term .sub.MOPS involved in the construction of the initial GIVE and implemented by the second method 302 uses in the manner of the first method for fitting the final GIVEs a scheme for inverse interpolation of the IPPs to the IGPs so as to ensure here the equitable distribution of the residuals, and which is similar to that used for the determination of the .sub.UVDE of the IGPs, is now described.

(127) This computation scheme therefore broadly reuses the distribution concept used within the framework of the first invention. Moreover, the final construction of the .sub.MOPS is ensured by an optimal computation reusing the set of residuals for which the IGP concerned is involved, thus allowing optimal fitting of the computation of the .sub.MOPS.

(128) Just as for the computation of the .sub.UVDE of the IGPs, we have found here the scheme ensuring the optimal fitting of the value of .sub.MOPS whatever the configuration of the IPPs around the IGPs.

(129) According to FIG. 11, the method for computing the standard deviations called .sub.MOPS, or variances .sub.MOPS.sup.2 of the residuals, associated with a first set of points IGPj of an ionospheric correction grid for a service area of an SBAS system is implemented by one or more computers, on the basis on the one hand of information in respect of ionospheric-error corrections calculated for the said points IGPj of the first set, j designating an integer index for identifying and scanning the said points IGPi of a portion of the ionospheric grid, structured as a meshed network of cells having a predetermined shape and corresponding to the SBAS service area, and on the basis on the other hand of information in respect of measurements of pseudo-distances of a second set of control pierce points IPPi which are contained in the cells of the service portion of the ionospheric grid, the measurements of pseudo-distances being performed by so-called RIMS control and telemetry stations.

(130) The points IGPj of the ionospheric grid portion corresponding to the coverage of the SBAS service area, forming a meshed network whose mesh cells have one and the same predetermined shape, this shape being included among triangular shapes and quadrilateral shapes, preferably rectangular, square or lozenge shapes.

(131) The provision of the information in respect of ionospheric-error corrections calculated for the said points IGPj of the first set and of the information in respect of measurements of pseudo-distances of the second set of control pierce points IPPi is implemented in the course of a prior step of calculating and providing the said information 304 forming a step of initialization 304 of the second method for optimally computing the .sub.MOPS.

(132) In contradistinction to what is done in the method of the prior art, the second method 302 according to the invention does not perform any IGP-wise computation of standard deviations called .sub.MOPS by scanning through a scan loop for the IGPs on the first set, but performs IPP-wise integrity verification tests by scanning a global scan loop 306 for the IPPi on the second set.

(133) The IPPi of the first set are partitioned into their membership cells or mesh cells and the global scan loop 306 for the IPPi comprises a first loop 208 for scanning the cells of the grid portion according to an order or a scan pattern which is predetermined, and comprises, nested in the first loop 308 for scanning the cells, a second local loop 309 for scanning the IPPi belonging to one and the same cell of the ionospheric grid portion.

(134) The method 302 for optimally computing the standard deviations .sub.MOPS by finals comprises a set of steps executed after the prior step 304.

(135) In a first step 310, a first commencing and initializing cell for first loop 308 is selected according to the initial rank that it occupies in the predetermined scan pattern for the cells. The scan index of the first loop being designated by m, the index m is set to 1 and corresponds to the initial rank 1 of the first cell of the pattern.

(136) Next, for each IPPi contained in the cell of current rank m in the order of scanning of the first loop, the following steps are executed.

(137) In a second step 312, for the relevant IPPi of rank i contained in the cell of current rank m, a residual, designated by Res.sub.i, referred to the vertical, is computed according to equation #21:

(138) ${\mathrm{Res}}_i=\frac{{\mathrm{STEC}}_i-{\mathrm{UISD}}_i}{F_{\mathrm{pp}\mathrm{standard}}}$
in which:

(139) STECi designates the ionospheric delay of the real line of sight, therefore dependent on the elevation;

(140) UISDi designates the vertical ionospheric delay interpolated according to the standard on the basis of the GIVDk of the IGPk of the mesh cell or cell surrounding the IPPi;

(141) F.sub.pp standard designates the standard rabattement function for mapping the ionospheric delay as a function of the elevation of the line of sight.

(142) In the same second step 312, the square of the residual Res.sub.i.sup.2 is computed.

