Geomagnetic sensor and azimuth calculation method thereof

• US 20070124075A1
• Filed: 06/13/2006
• Published: 05/31/2007
• Est. Priority Date: 11/25/2005
• Status: Active Grant

• Current Assignee: Samsung Electronics Co. Ltd.
• Original Assignee: Samsung Electronics Co. Ltd.
• Inventors: Choi, Sang-on, Lee, Woo-Jong
• Granted Patent: US 7,809,505 B2
• Time in Patent Office: Days
• US Class Current: 701/220
• CPC Class Codes: G01C 17/30 Earth-inductor compasses
• CPC Class Codes: G01C 17/38 Testing, calibrating, or compensating of compasses

Abstract

A geomagnetic sensor with 3-axis acceleration sensors is provided. The geomagnetic sensor a geomagnetic measurement module including flux gates of X, Y and Z axes mutually crossing at right angles, a tilt measurement module including acceleration sensors of X, Y and Z axes mutually crossing at right angles, a tilt calculator primarily calculating a pitch angle and a roll angle using output values of each acceleration sensors of the X and Y axes, and performing second calculation by adjusting at least one of the primarily calculated pitch angle and roll angle using an output value of the acceleration sensor of the Z axis, and a controller calculating an azimuth using the readjusted pitch angle and roll angle and an output value of the geomagnetic measurement module. Accordingly, the pitch angle and roll angle are precisely measured to calculate the azimuth.

Claims

1. A geomagnetic sensor, comprising:

a geomagnetic measurement module including flux gates of X, Y and Z axes mutually crossing at right angles;

a tilt measurement module including acceleration sensors of X, Y and Z axes mutually crossing at right angles;

a tilt calculator primarily calculating a pitch angle and a roll angle using output values of each acceleration sensor of the X and Y axes, and performing second calculation by adjusting at least one of the primarily calculated pitch angle and roll angle using an output value of the acceleration sensor of the Z axis; and

a controller calculating an azimuth using the readjusted pitch angle and roll angle and an output value of the geomagnetic measurement module.

2. The geomagnetic sensor of claim 1, wherein the tilt measurement module normalizes the output values of each acceleration sensor of the X, Y and Z axes into values of a preset range using the following equations, and transmits the normalized values to the tilt calculator:

${\mathrm{AX}}_{\mathrm{norm}}=\frac{\left({\mathrm{AX}}_{\mathrm{raw}}-{\mathrm{AX}}_{\mathrm{offset}}\right)}{{\mathrm{AX}}_{\mathrm{Scale}}}$ ${\mathrm{AY}}_{\mathrm{norm}}=\frac{\left({\mathrm{AY}}_{\mathrm{raw}}-{\mathrm{AY}}_{\mathrm{offset}}\right)}{{\mathrm{AY}}_{\mathrm{Scale}}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}$ ${\mathrm{AZ}}_{\mathrm{norm}}=\frac{\left({\mathrm{AZ}}_{\mathrm{raw}}-{\mathrm{AZ}}_{\mathrm{offset}}\right)}{{\mathrm{AZ}}_{\mathrm{Scale}}}$

where AX_norm, AY_norm and AZ_norm are the normalized output values of each acceleration sensor of the X, Y and Z axes respectively, AX_raw, AY_raw and AZ_raw are the real output values of each acceleration sensor of the X, Y and Z axes respectively, AX_offset, AY_offset and AZ_offset are the preset offset values of each acceleration sensor of the X, Y and Z axes respectively, and AX_scale, AY_scale and AZ_scale are the preset scale values of each acceleration sensor of the X, Y and Z axes respectively.

