Method and apparatus for measuring magnetic offset of geomagnetic sensor and portable electronic apparatus

• US 7,210,236 B2
• Filed: 06/10/2005
• Issued: 05/01/2007
• Est. Priority Date: 06/11/2004
• Status: Expired due to Fees

• Current Assignee: Yamaha Corporation
• Original Assignee: Yamaha Corporation
• Inventors: Sato, Hideki, Nihashi, Satoshi
• Primary Examiner(s): GUADALUPE, YARITZA
• Application Number:
  US11/150,643
• Publication Number:
  US 20050283988A1
• Time in Patent Office: 690 Days
• Field of Search: 333/52, 333/55.R, 33356-357, 333/16, 701/220, 702 92- 94, 455/575.1
• US Class Current: 33/356
• CPC Class Codes: G01C 17/38 Testing, calibrating, or compensating of compasses
• CPC Class Codes: G01D 3/0365 the undesired influence being measured using a separate sensor, which produces an influence related signal

Abstract

A method is designed for measuring a magnetic offset of a geomagnetic sensor equipped in a portable information terminal apparatus having a storage. The geomagnetic sensor has a magnetic sensitivity to a geomagnetic field and is affected by magnetization to cause the magnetic offset. In the method, an output of the geomagnetic sensor is measured to successively provide measurement data of the geomagnetic field from the output of the geomagnetic sensor. The measurement data is stored in the storage. The measurement data is read out from the storage when a number of the measurement data stored in the storage reaches a predetermined number, and an offset value of the magnetic offset is estimated based on the predetermined number of the measurement data read out from the storage.

Claims

1. A method of measuring a magnetic offset of a geomagnetic sensor equipped in a portable information terminal apparatus, the geomagnetic sensor having a magnetic sensitivity to a geomagnetic field in a plurality of axes of a coordinate system, and being affected by magnetization to cause the magnetic offset, the method comprising:

a data measurement step of measuring an output of the geomagnetic sensor and acquiring a plurality of measurement data of the geomagnetic field, each measurement data being represented by a data point in the coordinate system;

an offset estimation step of estimating an offset value of the magnetic offset of the geomagnetic sensor from the plurality of the measurement data of the geomagnetic field, the offset value being represented by an offset point in the coordinate system;

a mean value calculation step of calculating distances between the offset point corresponding to the offset value and a plurality of the data points corresponding to the plurality of the measurement data used for estimating of the offset value, and further calculating a mean value of the calculated distances between the offset point and the plurality of the data points;

a standard deviation calculation step of calculating a standard deviation of the calculated distances with respect to the calculated mean value of the distances; and

a validity judgment step of judging validity of the estimated offset value on the basis of the calculated standard deviation.

2. The method according to claim 1, wherein the portable information terminal apparatus has a first storage and a second storage, and the data measurement step successively acquires the measurement data from the geomagnetic sensor, the method further comprising:

a data storing step of storing the measurement data successively acquired by the data measurement step into the first storage, so that the offset estimation step reads out the plurality of the measurement data from the first storage and estimates the offset value of the magnetic offset from the plurality of the measurement data read out from the first storage; and

an offset storing step of storing the estimated offset data in the second storage when the validity of the estimated offset value is confirmed by the validity judgment step.

3. The method according to claim 1, wherein the portable information terminal apparatus has a first storage for storing the measurement data and a second storage for storing the offset value, and the data measurement step successively acquires the measurement data including previous measurement data and current measurement data, the method further comprising:

a distance calculation step of calculating a distance between a current data point corresponding to the current measurement data and a previous data point corresponding to the previous measurement data which has been stored in the first storage;

a determining step of determining whether the calculated distance between the current data point and the previous data point is greater than a predetermined distance;

a data storing step of storing the current measurement data in the first storage when the calculated distance is determined greater than the predetermined distance, thereby accumulating the measurement data in the first storage by repeating a routine of the distance calculation step, the determining step and the data storing step, so that the offset estimation step reads out the plurality of the measurement data from the first storage when a number of the measurement data stored in the first storage reaches a predetermined number and estimates the offset value of the magnetic offset from the plurality of the measurement data read out from the first storage; and

an offset storing step of storing the estimated offset data in the second storage when the validity of the estimated offset value is confirmed by the validity judgment step.

4. The method according to claim 1, further comprising a notifying step of notifying a user when the estimated offset value is judged not to be valid by the validity judgment step.