(143) Next, in a third step 314, the square of the residual computed Res.sub.i.sup.2 is distributed or dispersed between the IGPj having served for the computation of the UISDi of the IPPi considered.

(144) Given that the square of the residual of an IPPi is obtained by interpolation, this interpolation being normalized according to a normalized function defined by the RTCA DO-229E standard, it is therefore necessary to invert this interpolation in order to redistribute in a perfectly compliant manner the square of the residual Res.sub.i.sup.2, previously computed in the second step 312.

(145) The square of the residual Res.sub.i.sup.2 must be governed by the following equation #22:

(146) ${\mathrm{Res}}_i^2=\underset{k=1}{\overset{N_{\mathrm{IGP}}}{.Math.}}{w}_k.Math.{}_{\mathrm{Resk}}^2$

(147) in which N.sub.IGP is the number of IGPs of the mesh cell of predetermined shape that are used in the computation of Res.sub.i.sup.2 of the IPPi considered, this number possibly being 3 or 4, depending on the type of mesh cell used; k designates a numbering index in the mesh cell containing the IPPi of the IGPs of the said mesh cell, w.sub.k the weight of the IGPk computed by applying the standard according to the computation scheme defined in the standard.

(148) This interpolation being a barycentric interpolation, the sum of the weights w.sub.k is equal to 1, that is to say satisfies the relation: .sub.k=1.sup.N.sup.IGP w.sub.k=1

(149) The third step 314 is a method for determining the values of .sub.Resk.sup.2 to be allocated respectively to the IGPk of the IPPi considered such as described in FIG. 12, which method uses the LS Least Squares scheme to ensure the realization of this partition whatever the conditions.

(150) An observation equation is defined by the expression:
Xi=Hi.Math.Yi (equation #23)

(151) in which Hi=[w.sub.1 w.sub.2 w.sub.3 w.sub.4] designates a row vector with four components when four IGPs have been used to carry out the interpolation of the IPPi considered, each w.sub.k corresponding to the weight of an IGP.sub.k obtained with the computation scheme defined here by the RTCA DO-2290 standard of the EGNOS system, all versions up to and including the current version E, for the IPPi considered;

(152) $\mathrm{Yi}=\left[\begin{array}{c}{}_{\mathrm{Res}1}^2\\ {}_{\mathrm{Res}2}^2\\ {}_{\mathrm{Res}3}^2\\ {}_{\mathrm{REes}4}^2\end{array}\right]$
designates a column vector with four components of the distribution of the square of the residual Res.sub.i.sup.2 to be distributed over the four IGPk when the mesh cell of the IPPi considered comprises four IGPs, as result of solving the equation; Xi=Res.sub.i.sup.2 designates the quantity to be distributed computed in the second step 312.

(153) It should be noted that the case where only three IGPs belonging to a triangular mesh cell are used for the computation of the UISDi of the IPPi considered, it suffices to readapt the sizes of the vectors Hi and Yi, Hi then having a size [3,1] and Yi a size [1,3].

(154) The LS Least Squares scheme implemented in the third step determines the column vector Yi and solves the observation equation with the aid of the formula:
Yi=Hi.sup.t.Math.(Hi.Math.Hi.sup.t).sup.1.Math.Res.sub.i.sup.2 (equation #24)

(155) Thereafter, in a fourth step 316, a weighting coefficient pi as inverse of a weight is computed, this coefficient being representative of the quality of the measurement of the STECi rectified into VTECi by dividing by the rabattement function for mapping the IPPi considered, and expressed according to the following formula:

(156) $p_i=\frac{{}_{{\mathrm{VTEC}}_i}^2}{{}_{\mathrm{VTEC}\mathrm{NOMINAL}}^2}$

(157) in which .sub.VTEC.sub.i.sup.2 designates the measurement noise in respect of the pseudo-distance measured by the measurement terminal for the IPPi considered, and .sub.VTEC.sub.i.sub.NOMINAL.sup.2 designates a nominal reference measurement noise of the measurement terminal.

(158) The squares of the residuals .sub.Resk.sup.2 and the weight 1/pi associated with the IPPi considered are recorded in a saving memory.

(159) Next, in a fifth step 318, it is verified whether all the IPPi contained in the cell of current rank m have been tested.