3. The geomagnetic sensor of claim 2, wherein the tilt calculator primarily calculates the pitch angle and roll angle using the following equations:

$\begin{array}{c}{\mathrm{\theta <br><br>}}_X={\sin }^{-1}<br><br>\left({\mathrm{AX}}_{\mathrm{norm}}\right)\\ {\mathrm{\varphi <br><br>}}_Y={\sin }^{-1}<br><br>\left({\mathrm{AY}}_{\mathrm{norm}}/\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\theta <br><br>}}_X\right)\\ {\mathrm{\theta <br><br>}}_Z={\sin }^{-1}<br><br>\left({\mathrm{AZ}}_{\mathrm{mod}}\right)<br><br>\left\{\mathrm{wherein},\text{\hspace{1em}<br><br>}<br><br>{\mathrm{AZ}}_{\mathrm{mod}}=\frac{{\mathrm{AZ}}_{\mathrm{norm}}}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\varphi <br><br>}}_Y}\right\}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}\\ {\mathrm{\varphi <br><br>}}_Z={\sin }^{-1}<br><br>\left({\mathrm{AZ}}_{\mathrm{mod}}/\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\theta <br><br>}}_X\right)<br><br>\left\{\mathrm{wherein},\text{\hspace{1em}<br><br>}<br><br>{\mathrm{AZ}}_{\mathrm{mod}}=\frac{{\mathrm{AZ}}_{\mathrm{norm}}}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\theta <br><br>}}_X}\right\}\end{array}$

where θ

_X is the pitch angle calculated using the acceleration sensor of the X axis, Φ

_Y is the roll angle calculated using the acceleration sensor of the Y axis, θ

_Z is the pitch angle calculated using the acceleration sensor of the Z axis, and Φ

_Z is the roll angle calculated using the acceleration sensor of the Z axis.

4. The geomagnetic sensor of claim 3, wherein the tilt calculator performs the second calculation in a manner that when the θ

_X is between 0° and

45°

, if the θ

_Z is 0°

or more, the θ

_X becomes the pitch angle, or if the θ

_Z is under 0°

, 180°

−

θ

_X becomes the pitch angle,

when the θ

_X is 45°

or more, if Φ

_Y is under 45°

, 90°

−

θ

_Z becomes the pitch angle, or if the Φ

_Y is 45°

or more, the θ

_X becomes the pitch angle,

when the θ

_X is between −

45° and

0°

, if the θ

_Z is 0°

or more, the θ

_X becomes the pitch angle, or if the θ

_Z is under 0°

, −

180°

−

θ

_X becomes the pitch angle, or

when the θ

_X is under −

45°

, if the Φ

_Y is under 45°

, θ

_Z−

90°

becomes the pitch angle, or if the Φ

_Y is 45°

or more, the θ

_X becomes the pitch angle.

5. The geomagnetic sensor of claim 4, wherein the tilt calculator performs the second calculation in a manner that when the Φ

_Y is between 0° and

45°

, if the Φ

_Y is 0°

or more, the Φ

_Y becomes the roll angle, or if the Φ

_Z is under 0°

, 180°

−

Φ

_Y becomes the roll angle,

when the Φ

_Y is 45°

or more, if the Φ

_X is under 45°

, 90°

−

Φ

_Z becomes the roll angle, or if the θ

_X is 45°

or more, the Φ

_X becomes the roll angle,

when the Φ

_Y is between −

45° and

0°

, if the Φ

_Z is 0°

or more, the Φ

_Y becomes the roll angle, or if the Φ

_Z is under 0°

, −

180°

−

Φ

_Z becomes the roll angle, or

when the Φ

_Y is under −

45°

, if the θ

_X is under 45°

, Φ

_Z−

90°

becomes the roll angle, or if the θ

_X is 45°

or more, the Φ

_Y becomes the roll angle.

6. The geomagnetic sensor of claim 1, wherein the geomagnetic measurement module normalizes the output values of each flux gate of the X, Y and Z axes into values of a preset range using the following equations, and provides the normalized values to the controller:

$X_{\mathrm{norm}}=\frac{\left(X_{\mathrm{raw}}-X_{\mathrm{offset}}\right)}{X_{\mathrm{Scale}}}$ $Y_{\mathrm{norm}}=\frac{\left(Y_{\mathrm{raw}}-Y_{\mathrm{offset}}\right)}{Y_{\mathrm{Scale}}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}$ $Z_{\mathrm{norm}}=\frac{\left(Z_{\mathrm{raw}}-Z_{\mathrm{offset}}\right)}{Z_{\mathrm{Scale}}}$

where X_norm, Y_norm and Z_norm are the normalized output values of each flux gate of the X, Y and Z axes respectively, X_raw, Y_raw and Z_raw are the real output values of each flux gate of the X, Y and Z axes respectively, X_offset, Y_offset and Z_offset are the preset offset values of each flux gate of the X, Y and Z axes respectively, and X_scale, Y_scale and Z_Scale are the preset scale values of each flux gate of the X, Y and Z axes respectively.

