Method and device for simultaneous identification and correction of errors in the measurements of a magnetometer
First Claim
1. A method for identifying and correcting errors due to determined perturbations in the measurements of a magnetometer (2) mounted on board a vehicle (3), wherein:
- a theoretical model correcting the measurement errors of the magnetometer is defined in the form;
##EQU37## n being an integer greater than or equal to 1, in which;
Hc is the corrected field, A! is a matrix to be determined,Hm is the value measured by the magnetometer (2) of the magnetic field in a reference frame (R1) associated with said vehicle (3),the elements C!i are matrices to be determined, with respective dimensions (3×
mi), mi being an integer greater than or equal to 1,the elements E!i are matrices with respective dimensions (mi×
1), the coefficients of which are measurements of perturbing parameters or combinations of such measurements, andHp is a perturbing field to be determined;
the corrected field Hc is assumed to be the terrestrial field defined in the vehicle reference frame, so that;
##EQU38## with;
H representing the effective value of the magnetic field in a base reference frame (R2), and M! representing a change of frame matrix from said base reference frame (R2) to said vehicle reference frame (R1);
successive measurements Hm of the magnetic field are taken using the magnetometer during movements of the vehicle;
the coefficients of the various matrices E!i are determined on the basis of the measurements of the perturbing parameters, taken simultaneously with the Hm measurements;
the coefficients of the change of frame matrix M! are determined;
an error vector E with components Ex, Ey and Ez is defined, defined by the equation;
##EQU39## a composite error E2 =Ex2 +Ey2 +Ez2 is defined;
a system of equations formed by m equations of the type (∂
Σ
E2)/∂
c1=0, 1=1 to m, (∂
Σ
E2)/∂
c1 corresponding to the partial derivative of the sum of the composite errors Σ
E2 is defined, for all the measurements, with respect to a coefficient cl, the various coefficients cl representing the coefficients to be determined in said theoretical model, namely the coefficients of the matrix A!, of the matrices C!i and of the vector Hp, as well as at least one component of the effective magnetic field H;
said system of equations is solved so as to obtain said coefficients cl, including said component of the effective magnetic field H; and
the corrective model obtained on the basis of said coefficients is used to correct the errors due to determined perturbations in the measurements of said magnetometer (2).
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Abstract
The present invention relates to a method and a device for correcting measurement errors of a magnetometer mounted on a vehicle. According to the method, a theoretical corrective model is defined in accordance with the following equation: ##EQU1## where A!, C!i and Hp are elements to be determined, Hm is the measured field, H the effective field, and M! is a transformation matrix, and in which a vector error is defined in accordance with the following equation: ##EQU2## where the square of the error thus defined is determined and the coefficients of the model which minimize the sum of the squares of the error moduli for all the measurements taken are identified.
33 Citations
18 Claims
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1. A method for identifying and correcting errors due to determined perturbations in the measurements of a magnetometer (2) mounted on board a vehicle (3), wherein:
-
a theoretical model correcting the measurement errors of the magnetometer is defined in the form;
##EQU37## n being an integer greater than or equal to 1, in which;
Hc is the corrected field,A! is a matrix to be determined, Hm is the value measured by the magnetometer (2) of the magnetic field in a reference frame (R1) associated with said vehicle (3), the elements C!i are matrices to be determined, with respective dimensions (3×
mi), mi being an integer greater than or equal to 1,the elements E!i are matrices with respective dimensions (mi×
1), the coefficients of which are measurements of perturbing parameters or combinations of such measurements, andHp is a perturbing field to be determined; the corrected field Hc is assumed to be the terrestrial field defined in the vehicle reference frame, so that;
##EQU38## with;
H representing the effective value of the magnetic field in a base reference frame (R2), andM! representing a change of frame matrix from said base reference frame (R2) to said vehicle reference frame (R1); successive measurements Hm of the magnetic field are taken using the magnetometer during movements of the vehicle; the coefficients of the various matrices E!i are determined on the basis of the measurements of the perturbing parameters, taken simultaneously with the Hm measurements; the coefficients of the change of frame matrix M! are determined; an error vector E with components Ex, Ey and Ez is defined, defined by the equation;
##EQU39## a composite error E2 =Ex2 +Ey2 +Ez2 is defined;
a system of equations formed by m equations of the type (∂
Σ
E2)/∂
c1=0, 1=1 to m, (∂
Σ
E2)/∂
c1 corresponding to the partial derivative of the sum of the composite errors Σ
E2 is defined, for all the measurements, with respect to a coefficient cl, the various coefficients cl representing the coefficients to be determined in said theoretical model, namely the coefficients of the matrix A!, of the matrices C!i and of the vector Hp, as well as at least one component of the effective magnetic field H;said system of equations is solved so as to obtain said coefficients cl, including said component of the effective magnetic field H; and the corrective model obtained on the basis of said coefficients is used to correct the errors due to determined perturbations in the measurements of said magnetometer (2). - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18)
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Specification