(160) If not all the IPPi of the cell of current rank m have been tested, an as yet untested IPPi of the cell of current rank m is tested in the second local scan loop, the index i of the untested IPPi becoming the new index of the IPPi to be tested, and the second, third, fourth, fifth steps are repeated.

(161) If all the IPPi of the cell of current rank m have been tested, a sixth step 320 is executed in the course of which the scan rank m for scanning through the cells according to the predetermined pattern is incremented by one unit.

(162) After the sixth step 320, a seventh step 322 of testing for the end of the first loop is implemented in the course of which it is verified whether the incremented scan index m of the cells exceeds the rank of the last cell of the scan pattern.

(163) When the incremented scan index m of the cells does not exceed the rank of the last cell of the scan pattern, that is to say when the incremented scan index m is less than or equal to the scan index of the last cell of the pattern, i.e. the pattern's cell programmed to be swept last, the incremented scan index m of the first loop becomes the current scan index of the first loop, for each IPPi contained in the cell of current rank m in the order of scanning of the first loop, the steps of the second local loop are executed again.

(164) When the incremented scan index m of the cells exceeds the rank of the last cell of the scan pattern, an eighth step 324 followed by a ninth step 326 of computing the standard deviations of the IGPs of the service area is implemented for each IGP on the basis of an associated inherent list containing the residual portions of the IPPs having generated a residual for the IGP considered and the weights 1/p to be associated.

(165) Considering a given IGP, the standard deviation .sub.MOPS is computed in the eighth step 324 according to equation #25:

(166) ${}_{\mathrm{MOPS}}=\sqrt{\frac{1}{P_S}\underset{i=1}{\overset{\mathrm{Nipp}}{.Math.}}\frac{1}{p_i}{}_{{\mathrm{Res}}_{\mathrm{ippi}}}^2}$

(167) with: P.sub.S, the sum of the normalized weights 1/p.sub.i of each residual that are available for the following IGP considered:

(168) $\mathrm{Ps}=\underset{i=1}{\overset{N_{\mathrm{ipp}}}{.Math.}}\frac{1}{p_i}$ N.sub.ipp being the number of IPPs having generated a residual for the IGP concerned, .sub.Res.sub.ipp i.sup.2 the residual interpolated as inverse at the IGP considered for the IPPi forming part of the IPPs having generated a residual for the IGP concerned.

(169) In contradistinction to the conventionally used methods, the weights 1/pi are defined here solely as a function of the quality of the STEC measurement obtained on each IPP having generated a residual for the IGP concerned.

(170) In the ninth step 326, the value of the .sub.MOPS computed in the eighth step 324 for the IGP considered is expanded according to the number of IPPi having contributed to its estimation by a Student's factor making it possible to define the confidence index of the value measured with respect to a Gaussian assumption so as to obtain a new value of .sub.MOPS according to the expression:

(171) 0${}_{\mathrm{MOPS}}\left(\frac{t_{v_k,0.99999995}}{5.33}\right){}_{\mathrm{MOPS}}$

(172) with: t.sub.v.sub.k.sub.,0.99999995 the Student's factor as a function of v.sub.k, the degree of freedom (here it is the number of IPP) making it possible to bound an error with a probability of 10.sup.7 required by the aeronautical standard; and 5.33 which is the value obtained when the Gaussian assumption is applied, for the same probability as that defined hereinabove, that is to say 0.999999995 of confidence.

(173) When the loop for computing the standard deviations .sub.MOPS of the IGPs has scanned through all the IGPs of the area of the SBAS service, the second method for computing the .sub.MOPS is stopped.

(174) As a variant and in a manner equivalent to the execution of the eighth and ninth steps 324, 326, for an IGP considered it is possible to compute the .sub.MOPS on the basis of a weighted Least squares scheme using as inverse pi of weight for each relevant IPPi having generated a residual for the IGP considered, it being possible for the expression for such a weight inverse to be:

(175) $p_i=\frac{1}{w_i}{}_{{\mathrm{VTEC}}_i}^2\mathrm{or}{p}_i=\frac{1}{w_i}\frac{{}_{{\mathrm{VTEC}}_i}^2}{{}_{\mathrm{VTEC}\mathrm{NOMINAL}}^2},$
the inverse pi of the weight being representative of the measurement quality associated with the IPP considered, and w.sub.i being the weight of the IPPi according to the IGP such as defined by the DO-229 standard.