7. The geomagnetic sensor of claim 6, wherein the controller calculates the azimuth by applying the normalized output values of each flux gate of the X, Y and Z and the readjusted pitch angle and roll angle to the following equation:

$\mathrm{\psi <br><br>}={\tan }^{-1}<br><br>\left(\frac{Y_{\mathrm{norm}}*\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>}-Z_{\mathrm{norm}}*\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>}}{\begin{array}{c}{X}_{\mathrm{norm}}*\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\theta <br><br>}-Y_{\mathrm{norm}}*\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\theta <br><br>}*\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>}-\\ Z_{\mathrm{norm}}*\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\theta <br><br>}*\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>}\end{array}}\right),$

where X_norm, Y_norm and Z_norm are the normalized output values of each flux gate of the X, Y and Z axes respectively, θ

is the pitch angle, and Φ

is the roll angle.

8. A method of calculating an azimuth, comprising:

(a) calculating output values of flux gates of X, Y and Z axes using the flux gates of the X, Y and Z axes mutually crossing at right angles;

(b) primarily calculating a pitch angle and a roll angle using acceleration sensors of X, Y and Z axes mutually crossing at right angles;

(c) adjusting at least one of the primarily calculated pitch angle and roll angle using an output value of the acceleration sensor of the Z axis; and

(d) calculating the azimuth using the readjusted pitch angle and roll angle and an output value of a geomagnetic measurement module.

9. The method of claim 8, wherein in the step of (b), the output values of each acceleration sensor of the X, Y and Z axes are normalized into values of a preset range using the following equations:

${\mathrm{AX}}_{\mathrm{norm}}=\frac{\left({\mathrm{AX}}_{\mathrm{raw}}-{\mathrm{AX}}_{\mathrm{offset}}\right)}{{\mathrm{AX}}_{\mathrm{Scale}}}$ ${\mathrm{AY}}_{\mathrm{norm}}=\frac{\left({\mathrm{AY}}_{\mathrm{raw}}-{\mathrm{AY}}_{\mathrm{offset}}\right)}{{\mathrm{AY}}_{\mathrm{Scale}}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}$ ${\mathrm{AZ}}_{\mathrm{norm}}=\frac{\left({\mathrm{AZ}}_{\mathrm{raw}}-{\mathrm{AZ}}_{\mathrm{offset}}\right)}{{\mathrm{AZ}}_{\mathrm{Scale}}}$

where AX_norm, AY_norm and AZ_norm are the normalized output values of each acceleration sensor of the X, Y and Z axes respectively, AX_raw, AY_raw and AZ_raw are the real output values of each acceleration sensor of the X, Y and Z axes respectively, AX_offset, AY_offset and AZ_offset are the preset offset values of each acceleration sensor of the X, Y and Z axes respectively, and AX_scale, AY_scale and AZ_scale are the preset scale values of each acceleration sensor of the X, Y and Z axes respectively.

10. The method of claim 9, wherein in the step of (b), the pitch angle and roll angle are primarily calculated using the following equations:

$\begin{array}{c}{\mathrm{\theta <br><br>}}_X={\sin }^{-1}<br><br>\left({\mathrm{AX}}_{\mathrm{norm}}\right)\\ {\mathrm{\varphi <br><br>}}_Y={\sin }^{-1}<br><br>\left({\mathrm{AY}}_{\mathrm{norm}}/\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\theta <br><br>}}_X\right)\\ {\mathrm{\theta <br><br>}}_Z={\sin }^{-1}<br><br>\left({\mathrm{AZ}}_{\mathrm{mod}}\right)<br><br>\left\{\mathrm{wherein},{\mathrm{AZ}}_{\mathrm{mod}}=\frac{{\mathrm{AZ}}_{\mathrm{norm}}}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\varphi <br><br>}}_{\text{\hspace{1em}<br><br>}<br><br>Y}}\right\}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}\\ {\mathrm{\varphi <br><br>}}_Z={\sin }^{-1}<br><br>\left({\mathrm{AZ}}_{\mathrm{mod}}/\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\theta <br><br>}}_X\right)<br><br>\left\{\mathrm{wherein},{\mathrm{AZ}}_{\mathrm{mod}}=\frac{{\mathrm{AZ}}_{\mathrm{norm}}}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\theta <br><br>}}_X}\right\}\end{array}$

where θ

_X is the pitch angle calculated using the acceleration sensor of the X axis, Φ

_Y is the roll angle calculated using the acceleration sensor of the Y axis, θ

_Z is the pitch angle calculated using the acceleration sensor of the Z axis, and Φ

_Z is the roll angle calculated using the acceleration sensor of the Z axis.

