Method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system
A method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system includes a first step of measurements of N rotation matrices {circumflex over (K)} l for detecting the posture of a head corresponding to a set of different targeting actions Vi, in which measurements one or more different preset elements of pilot/driver information displayed in the viewing device D v are superposed or aligned with one or more corresponding landmarks of the real outside world; then a second step of conjointly calculating the relative orientation matrix {circumflex over (R)}(S1/v) of the DDP tracking first element S1 with respect to the viewing device D v and/or the relative orientation matrix {circumflex over (R)}(ref/S2) of the external reference device D Ref with respect to the DDP fixed solid second element S2 to respectively be the right-side bias rotation matrix {circumflex over (D)} and the left-side bias rotation matrix Ĝ, which are solutions of the system of dual harmonization equations: Û i =Ĝ·{circumflex over (K)} i ·{circumflex over (D)}, i varying from 1 to N.
1. A method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system,
the worn/borne head-up viewing system being located on-board a carrier vehicle and comprising:
a transparent worn/borne head-up viewing device D v ,
an exterior reference device D ref having an exterior reference coordinate system R ref , that is a coordinate system of the carrier vehicle or a local geographic coordinate system or a terrestrial coordinate system;
the DDP posture-detecting subsystem comprising:
a tracking solid first element S1 tightly attached to the transparent worn/borne head-up viewing device D v ; and
a fixed solid second element S2 tightly joined to the exterior reference device D ref , wherein the DDP posture-detecting subsystem is configured to measure and determine a relative orientation {circumflex over (K)} of the tracking solid first element S1 with respect to the fixed solid second element S2,
a dual harmonization subsystem configured to harmonize the worn/borne head-up viewing system and the DDP posture-detecting subsystem,
the method for dual harmonization comprising:
in a first step, a series of a preset number N of measurements of relative orientations {circumflex over (K)} i , i varying from 1 to N, of the tracking solid first element S1 with respect to the fixed solid second element S2 of the DDP posture-detecting subsystem, corresponding to different targeting actions Vi, i varying from 1 to N, that are carried out, in which measurements of one or more different preset elements of pilot/driver information displayed in the transparent worn/borne head-up viewing device D v are superposed or aligned with one or more corresponding landmarks of a real outside world, theoretical rotation matrices Û i of which in the exterior reference coordinate system are known; then
in a second step, and using a dual harmonization algorithm, conjointly calculating a relative orientation matrix {circumflex over (R)}(S1/v) of the tracking solid first element S1 of the DDP posture-detecting subsystem with respect to the transparent worn/borne head-up viewing device D v and/or a relative orientation matrix {circumflex over (R)}(ref/S2) of the exterior reference device D ref with respect to the fixed solid second element S2 of the DDP posture-detecting subsystem to respectively be a right-side bias rotation matrix {circumflex over (D)} and a left-side bias rotation matrix Ĝ, which are conjoint solutions of a system of dual harmonization equations: Û i =Ĝ·{circumflex over (K)} i ·{circumflex over (D)}, i varying from 1 to N.
2. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 1 , wherein
a minimum required number N of measurements depends on a number L of erroneous or inexploitable degrees of angular freedom of the rotation matrices {circumflex over (R)}(S1/v) and {circumflex over (R)}(ref/S2) of the head-up viewing system, said number L being an integer higher than or equal to 1 and lower than or equal to 6, and
the solution of the system of equations Û i =Ĝ·{circumflex over (K)} i ·{circumflex over (D)}, i varying from 1 to N, uses a rectification operator π(.) that converts any given matrix A into a 3×3 square rotation matrix π(A), which matrix π(A), of all the 3×3 rotation matrices, is the closest in the least-squares sense to all of the terms of the matrix π(A)−A, to determine the right-side rotation {circumflex over (D)} and the left-side rotation Ĝ.
3. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2 , wherein and in a first configuration,
the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the number of erroneous or inexploitable degrees of angular freedom of the left-side bias rotation matrix Ĝ is equal to three,
the first step carries out a number N higher than or equal to 3 of measurements, for which measurements the targeting actions Vi correspond to an alignment of displayed three-dimensional reference marks with observed exterior three-dimensional reference marks, and
the second step of solving the system of dual harmonization equations comprises a first set of substeps consisting in:
in a first substep, choosing a “pivot” measurement as the first measurement among the N measurements, this pivot measurement corresponding to i equal to 1, and for i=2, . . . , N the rotation matrices Û 1,i and {circumflex over (K)} 1,i are calculated using the equations: Û 1,i =Û 1 T ·Û i and {circumflex over (K)} 1,i ={circumflex over (K)} 1 T ·{circumflex over (K)} i ; then
in a second substep, determining for i=2, . . . , N the principle unit vectors of the rotations Û 1,i and {circumflex over (K)} 1,i and designated by {right arrow over (u)} i and {right arrow over (k)} i , respectively; then
in a third substep, calculating the right matrix {circumflex over (D)} using the equation:
D
^
=
π
(
∑
i
>
2
(
k
→
i
·
u
→
i
T
)
)
then
in a fourth substep, determining the left-side rotation matrix Ĝ on the basis of the matrix {circumflex over (D)} calculated in the third substep, using the equation:
G
^
=
π
(
∑
i
>
1
(
U
^
i
·
D
^
T
·
K
^
i
T
)
)
.
4. A worn/borne head-up viewing system located on-board a carrier vehicle and comprising:
the transparent worn/borne head-up viewing device D v ,
the reference device D ref having a reference coordinate system R ref , that is either a coordinate system of the carrier vehicle or a local geographic coordinate system or a terrestrial coordinate system;
the DDP posture-detecting subsystem comprising:
the tracking solid first element S1 tightly attached to the transparent worn/borne head-up viewing device D v ;
the fixed solid second element S2 tightly joined to the reference device D ref , and
the dual harmonization subsystem for harmonizing the head-up viewing system and the DDP posture-detecting subsystem, the dual harmonization subsystem comprising a dual harmonization processor and an HMI interface for managing the acquisitions of the harmonization measurements,
the worn/borne head-up viewing system being wherein the dual harmonization subsystem and the DDP posture-detecting subsystem are configured to:
in a first step, carry out a series of a preset number N of measurements of relative orientations {circumflex over (K)} i , i varying from 1 to N, of the tracking solid first element S1 with respect to the fixed solid second element S2 of the DDP posture-detecting subsystem, corresponding to different targeting actions Vi, i varying from 1 to N, in which measurements one or more different preset elements of pilot/driver information displayed in the transparent worn/borne head-up viewing device D v are superposed or aligned with one or more corresponding landmarks of the real outside world; then
in a second step, and using a dual harmonization algorithm, conjointly calculate the relative orientation matrix {circumflex over (R)}(S1/v) of the tracking solid first element S1 of the posture-detecting subsystem with respect to the transparent worn/borne head-up viewing device D v and/or the relative orientation matrix {circumflex over (R)}(ref/S2) of the external reference device D ref with respect to the fixed solid second element S2 of the posture-detecting subsystem to respectively be the right-side bias rotation matrix {circumflex over (D)} and the left-side bias rotation matrix Ĝ, which are conjoint solutions of the system of dual harmonization equations: Û i =Ĝ·{circumflex over (K)} i ·{circumflex over (D)}, i varying from 1 to N;
the minimum required number N of measurements depends on the number L of erroneous or inexploitable degrees of angular freedom of the rotation matrices {circumflex over (R)}(S1/v) and {circumflex over (R)}(ref/S2) of the head-up viewing system, said number L being an integer higher than or equal to 1 and lower than or equal to 6,
the solution of the system of equations Û i =Ĝ·{circumflex over (K)} i ·{circumflex over (D)}, i varying from 1 to N, uses a rectification operator π(.) that converts any given matrix A into a 3×3 square rotation matrix π(A), which matrix π(A), of all the 3×3 rotation matrices, is the closest in the least-squares sense to all of the terms of the matrix π(A)−A, to determine the right-side rotation {circumflex over (D)} and the left-side rotation Ĝ; and
wherein the dual harmonization subsystem and the DDP posture-detecting subsystem are configured to implement the first and second steps such as defined in claim 3 .
5. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 3 , wherein and in a second configuration,
the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the single erroneous or inexploitable degree of angular freedom of the left-side bias rotation matrix Ĝ is the azimuth angle, the elevation and roll angles being assumed to be known with a sufficient precision; and
the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of displayed three-dimensional reference marks with observed three-dimensional reference marks, and
the second step of solving the system of dual harmonization equations comprises a second set of substeps consisting in:
in a fourth substep for i=2, . . . , N, calculating the matrices Û 1,i and the vectors {right arrow over (q)} i using the equations:
Û 1,i =Û 1 T ·Û i and {right arrow over (q)} i ={circumflex over (Q)} 1 T ·{circumflex over (K)} i ,
the vector {right arrow over (k)} being defined by the equation
k
→
=
(
0
0
1
)
;
then
in an initialization fifth substep, initializing a first sequence of matrices {{circumflex over (D)} [s] }, [s] designating the current integer rank of advancement through the sequence {{circumflex over (D)} [s] }, by setting {circumflex over (D)} [0] equal to I 3 , I 3 being the identity matrix; then
repeating an iterative sixth substep in which iteration [s+1] is passed to from iteration [s] by calculating the vector value {right arrow over (d)} [s+1] , then the value {circumflex over (D)} [s+1] of the first matrix sequence {{circumflex over (D)} [s] }, using the following equations:
d
→
[
s
+
1
]
=
∑
i
≥
2
(
U
^
1
,
i
·
D
^
[
s
]
T
·
q
→
i
)
∑
i
≥
2
(
U
^
1
,
i
·
D
^
T
·
q
→
i
)
D
^
[
s
+
1
]
=
π
(
∑
i
≥
2
(
q
→
i
·
d
→
[
s
+
1
]
T
·
U
^
1
,
i
)
)
the sequence {{right arrow over (d)} [s] } being an auxiliary second sequence of vectors and the sequence {{circumflex over (D)} [s] } converging to {circumflex over (D)}; and
stopping in a seventh substep the iterative process carried out throughout the sixth substep when the limit {circumflex over (D)} is approximated with a sufficient precision defined by a preset threshold value.
6. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2 , wherein and in a second configuration,
the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the single erroneous or inexploitable degree of angular freedom of the left-side bias rotation matrix Ĝ is the azimuth angle, the elevation and roll angles being assumed to be known with a sufficient precision; and
the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of displayed three-dimensional reference marks with observed three-dimensional reference marks, and
the second step of solving the system of dual harmonization equations comprises a second set of substeps consisting in:
in a fourth substep for i=2, . . . , N, calculating the matrices Û 1,i and the vectors {right arrow over (q)} i using the equations:
Û 1,i =Û 1 T ·Û i and {right arrow over (q)} i ={circumflex over (Q)} 1 T ·{right arrow over (k)},
the vector {right arrow over (k)} being defined by the equation
k
→
=
(
0
0
1
)
;
then
in an initialization fifth substep, initializing a first sequence of matrices {{circumflex over (D)} [s] }, [s] designating the current integer rank of advancement through the sequence {{circumflex over (D)} [s] }, by setting {circumflex over (D)} [0] equal to I 3 , I 3 being the identity matrix; then
repeating an iterative sixth substep in which iteration [s+1] is passed to from iteration [s] by calculating the vector value {right arrow over (d)} [s+1] , then the value {circumflex over (D)} [s+1] of the first matrix sequence {{circumflex over (D)} [s] }, using the following equations:
d
→
[
s
+
1
]
=
∑
i
≥
2
(
U
^
1
,
i
·
D
^
[
s
]
T
·
q
→
i
)
∑
i
≥
2
(
U
^
1
,
i
·
D
^
T
·
q
→
i
)
D
^
[
s
+
1
]
=
π
(
∑
i
>
2
(
q
→
i
·
d
→
[
s
+
1
]
T
·
U
^
1
,
i
)
)
the sequence {{right arrow over (d)} [s] } being an auxiliary second sequence of vectors and the sequence {{circumflex over (D)} [s] } converging to {circumflex over (D)}; and
stopping in a seventh substep the iterative process carried out throughout the sixth substep when the limit {circumflex over (D)} is approximated with a sufficient precision defined by a preset threshold value.
7. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2 , wherein and in a third configuration,
the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the number of erroneous or inexploitable degrees of angular freedom of the left-side bias rotation matrix Ĝ is equal to three, and
the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of a plurality of different targeting directions {right arrow over (x)} i with a plurality of targeted exterior directions {right arrow over (y)} i that are known in the reference exterior coordinate system R ref , without roll adjustment, the vector families {{right arrow over (x)} i } and {{right arrow over (y)} i } both being free; and
the second step of solving the system of dual harmonization equations: {right arrow over (y)} i =Ĝ·{circumflex over (K)} i ·{circumflex over (D)}·{right arrow over (x)} i for i varying from 1 to N comprises a third set of the following substeps consisting in:
in an initialization eighth substep, initializing a first sequence of left matrices {Ĝ [s] }, [s] designating the integer rank of advancement through this first sequence, by setting Ĝ [0] equal to I 3 , I 3 being the identity matrix; then
repeating an iterative ninth substep in which iteration [s+1] is passed to from iteration [s] by calculating the matrix {circumflex over (D)} [s+1] then the matrix Ĝ [s+1] using the following equations:
D
^
[
s
+
1
]
=
π
(
∑
i
>
1
(
K
^
i
T
·
G
^
[
s
]
T
·
y
→
i
·
x
→
i
T
)
)
G
^
[
s
+
1
]
=
π
(
∑
i
>
1
(
y
→
i
·
x
→
i
T
·
D
^
[
s
+
1
]
T
·
K
^
i
T
)
)
the sequence {{circumflex over (D)} [s] }, being a second sequence of right matrices, and the sequences {circumflex over (D)} [s] and Ĝ [s] converging to {circumflex over (D)} and Ĝ, respectively; and
stopping in a stopping tenth substep the iterative process executed throughout the ninth substep when the limits {circumflex over (D)} and Ĝ are approximated with a sufficient precision.
8. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2 , wherein and in a fourth configuration,
the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the left-side bias rotation matrix Ĝ is assumed to be known, and
the first step carries out a number N higher than or equal to 3 of measurements, for which measurements the targeting actions Vi correspond to an alignment of N different targeting directions {right arrow over (x)} i with one and the same targeted direction {right arrow over (y 0 )}, which targeted direction is known in the reference exterior coordinate system R ref , without roll adjustment, the vector family {{right arrow over (x)} i } being free; and
the second step of solving the system of dual harmonization equations: Ĝ·{circumflex over (K)} i ·{circumflex over (D)}·{right arrow over (x)} i ={right arrow over (y)} 0 for i varying from 1 to N determines the right bias rotation matrix {circumflex over (D)} via the following equation:
D
^
=
π
(
∑
i
>
1
(
K
^
i
T
·
G
^
T
·
y
→
0
·
x
→
i
T
)
)
.
9. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2 , wherein and in a fifth configuration,
the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the left-side bias rotation matrix Ĝ is assumed to be known, and
the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of N different targeting directions {right arrow over (x)} i with one and the same unknown targeted exterior direction {right arrow over (y)} 0 , without roll adjustment, the vector family {{right arrow over (x)} i } being free; and
the second step of solving the system of dual harmonization equations: Ĝ·{circumflex over (K)} i ·{circumflex over (D)}·{right arrow over (x)} i ={right arrow over (y)} 0 for i varying from 1 to N comprises a fifth set of substeps consisting in:
in an initialization eleventh substep, initializing a first sequence of right matrices {{circumflex over (D)} [s] }, [s] designating the integer rank of advancement through the sequence {{circumflex over (D)} [s] }, by setting {circumflex over (D)} [0] equal to I 3 , I 3 being the identity matrix; then
repeating an iterative twelfth substep in which iteration [s+1] is passed to from iteration [s] by calculating the vector {right arrow over (y)} [s+1] then the matrix {circumflex over (D)} [s+1] using the following equations:
y
→
[
s
+
1
]
=
∑
i
≥
1
(
G
^
·
K
^
i
·
D
^
[
s
]
·
x
→
i
)
∑
i
≥
1
(
G
^
·
K
^
i
·
D
^
[
s
]
·
x
→
i
)
D
^
[
s
+
1
]
=
π
(
∑
i
>
1
(
K
^
i
T
·
G
^
T
·
y
→
[
s
+
1
]
·
x
→
i
T
)
)
the sequence {{right arrow over (y)} [s] } being a second sequence of external direction vectors, and the sequences {{right arrow over (y)} [s] } and {{circumflex over (D)} [s] } converging to {right arrow over (y)} 0 and {circumflex over (D)}, respectively; and
stopping in a stopping thirteenth substep the iterative process carried out throughout the twelfth substep when the limits {right arrow over (y)} 0 and {circumflex over (D)} are approximated with a sufficient precision defined by one or two preset threshold values.
10. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2 , wherein and in a sixth configuration,
the number of erroneous or inexploitable degrees of angular freedom of the right-side bias rotation matrix {circumflex over (D)} is equal to three and the left-side bias rotation matrix Ĝ is unknown and indeterminable, and
the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of N different targeting directions {right arrow over (x)} i with one and the same unknown targeted exterior direction {right arrow over (y)} 0 , without roll adjustment, the vector family {{right arrow over (x)} i } being free, and reduces the solution of the system of dual harmonization equations: Ĝ·{circumflex over (K)} i ·{circumflex over (D)}·{right arrow over (x)} i ={right arrow over (y)} 0 for i varying from 1 to N to the solution of the reduced system of dual harmonization equations:
{circumflex over (K)} i ·{circumflex over (D)}·{right arrow over (x)} i ={right arrow over (z)} 0 for i varying from 1 to 4, noting {right arrow over (z)} 0 =Ĝ T ·{right arrow over (y)} 0 ; and
the second step of solving the reduced system of dual harmonization equations comprises a sixth set of substeps consisting in:
in an initialization fourteenth substep, initializing a first sequence of right matrices {{circumflex over (D)} [s] }, [s] designating the integer rank of advancement through the sequence {{circumflex over (D)} [s] }, {circumflex over (D)} [0] being set equal to I 3 , I 3 being the identity matrix; then
repeating an iterative fifteenth substep in which iteration [s+1] is passed to from iteration [s] by calculating the vector {right arrow over (z)} [s+1] then the matrix of the first matrix sequence using the following equations:
z
→
[
s
+
1
]
=
∑
i
≥
1
(
K
^
i
·
D
^
[
s
]
·
x
→
i
)
∑
i
≥
1
(
K
^
i
·
D
^
[
s
]
·
x
→
i
)
D
^
[
s
+
1
]
=
π
(
∑
i
>
1
(
K
^
i
T
·
z
→
[
s
+
1
]
·
x
→
i
T
)
)
the sequence {{right arrow over (z)} [s] } being a second auxiliary sequence of vectors and the sequence {{circumflex over (D)} [s] } converging to {circumflex over (D)}; and
stopping in a stopping sixteenth substep the iterative process carried out throughout the fifteenth substep when the limit {circumflex over (D)} is approximated with a sufficient precision defined by a preset threshold value.
11. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2 , wherein and in a seventh configuration,
the number of erroneous or inexploitable degrees of angular freedom of the left-side bias rotation matrix Ĝ is equal to three and the right-side bias rotation matrix {circumflex over (D)} is assumed to be known; and
the first step carries out a number N higher than or equal to 3 of measurements, for which measurements the targeting actions Vi correspond to an alignment of one and the same known targeting direction {right arrow over (x)} 0 with N known targeted exterior directions {right arrow over (y)} i , without roll adjustment, the vector family {{right arrow over (y)} i } being free, and
the second step of solving the system of dual harmonization equations: Ĝ·{circumflex over (K)} i ·{circumflex over (D)}·{right arrow over (x)} 0 ={right arrow over (y)} i for i varying from 1 to N determines the sought left rotation matrix Ĝ using the equation:
G
^
=
π
(
∑
i
>
1
(
y
→
i
·
x
→
0
T
·
D
^
T
·
K
^
i
T
)
)
.
12. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 2 , wherein and in an eighth configuration,
the number of erroneous or inexploitable degrees of angular freedom of the left-side bias rotation matrix Ĝ is equal to three and the right-side bias rotation matrix {circumflex over (D)} is assumed to be known, and
the first step carries out a number N higher than or equal to 4 of measurements, for which measurements the targeting actions Vi correspond to an alignment of one and the same unknown targeting direction {right arrow over (x)} 0 with N known targeted exterior directions {right arrow over (y)} i , without roll adjustment, the vector family {{right arrow over (y)} i } being free; and
the second step of solving the system of dual harmonization equations: Ĝ·{circumflex over (K)} i ·{circumflex over (D)}·{right arrow over (x)} 0 ={right arrow over (y)} i for i varying from 1 to N comprises an eighth set of substeps consisting in:
in a seventeenth substep, initializing a first sequence of left matrices {Ĝ [s] }, [s] designating the integer rank of advancement through the sequence {Ĝ [s] }, Ĝ [0] being initialized set equal to I 3 , I 3 being the identity matrix; then
repeating an iterative eighteenth substep in which iteration [s+1] is passed to from iteration [s] by calculating the vector {right arrow over (x)} [s+1] then the matrix Ĝ [s+1] using the following equations:
x
→
[
s
+
1
]
=
∑
i
≥
1
(
D
^
T
·
K
^
i
T
·
G
^
[
s
]
T
·
y
→
i
)
∑
i
≥
1
(
D
^
T
·
K
^
i
T
·
G
^
[
s
]
T
·
y
→
i
)
G
^
[
s
+
1
]
=
π
(
∑
i
>
1
(
y
→
i
·
x
→
[
s
+
1
]
T
·
D
^
T
·
K
^
i
T
)
)
the sequence {{right arrow over (x)} [s] } being a second sequence of sight direction vectors, the sequences Ĝ [s] and {right arrow over (x)} [s] converging to Ĝ and {right arrow over (x)} 0 , respectively; and
in a stopping nineteenth substep stopping the iterative process carried out throughout the eighteenth substep when the limits Ĝ and optionally {right arrow over (x)} 0 are approximated with a sufficient precision defined by one or two preset threshold values.