(176) The weight w.sub.i can also be computed and modified into a weight dependent on the significance that one wishes to accord to the positioning of the IPPs. For example, a weighting denoted w.sub.i center norm, attaining the most significant weight at the centre of the cell used for the bilinear interpolation, is applied, since it is here that the maximum of the interpolation errors are assumed to be concentrated.

(177) The weight w.sub.i center norm then used, corresponding to the fit at the centre of the cells, is computed on the basis of the weights on determined according to the MOPS-DO-229 standard as follows.

(178) A first modified weight w.sub.i center ini is computed for each non-zero weight of the IPP i having been used for the interpolation according to the formula:

(179) $w_{i\mathrm{center}\mathrm{ini}}=.Math.w_i-\frac{1}{N_{\mathrm{IGP}}}.Math.$

(180) Next, the weight w.sub.i center norm used is computed according to the formula:

(181) If w.sub.i=0, then the IPP is not used for the computation of the .sub.MOPS of the IGP considered

(182) If

(183) $0<w_i<\frac{1}{N_{\mathrm{IGP}}},\mathrm{then}{w}_{i\mathrm{center}\mathrm{norm}}=w_i$

(184) Otherwise

(185) $w_{i\mathrm{center}\mathrm{norm}}=1-\frac{w_{i\mathrm{center}\mathrm{ini}}}{\underset{i=1}{\overset{N_{\mathrm{IGP}}}{.Math.}}{w}_{i\mathrm{center}\mathrm{ini}}},$
in which N.sub.IGP corresponds to the number of IGP having served in the interpolation of the ionospheric delay at the IPPi. In this case the expression for the weight inverse pi for each relevant IPPi having generated a residual for the IGP considered, may be written:

(186) $p_i=\frac{1}{w_{i\mathrm{centre}\mathrm{norm}}}{}_{{\mathrm{VTEC}}_i}^2\mathrm{or}$$p_i=\frac{1}{w_{i\mathrm{centre}\mathrm{norm}}}\frac{{}_{{\mathrm{VTEC}}_i}^2}{{}_{\mathrm{VTEC}{\mathrm{NOMINAL}}^2}}.$

(187) Designating by P a diagonal weighting matrix of dimension equal to the number N.sub.ipp of the IPPs having generated residuals for the computation of the .sub.MOPS of the IGP considered, we put:

(188) $P=\left[\begin{array}{ccc}\frac{1}{p_1}& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& & \mathrm{.Math.}\\ 0& \mathrm{.Math.}& \frac{1}{p_{N_{\mathrm{ipp}}}}\end{array}\right]$

(189) We designate by K the observation matrix of size N.sub.ipp1 and defined by: K=[1 . . . 1]

(190) With the matrix of the residuals of size 1N.sub.ipp denoted Z and defined by:

(191) $Z=\left[\begin{array}{c}{}_{{\mathrm{Res}}_{{\mathrm{ipp}}_1}}^2\\ \mathrm{.Math.}\\ {}_{{\mathrm{Res}}_{{\mathrm{ippN}}_{\mathrm{ipp}}}}^2\end{array}\right]$

(192) the computation of the standard deviation .sub.MOPS of the IGP considered may finally be written in an equivalent manner by the expression:

(193) $\begin{array}{cc}{}_{\mathrm{MOPS}}=\left(\frac{t_{v_k,0.99999995}}{5.33}\right).Math.\sqrt{{\left(K.Math.P.Math.K^t\right)}^{-1}.Math.K.Math.P.Math.X^t}& \left(\mathrm{equation}\mathrm{\#25}\right)\end{array}$

(194) with:

(195) t.sub.v.sub.k.sub.,0.99999995, the Student's factor having (N.sub.ipp1) degrees of freedom for a risk of 10.sup.7.

(196) It should be noted that the expansion factors considered hereinabove for the various forms of computation of the .sub.MOPS correspond to the particular case of a confidence level taken equal to 10.sup.7, appropriate to certain aeronautical services.