5. The method according to claim 1, further comprising a comparing step of comparing with one anther the plurality of the measurement data each of which is used for the estimating of the offset value and each of which is denoted by a set of coordinate components corresponding to a set of the axes of the coordinate system, such that the comparing is done in terms of the coordinate components of the measurement data for each axis to obtain a difference between a maximum value and a minimum value of the coordinate components for each axis, wherein the validity judgment step judges the validity of the estimated offset value on the basis of the obtained difference between the maximum value and the minimum value of the coordinate components for each axis in addition to the calculated standard deviation.

6. The method according to claim 1, wherein the data measurement step measures the output of the geomagnetic sensor which is selected from a group consisting of a Giant Magnetoresistive device, a Tunneling Magnetoresistive device, a Magnetoresistive device, a Hall device, a Magneto Impedance device and a flux gate sensor.

7. The method according to claim 1, wherein the data measurement step measures the output of the geomagnetic sensor having a magnetic sensitivity either in two axes of a two dimensional coordinate system or three axes of a three dimensional coordinate system, such that each measurement data is represented by a data point in either of the two dimensional coordinate system or the three dimensional coordinate system.

8. A method of measuring a magnetic offset of a geomagnetic sensor equipped in a portable information terminal apparatus having a storage, the geomagnetic sensor having a magnetic sensitivity to a geomagnetic field in a plurality of axes of a coordinate system and being affected by magnetization to cause the magnetic offset, the method comprising:

a data measurement step of measuring an output of the geomagnetic sensor, and successively providing a plurality of measurement data of the geomagnetic field including previous measurement data and current measurement data, each measurement data being represented by a data point in the coordinate system;

a distance determining step of calculating a distance between a current data point corresponding to the current measurement data and a previous data point corresponding to the previous measurement data which has been stored in the storage, and determining whether the calculated distance between the current data point and the previous data point is greater than a predetermined distance;

a data storing step of storing the current measurement data in the storage when the calculated distance is determined greater than the predetermined distance, thereby accumulating the measurement data in the storage; and

an offset estimation step of reading a plurality of the measurement data from the storage and estimating an offset value of the magnetic offset from the plurality of the measurement data read out from the storage.

9. A method of measuring a magnetic offset of a geomagnetic sensor equipped in a portable information terminal apparatus having a storage and an inclination sensor, the geomagnetic sensor having a magnetic sensitivity to a geomagnetic field in two axes of a two dimensional coordinate system and being affected by magnetization to cause the magnetic offset, the inclination sensor sensing an inclination angle of the portable information terminal apparatus, the method comprising:

a data measurement step of measuring an output of the geomagnetic sensor, and successively providing a plurality of the measurement data of the geomagnetic field including preceding measurement data and succeeding measurement data;

an inclination measurement step of measuring an output of the inclination sensor and successively providing a plurality of angle data which represent the inclination angles of the portable information terminal apparatus and which include preceding angle data measured concurrently with the preceding measurement data and succeeding angle data measured concurrently with the succeeding measurement data;

a data storing step of storing the succeeding measurement data in the storage when a difference between a inclination angle of the portable information terminal apparatus denoted by the succeeding angle data and another inclination angle of the portable information terminal apparatus denoted by the preceding angle data is greater than a predetermined difference, thereby accumulating the measurement data in the storage by repeating a routine of the data measurement step, the inclination measurement step and the data storing step; and

an offset estimation step of reading out a plurality of the accumulated measurement data from the storage and estimating the offset value of the magnetic offset from the plurality of the accumulated measurement data read out from the storage.

10. The method according to claim 9, wherein the offset estimation step reads out the plurality of the accumulated measurement data from the storage to estimate the offset value when a number of the measurement data accumulated in the storage reaches a predetermined number, the method further comprising:

a mean value calculation step of calculating distances between an offset point defined in the two dimensional coordinate system in correspondence to the estimated offset value and a plurality of data points defined in the two dimensional coordinate system in correspondence to the plurality of the measurement data used for the estimating of the offset value, and further calculating a mean value of the calculated distances between the offset point and the plurality of the data points;

a standard deviation calculation step of calculating a standard deviation of the calculated distances with respect to the calculated mean value of the distances;

a validity judgment step of judging validity of the estimated offset value on the basis of the calculated standard deviation; and

an offset storing step of storing the estimated offset data when the validity of the estimated offset value is confirmed by the validity judgment step.

11. A method of measuring a magnetic offset of a geomagnetic sensor equipped in a portable information terminal apparatus having a storage, the geomagnetic sensor having a magnetic sensitivity to a geomagnetic field and being affected by magnetization to cause the magnetic offset, the method comprising:

a data measurement step of measuring an output of the geomagnetic sensor and successively providing measurement data of the geomagnetic field from the output of the geomagnetic sensor;

a data storing step of storing the measurement data into the storage; and

an offset estimation step of reading out the measurement data from the storage when a number of the measurement data stored in the storage reaches a predetermined number, and estimating an offset value of the magnetic offset based on the predetermined number of the measurement data read out from the storage.