11. The method of claim 10, wherein in the step of (c), the pitch angle is readjusted in a manner that when the θ

_X is between 0° and

45°

, if the θ

_Z is 0°

or more, the θ

_X becomes the pitch angle, or if the θ

_Z is under 0°

, 180°

−

θ

_X becomes the pitch angle,

when the θ

_X is 45°

or more, if Φ

_Y is under 45°

, 90°

−

Φ

_Z becomes the pitch angle, or if the Φ

_Y is 45°

or more, the θ

_X becomes the pitch angle,

when the θ

_X is between −

45° and

0°

, if the θ

_Z is 0°

or more, the θ

_X becomes the pitch angle, or if the θ

_Z is under 0°

, −

180°

−

θ

_X becomes the pitch angle, or

when the θ

_X is under 45°

, if the Φ

_Y is under −

45°

, θ

_Z−

90°

becomes the pitch angle, or if the Φ

_Y is 45°

or more, the θ

_X becomes the pitch angle.

12. The method of claim 11, wherein in the step of (c), the roll angle is readjusted in a manner that when the Φ

_Y is between 0° and

45°

, if the Φ

_Z is 0°

or more, the Φ

_Z becomes the roll angle, or if the Φ

_Z is under 0°

, 180°

−

Φ

_Y becomes the roll angle,

when the Φ

_Y is 45°

or more, if the Φ

_X is under 45°

, 90°

−

Φ

_Z becomes the roll angle, or if the θ

_X is 45°

or more, the Φ

_Y becomes the roll angle,

when the Φ

_Y is between −

45° and

0°

, if the Φ

_Z is 0°

or more, the Φ

_Y becomes the roll angle, or if the Φ

_Z is under 0°

, −

180°

−

Φ

_Y becomes the roll angle, or

when the Φ

_Y is under −

45°

, if the θ

_X is under 45°

, Φ

_Z−

90°

becomes the roll angle, or if the θ

_X is 45°

or more, the Φ

_Y becomes the roll angle.

13. The method of claim 9, wherein in the step of (a), the output values of each flux gate of the X, Y and Z axes are normalized into values of a preset range using the following equations:

$\begin{array}{c}{X}_{\mathrm{norm}}=\frac{\left(X_{\mathrm{raw}}-X_{\mathrm{offset}}\right)}{X_{\mathrm{Scale}}}\\ Y_{\mathrm{norm}}=\frac{\left(Y_{\mathrm{raw}}-Y_{\mathrm{offset}}\right)}{Y_{\mathrm{Scale}}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}\\ Z_{\mathrm{norm}}=\frac{\left(Z_{\mathrm{raw}}-Z_{\mathrm{offset}}\right)}{Z_{\mathrm{Scale}}}\end{array}$

where X_norm, Y_norm and Z_norm are the normalized output values of each flux gate of the X, Y and Z axes respectively, X_raw, Y_raw and Z_raw are the real output values of each flux gate of the X, Y and Z axes respectively, X_offset, Y_offset and Z_offset are the preset offset values of each flux gate of the X, Y and Z axes respectively, and X_Scale, Y_Scale and Z_Scale are the preset scale values of each flux gate of the X, Y and Z axes respectively.

14. The method of claim 13, wherein in the step of (d), the azimuth is calculated by applying the normalized output values of each flux gate of the X, Y and Z and the readjusted pitch angle and roll angle to the following equation:

$\mathrm{\psi <br><br>}={\tan }^{-1}<br><br>\left(\frac{Y_{\mathrm{norm}}*\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>}-Z_{\mathrm{norm}}*\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>}}{X_{\mathrm{norm}}*\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\theta <br><br>}-Y_{\mathrm{norm}<br><br>\text{\hspace{1em}<br><br>}}*\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\theta <br><br>}*\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>}-Z_{\mathrm{norm}}*\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\theta <br><br>}*\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>}}\right),$

where X_norm, Y_norm and Z_norm are the normalized output values of each flux gate of the X, Y and Z axes respectively, θ

is the pitch angle, and Φ

is the roll angle.