(197) Generally, the expansion factor for .sub.MOPS, denoted d.sub.k is equal to

(198) $\left(\frac{t_{v_k,}}{G\left(p\right)}\right)$
with:

(199) t.sub.v.sub.k.sub., designating the Student's factor dependent on v.sub.k the degree of freedom and dependent on the confidence probability , the said Student's factor t.sub.v.sub.k.sub., making it possible to bound an error with a predetermined confidence level (1-p) required by the SBAS service, the confidence probability being related to the confidence level (1-p) by the relation

(200) 0$=1-\frac{1}{2}.Math.p,$
and the degree of freedom v.sub.k being equal here to the number of IPP having generated a residual for the IGP concerned minus one;

(201) G(p) is the value obtained when the Gaussian assumption is applied for the same confidence probability (1-p) or for the same probability p of the risk that one wishes to bound, that is to say the limit of the Student's factor t.sub.v.sub.k.sub., when the degree of freedom v.sub.k tends to infinity; G(p) is defined by the expression G(p)=erf.sup.1(1p){square root over (2)}, erf.sup.1() designating the reciprocal function of the error function and (1-p) designating the confidence level required.

(202) As a variant of the execution of the eighth and ninth steps 324, 326, and in a manner which simplifies the computation of the standard deviation .sub.MOPS, a sorting is performed on the residuals computed by the inverse interpolation scheme for an IGP considered as a function of the quality of the measurement of the residual Red.sub.i.sup.2 associated with a given IPPi. This makes it possible to simplify the computation of the standard deviation .sub.MOPS and to trim the list of the squares of residuals interpolated as inverse at the IGP considered. In this scheme, perfect control of the amount of residual applied to each IGP by virtue of the application of the inverse interpolation scheme is maintained.

(203) After having performed a relevant sorting of the residuals applied to the IGPs concerned, the standard deviation .sub.MOPS is computed according to the equation:

(204) ${}_{\mathrm{MOPS}\_\mathrm{simp}}=\sqrt{\frac{1}{N_{\mathrm{ipp}\_\mathrm{fil}}}\underset{i=1}{\overset{\mathrm{Nipp}\_\mathrm{fil}}{.Math.}}{}_{{\mathrm{Res}}_{\mathrm{ippi}}}^2}$

(205) with: N.sub.ipp_fil being the number of IPPs having generated a residual for the IGP concerned and whose measurement quality is sufficient, .sub.Res.sub.ipp i.sup.2 being the square of a residual applied to the IGP considered and generated by a sorted IPPi, that is to say having a quality measurement.

(206) Reusing the previous matrix formulation, this gives in the particular case of a confidence level equal to 10.sup.7:

(207) $\begin{array}{cc}{}_{\mathrm{MOPS}}=\left(\frac{t_{v_k,0.99999995}}{5.33}\right).Math.\sqrt{{\left(K.Math.K^t\right)}^{-1}.Math.K.Math.X^t}& \left(\mathrm{equation}\mathrm{\#26}\right)\end{array}$

(208) The inverse interpolation scheme, implemented in the first method 202 for fitting the GIVEs, is here also used in the second method 302 for optimally computing the term .sub.MOPS which makes it possible to compensate for the deviations induced by the standard used in the computation of ionospheric delays at the level of the user. Applied in this second method, the inverse interpolation scheme makes it possible to guarantee correct distribution of the estimated residuals so as to give each IGP the value of residual as a function of the effective contribution of each IPP in relation to this IGP.

(209) An SBAS satellite-based augmentation system for augmenting the performance of a global navigation satellite system GNSS, configured to execute the second method of optimal computation of FIG. 11, comprises SBAS service(s) user terminals, one or more satellites for augmenting the satellites of the GNSS system and for broadcasting information messages to the user terminals, one or more RIMS observation stations furnished with GNSS receivers, and one or more computers.

(210) The SBAS system is configured to compute in an optimal manner variances of the residuals of a first set of IGP points of an ionospheric correction grid for a service area of an SBAS system, the ionospheric correction grid being structured as a meshed network of cells of predetermined polygonal shape, the cells of the meshed network corresponding projectively to the SBAS service area and having as vertices IGP points of the first set.

