Method for estimating the movement of an object moving in a magnetic field

1. A method comprising the steps of:

(a) acquiring, by a magnetic measurement unit integral with an object moving in an ambient magnetic field, at least one component:

of the magnetic field and/or

of at least one i-th derivative of the magnetic field, with i≥1, at the magnetic measurement unit;

(b) estimating, by a data processing unit, a movement of said object, wherein at least one component of said movement is estimated using at least one component of the equation ∇ {dot over (n)} B=f n (Ω)·∇ n B+g n (∇ n+1 B)·V, with n+1≥i and n≥1, and n≥1, where ∇ n B is an n-th derivative of the magnetic field, Ω the instantaneous angular velocity, V the instantaneous linear velocity, and f n and g n predetermined functions;

(c) adjusting, by a driving unit of the object, at least one of a speed or a direction of movement of the object in response to the estimated movement.

2. The method according to claim 1 , wherein at least (n+2)(n+4) components of the magnetic field and/or at least one i-th derivative of the magnetic field are acquired at step (a), and 3 n+1 components of the equation ∇ {dot over (n)} B=f n (Ω)·∇ n B+g n (∇ n+1 B)·V are used at step (b).

3. The method according to claim 1 , wherein at least one relationship between components of the equation ∇ {dot over (n)} B=f n (Ω)·∇ n B+g n (∇ n+1 B)·V is determined at step (b) by application of the local version of at least one Maxwell equation to the components of the n-th derivative of the magnetic field ∇nB.

4. The method according to claim 1 , wherein at least one component of at least one supplementary equation ∇ {dot over (n)} B=f k (Ω)·∇ k B+g n (∇ k+1 B)·V with k Σ, is also used at step (b).

5. The method according to claim 4 , wherein k=0, f 0 =skew, g 0 =id such that the supplementary equation is {dot over (B)}=−Ω×B+∇B·V.

6. The method according to claim 1 , wherein step (a) further includes acquiring, by an inertial measurement sensor integral with said object, at least one component of the angular velocity Ω.

7. A method comprising the steps of:

(a) acquiring, by a magnetic measurement unit integral with an object moving in an ambient magnetic field, at least one component:

of the magnetic field and/or

of at least one i-th derivative of the magnetic field, with i≥1, at the magnetic measurement unit;

(b) estimating, by a data processing unit, a movement of said object, wherein at least one component of said movement is estimated using at least one component of the equation ∇ {dot over (n)} B=f n (Ω)·∇ n B+g n (∇ n+1 B)·V, with n+1≥i and n≥1 where ∇ n B is an n-th derivative of the magnetic field, Ω the instantaneous angular velocity, V the instantaneous linear velocity, and f n and g n predetermined functions;

(c) capturing an image of a scene with a camera of the object,

(d) displaying the image together with overlapping visual information, and

(e) adjusting a position of the overlapping visual information in the displayed image in response to the estimated movement.

8. The method according to claim 7 , wherein at least (n+2)(n+4) components of the magnetic field and/or at least one i-th derivative of the magnetic field are acquired at step (a), and 3 n+1 components of the equation ∇ {dot over (n)} B=f n (Ω)·∇ n B+g n (∇ n+1 B)·V are used at step (b).

9. The method according to claim 7 , wherein at least one relationship between components of the equation ∇ {dot over (n)} B=f n (Ω)·∇ n B+g n (∇ n+1 B)·V is determined at step (b) by application of the local version of at least one Maxwell equation to the components of the n-th derivative of the magnetic field ∇ n B.

10. The method according to claim 7 , wherein at least one component of at least one supplementary equation ∇ {dot over (k)} B=f k (Ω)·∇ k B+g n (∇ k+1 B)·V with k∈, is also used at step (b).

11. The method according to claim 7 , wherein step (a) further includes acquiring, by an inertial measurement sensor integral with said object, at least one component of the angular velocity Ω.

12. A method comprising the steps of:

(a) acquiring, by a magnetic measurement unit integral with an object moving in an ambient magnetic field, at least one component:

of the magnetic field and/or

of at least one i-th derivative of the magnetic field, with i≥1, at the magnetic measurement unit;

(b) estimating, by a data processing unit, a movement of said object, wherein at least one component of said movement is estimated using at least one component of the equation ∇ {dot over (n)} B=f n (Ω)·∇ n B+g n (∇ n+1 B)·V, with n+1≥i and n≥1, where ∇ n B is an n-th derivative of the magnetic field, Ω the instantaneous angular velocity, V the instantaneous linear velocity, and f n and g n predetermined functions;

(c) displaying a virtual scene on a display of the object, and

(d) adjusting a position of an array of rendered pixels relative to the virtual scene in response to the estimated movement.

13. The method according to claim 12 , wherein at least (n+2)(n+4) components of the magnetic field and/or at least one i-th derivative of the magnetic field are acquired at step (a), and 3 n+1 components of the equation ∇ {dot over (n)} B=f n (Ω)·∇ n B+g n (∇ n+1 B)·V are used at step (b).

14. The method according to claim 12 , wherein at least one relationship between components of the equation ∇ {dot over (n)} B=f n (Ω)·∇ n B+g n (∇ n+1 B)·V is determined at step (b) by application of the local version of at least one Maxwell equation to the components of the n-th derivative of the magnetic field ∇ n B.

15. The method according to claim 12 , wherein at least one component of at least one supplementary equation ∇ {dot over (k)} B=f k (Ω)·∇ k B+g n (∇ k+1 B)·V, with k∈, is also used at step (b).

16. The method according to claim 12 , wherein step (a) further includes acquiring, by an inertial measurement sensor integral with said object, at least one component of the angular velocity Ω.

17. A method comprising the steps of:

(a) acquiring, by a magnetic measurement unit integral with an object moving in an ambient magnetic field, at least one component:

of the magnetic field and/or

of at least one i-th derivative of the magnetic field, with i≥1, at the magnetic measurement unit;

(b) estimating, by a data processing unit, a movement of said object, wherein at least one component of said movement is estimated using at least one component of the equation ∇ {dot over (n)} B=f n (Ω)·∇ n B+g n (∇ n+1 B)·V, with n+1≥i and n≥1, where ∇ n B is an n-th derivative of the magnetic field, Ω the instantaneous angular velocity, V the instantaneous linear velocity, and f n and g n predetermined functions;

(c) displaying visual information on a transparent display surface of the object, and

(d) adjusting a position of the visual information on the transparent display surface in response to the estimated movement.

18. The method according to claim 17 , wherein at least (n+2)(n+4) components of the magnetic field and/or at least one i-th derivative of the magnetic field are acquired at step (a), and 3 n+1 components of the equation ∇ {dot over (n)} B=f n (Ω)·∇ n B+g n (∇ n+1 B)·V are used at step (b).

19. The method according to claim 17 , wherein at least one relationship between components of the equation ∇ {dot over (n)} B=f n (Ω)·∇ n B+g n (∇ n+1 B)·V is determined at step (b) by application of the local version of at least one Maxwell equation to the components of the n-th derivative of the magnetic field ∇ n B.

20. The method according to claim 17 , wherein at least one component of at least one supplementary equation ∇ {dot over (k)} B=f k (Ω)·∇ k B+g n (∇ k+1 B)·V, with k∈, is also used at step (b).