15. At least one computer readable medium storing instructions that control at least one processor to perform a method of calculating an azimuth, comprising:

(a) calculating output values of flux gates of X, Y and Z axes using the flux gates of the X, Y and Z axes mutually crossing at right angles;

(b) primarily calculating a pitch angle and a roll angle using acceleration sensors of X, Y and Z axes mutually crossing at right angles;

(c) adjusting at least one of the primarily calculated pitch angle and roll angle using an output value of the acceleration sensor of the Z axis; and

(d) calculating the azimuth using the readjusted pitch angle and roll angle and an output value of a geomagnetic measurement module.

16. At least one computer readable medium as recited in claim 15, wherein in the step of (b), the output values of each acceleration sensor of the X, Y and Z axes are normalized into values of a preset range using the following equations:

$\begin{array}{c}{\mathrm{AX}}_{\mathrm{norm}}=\frac{\left({\mathrm{AX}}_{\mathrm{raw}}-{\mathrm{AX}}_{\mathrm{offset}}\right)}{{\mathrm{AX}}_{\mathrm{Scale}}}\\ {\mathrm{AY}}_{\mathrm{norm}}=\frac{\left({\mathrm{AY}}_{\mathrm{raw}}-{\mathrm{AY}}_{\mathrm{offset}}\right)}{{\mathrm{AY}}_{\mathrm{Scale}}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}\\ {\mathrm{AZ}}_{\mathrm{norm}}=\frac{\left({\mathrm{AZ}}_{\mathrm{raw}}-{\mathrm{AZ}}_{\mathrm{offset}}\right)}{{\mathrm{AZ}}_{\mathrm{Scale}}}\end{array}$

where AX_norm, AY_norm and AZ_norm are the normalized output values of each acceleration sensor of the X, Y and Z axes respectively, AX_raw, AY_raw and AZ_raw are the real output values of each acceleration sensor of the X, Y and Z axes respectively, AX_offset, AY_offset and AZ_offset are the preset offset values of each acceleration sensor of the X, Y and Z axes respectively, and AX_scale, AY_scale and AZ_scale are the preset scale values of each acceleration sensor of the X, Y and Z axes respectively.

17. At least one computer readable medium as recited in claim 16, wherein in the step of (b), the pitch angle and roll angle are primarily calculated using the following equations:

$\begin{array}{c}{\mathrm{\theta <br><br>}}_X={\sin }^{-1}<br><br>\left({\mathrm{AX}}_{\mathrm{norm}}\right)\\ {\mathrm{\varphi <br><br>}}_Y={\sin }^{-1}<br><br>\left({\mathrm{AY}}_{\mathrm{norm}}/\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\theta <br><br>}}_X\right)\\ {\mathrm{\theta <br><br>}}_Z={\sin }^{-1}<br><br>\left({\mathrm{AZ}}_{\mathrm{mod}}\right)<br><br>\left\{\mathrm{wherein},{\mathrm{AZ}}_{\mathrm{mod}}=\frac{{\mathrm{AZ}}_{\mathrm{norm}}}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\varphi <br><br>}}_{\text{\hspace{1em}<br><br>}<br><br>Y}}\right\}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}\\ {\mathrm{\varphi <br><br>}}_Z={\sin }^{-1}<br><br>\left({\mathrm{AZ}}_{\mathrm{mod}}/\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\theta <br><br>}}_X\right)<br><br>\left\{\mathrm{wherein},{\mathrm{AZ}}_{\mathrm{mod}}=\frac{{\mathrm{AZ}}_{\mathrm{norm}}}{\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\theta <br><br>}}_X}\right\}\end{array}$

where θ

_X is the pitch angle calculated using the acceleration sensor of the X axis, Φ

_Y is the roll angle calculated using the acceleration sensor of the Y axis, θ

_Z is the pitch angle calculated using the acceleration sensor of the Z axis, and Φ

_Z is the roll angle calculated using the acceleration sensor of the Z axis.