13. The method for dual harmonization of a DDP posture-detecting subsystem integrated into a worn/borne head-up viewing system according to claim 1 , wherein
the worn/borne head-up viewing system is intended to be located on-board a carrier vehicle comprised in the set of all aircraft, aeroplanes, helicopters, motor vehicles and robots.
14. A worn/borne head-up viewing system located on-board a carrier vehicle and comprising:
a transparent worn/borne head-up viewing device D v ,
a reference device D ref having a reference coordinate system R ref , that is a coordinate system of the carrier vehicle or a local geographic coordinate system or a terrestrial coordinate system;
a DDP posture-detecting subsystem comprising:
a tracking solid first element S1 tightly attached to the transparent worn/borne head-up viewing device D v ; and
a fixed solid second element S2 tightly joined to the reference device D ref , wherein the DDP posture-detecting subsystem is configured to measure and determine a relative orientation {circumflex over (K)} of the tracking solid first element S1 with respect to the fixed solid second element S2,
a dual harmonization subsystem configured to harmonize the head-up viewing system and the DDP posture-detecting subsystem, the dual harmonization subsystem comprising a dual harmonization processor and an HMI interface for managing acquisitions of harmonization measurements,
the worn/borne head-up viewing system being wherein the dual harmonization subsystem and the DDP posture-detecting subsystem are configured to:
in a first step, carry out a series of a preset number N of measurements of relative orientations {circumflex over (K)} i , varying from 1 to N, of the tracking solid first element S1 with respect to the fixed solid second element S2 of the DDP posture-detecting subsystem, corresponding to different targeting actions Vi, i varying from 1 to N, in which measurements of one or more different preset elements of pilot/driver information displayed in the transparent worn/borne head-up viewing device D v are superposed or aligned with one or more corresponding landmarks of a real outside world; then
in a second step, and using a dual harmonization algorithm, conjointly calculate a relative orientation matrix {circumflex over (R)}(S1/v) of the tracking solid first element S1 of the DDP posture-detecting subsystem with respect to the transparent worn/borne head-up viewing device D v and/or a relative orientation matrix {circumflex over (R)}(ref/S2) of the exterior reference device D ref with respect to the fixed solid second element S2 of the DDP posture-detecting subsystem to respectively be a right-side bias rotation matrix {circumflex over (D)} and a left-side bias rotation matrix Ĝ, which are conjoint solutions of the system of dual harmonization equations: Û i =Ĝ·{circumflex over (K)} i ·{circumflex over (D)}, i varying from 1 to N.
15. The worn/borne head-up viewing system located on-board a carrier vehicle according to claim 14 , wherein
the minimum required number N of measurements depends on the number L of erroneous or inexploitable degrees of angular freedom of the rotation matrices {circumflex over (R)}(S1/v) and {circumflex over (R)}(ref/S2) of the head-up viewing system, said number L being an integer higher than or equal to 1 and lower than or equal to 6, and
the solution of the system of equations Û i =Ĝ·{circumflex over (K)} i ·{circumflex over (D)}, i varying from 1 to N, uses a rectification operator π(.) that converts any given matrix A into a 3×3 square rotation matrix π(A), which matrix π(A), of all the 3×3 rotation matrices, is the closest in the least-squares sense to all of the terms of the matrix π(A)−A, to determine the right-side rotation {circumflex over (D)} and the left-side rotation Ĝ.
16. A carrier vehicle, comprised in the set of all aircraft, aeroplanes, helicopters, motor vehicles and robots, and in which is installed a worn/borne head-up viewing system defined according to claim 14 .