(211) The electronic computer or computers of the SBAS system are configured to:

(212) on the basis of predetermined information in respect of ionospheric error correction of the IGP points of the first set, and of measurements of pseudo-distances of a second set of control and observation pierce points IPP which are contained in the cells of the ionospheric grid, for each observation pierce point IPPi of the second set, a residual, designated by Res.sub.i, referred to the vertical, according to the equation:

(213) ${\mathrm{Res}}_i=\frac{{\mathrm{STEC}}_i-{\mathrm{UISD}}_i}{F_{\mathrm{pp}\mathrm{standard}}}$

(214) in which: STECi designates the ionospheric delay, measured by an observation station, of the real line of sight and which is dependent on the elevation of the said line of sight; UISDi designates the vertical ionospheric delay interpolated according to the standard of the user terminal on the basis of the GIVDk of the IGPk of the mesh cell surrounding the IPPi; F.sub.pp standard designates the standard rabattement function for mapping the ionospheric delay as a function of the elevation of the line of sight,

(215) and then compute the square of the residual;

(216) and thereafter for each observation pierce point IPPi of the second set,

(217) determine values of variance increments .sub.Resk.sup.2 to be allocated respectively to the IGPk of the mesh cell m of the IPPi considered by an inverse interpolation scheme using a Least Squares scheme in which a vector Yi of distribution of the square of the residual Res.sub.i.sup.2 of the IPPi considered is computed according to the equation:
Yi=Hi.sup.t.Math.(Hi.Math.Hi.sup.t).sup.1.Math.Res.sub.i.sup.2

(218) in which H=[w.sub.1 w.sub.2, . . . w.sub.NIGP] designates a row vector with N.sub.IGP components for carrying out the interpolation of the IPPi considered; each component w.sub.k, k varying from 1 to N.sub.IGP, corresponding to the weight of an IGP.sub.k obtained with the direct interpolation computation scheme defined by the standard for the IPPi considered;

(219) ${}^{*}\mathrm{Yi}=\left[\begin{array}{c}{}_{\mathrm{Res}1}^2\\ {}_{\mathrm{Res}2}^2\\ \mathrm{.Math.}\\ {}_{\mathrm{ResNIGP}}^2\end{array}\right]$
designates a column vector with N.sub.IGP components of the distribution of the square of the residual Res.sub.i.sup.2 to be distributed over the N.sub.IGP IGPk when the mesh cell of the IPPi considered comprises N.sub.IGP IGP, as result of solving the equation; Res.sub.i.sup.2 designates the square of the residual to be distributed, and then

(220) determine a weighting coefficient pi as inverse of a weight, this weighting coefficient being representative of the quality of the measurement of the STECi rectified into VTECi by dividing by the rabattement function for mapping the IPPi considered, and expressed according to the following formula:

(221) $p_i=\frac{{}_{{\mathrm{VTEC}}_i^2}}{{}_{\mathrm{VTEC}{\mathrm{NOMINAL}}^2}}$

(222) in which w.sub.i designates the weight of the IPPi according to the IGP such as defined by the DO-229 standard. .sub.VTEC.sub.i.sup.2 designates the measurement noise in respect of the pseudo-distance measured by the measurement terminal for the IPPi considered, and .sub.VTEC.sub.i.sup.2 designates a nominal reference measurement noise of the measurement terminal;

(223) thereafter, after having computed all the Yi and pi corresponding to the first set of the pierce points IPPi observed,

(224) for each IGP, compute an unexpanded-residual variance according to the equation:

(225) ${}_{\mathrm{MOPS}}=\sqrt{\frac{1}{\mathrm{Ps}}\underset{i=1}{\overset{\mathrm{Nipp}}{.Math.}}\frac{1}{p_i}{}_{{\mathrm{Res}}_{\mathrm{ippi}}}^2}$

(226) with: Ps, the sum of the normalized weights 1/p.sub.i of each residual that are available for the following IGP considered:

(227) $\mathrm{Ps}=\underset{i=1}{\overset{N_{\mathrm{ipp}}}{.Math.}}\frac{1}{p_i}$ N.sub.ipp being the number of IPPs having generated a residual for the IGP concerned, .sub.Res.sub.ipp i.sup.2 the residual interpolated as inverse at the IGP considered for the IPPi forming part of the IPPs having generated a residual for the IGP concerned.

(228) As a variant, the SBAS satellite-based augmentation system is configured to execute one of the variants, described hereinabove, of the second method of optimal computation.