18. At least one computer readable medium as recited in claim 17, wherein in the step of (c), the pitch angle is readjusted in a manner that when the θ

_X is between 0° and

45°

, if the θ

_Z is 0°

or more, the θ

_X becomes the pitch angle, or if the θ

_Z is under 0°

, 180°

−

θ

_X becomes the pitch angle,

when the θ

_X is 45°

or more, if Φ

_Y is under 45°

, 90°

−

θ

_Z becomes the pitch angle, or if the Φ

_Y is 45°

or more, the θ

_X becomes the pitch angle,

when the θ

_X is between −

45° and

0°

, if the θ

_Z is 0°

or more, the θ

_X becomes the pitch angle, or if the θ

_Z is under 0°

, −

180°

−

θ

_X becomes the pitch angle, or

when the θ

_X is under −

45°

, if the Φ

_Y is under 45°

, θ

_Z−

90°

becomes the pitch angle, or if the Φ

_Y is 45°

or more, the θ

_X becomes the pitch angle.

19. At least one computer readable medium as recited in claim 18, wherein in the step of (c), the roll angle is readjusted in a manner that when the Φ

_Y is between 0° and

,45°

, if the Φ

_Z is 0°

or more, the Φ

_Z becomes the roll angle, or if the Φ

_Z is under 0°

, 180 °

−

Φ

_Y becomes the roll angle,

when the Φ

_Y is 45°

or more, if the Φ

_X is under 45°

, 90°

−

Φ

_Z becomes the roll angle, or if the θ

_X is 45°

or more, the Φ

_Y becomes the roll angle,

when the Φ

_Y is between −

45° and

0°

, if the Φ

_Z is 0°

or more, the Φ

_Y becomes the roll angle, or if the Φ

_Z is under 0°

, −

180°

−

Φ

_Y becomes the roll angle, or

when the Φ

_Y is under −

45°

, if the θ

_X is under 45°

, Φ

_Z−

90°

becomes the roll angle, or if the θ

_X is 45°

or more, the Φ

_Y becomes the roll angle.

20. At least one computer readable medium as recited in 16, wherein in the step of (a), the output values of each flux gate of the X, Y and Z axes are normalized into values of a preset range using the following equations:

$\begin{array}{c}{X}_{\mathrm{norm}}=\frac{\left(X_{\mathrm{raw}}-X_{\mathrm{offset}}\right)}{X_{\mathrm{Scale}}}\\ Y_{\mathrm{norm}}=\frac{\left(Y_{\mathrm{raw}}-Y_{\mathrm{offset}}\right)}{Y_{\mathrm{Scale}}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}\\ Z_{\mathrm{norm}}=\frac{\left(Z_{\mathrm{raw}}-Z_{\mathrm{offset}}\right)}{Z_{\mathrm{Scale}}}\end{array}$

where X_norm, Y_norm and Z_norm are the normalized output values of each flux gate of the X, Y and Z axes respectively, X_raw, Y_raw and Z_raw are the real output values of each flux gate of the X, Y and Z axes respectively, X_offset, Y_offset and Z_offset are the preset offset values of each flux gate of the X, Y and Z axes respectively, and X_Scale, Y_Scale and Z_Scale are the preset scale values of each flux gate of the X, Y and Z axes respectively.

21. At least one computer readable medium as recited in 20, wherein in the step of (d), the azimuth is calculated by applying the normalized output values of each flux gate of the X, Y and Z and the readjusted pitch angle and roll angle to the following equation:

$\mathrm{\psi <br><br>}={\tan }^{-1}<br><br>\left(\frac{Y_{\mathrm{norm}}*\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>}-Z_{\mathrm{norm}}*\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>}}{X_{\mathrm{norm}}*\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\theta <br><br>}-Y_{\mathrm{norm}<br><br>\text{\hspace{1em}<br><br>}}*\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\theta <br><br>}*\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>}-Z_{\mathrm{norm}}*\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\theta <br><br>}*\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>}}\right),$

where X_norm, Y_norm and Z_norm are the normalized output values of each flux gate of the X, Y and Z axes respectively, θ

is the pitch angle, and Φ

is the roll angle.