12. An azimuth measurement method performed in a portable electronic apparatus having a geomagnetic sensor and a foldable body handled by opening operation and closing operation, the method comprising the steps of:

using the geomagnetic sensor to measure a geomagnetism with a certain offset and outputting measurement data of the geomagnetism such that the measurement data may contain an error due to the offset;

detecting an azimuth direction based on the measurement data from the geomagnetic sensor;

detecting the opening operation or the closing operation of the foldable body;

commencing acquisition of a series of the measurement data from the geomagnetic sensor when either of the opening operation or the closing operation of the foldable body is detected;

estimating a value of the offset on the basis of the acquired series of the measurement data; and

setting the estimated value of the offset for use in correcting the error contained in the measurement data during the detection of the azimuth direction.

13. A method of measuring a magnetic offset of a geomagnetic sensor which has a magnetic sensitivity to a geomagnetism in axes X, Y and Z of a coordinate system XYZ, and which is affected by magnetization to cause the magnetic offset, the method comprising:

a data measurement step of measuring an output of the geomagnetic sensor and acquiring a plurality of measurement data (xi, yi, zi) (i=1, . . . , N) of the geomagnetism; and

an offset estimation step of estimating an offset value (X0, Y0, Z0) of the magnetic offset of the geomagnetic sensor from the plurality of the measurement data (xi, yi, zi) (i=1, . . . , N) of the geomagnetism,

wherein the offset value (X0, Y0, Z0) is estimated by the steps (1) through (6) of;

(1) assuming a compass sphere of the geomagnetic sensor having a radius R in the coordinate system XYZ, and making an equation (xi−

X0)²+(yi−

Y0)²+(zi−

Z0)²=R² for each of the measurement data (xi, yi, zi) (i=1, . . . , N);

(2) defining a square error ε

for the above equations;

$\begin{array}{c}\mathrm{\varepsilon <br><br>}=<br><br>\sum <br><br>{\left\{{\left(x_i-X<br><br><br><br>0\right)}^2+{\left(y_i-Y<br><br><br><br>0\right)}^2+<br><br>{\left(z_i-Z<br><br><br><br>0\right)}^2-R^2\right\}}^2\\ =<br><br>\sum <br><br>\{\left(x_i^2+y_i^2+z_i^2\right)-2<br><br>x_i<br><br>X<br><br><br><br>0-2<br><br>y_i<br><br>Y<br><br><br><br>0-2<br><br>z_i<br><br>Z<br><br><br><br>0+\\ {<br><br>\left(X<br><br><br><br>0^2+Y<br><br><br><br>0^2+Z<br><br><br><br>0^2\right)-R^2\}}^2\end{array}$

(3) shaping the square error ε

as follows;

ε

=Σ

(a_i+b_iX0+c_iY0+d_iZ0+D)²

where, a_i=xi²+yi²+zi², b_i=−

2xi, c_i=−

2yi, d_i=−

2zi and D=(X0²+Y0²+Z0²)−

R²;

(4) differentiating ε

with the variables X0, Y0, Z0, and D as follows for setting the square error ε

to the minimum;

$\{\begin{array}{c}<br><br>\frac{\partial <br><br>\mathrm{\varepsilon <br><br>}}{\partial <br><br>X<br><br><br><br>0}=2<br><br>\sum <br><br>\left(a_i+b_i<br><br>X<br><br><br><br>0+c_i<br><br>Y<br><br><br><br>0+d_i<br><br>Z<br><br><br><br>0+D\right)<br><br>b_i=0\\ <br><br>\frac{\partial <br><br>\mathrm{\varepsilon <br><br>}}{\partial <br><br>Y<br><br><br><br>0}=2<br><br>\sum <br><br>\left(a_i+b_i<br><br>X<br><br><br><br>0+c_i<br><br>Y<br><br><br><br>0+d_i<br><br>Z<br><br><br><br>0+D\right)<br><br>c_i=0\\ \frac{\partial <br><br>\mathrm{\varepsilon <br><br>}}{\partial <br><br>Z<br><br><br><br>0}=2<br><br>\sum <br><br>\left(a_i+b_i<br><br>X<br><br><br><br>0+c_i<br><br>Y<br><br><br><br>0+d_i<br><br>Z<br><br><br><br>0+D\right)<br><br>d_i=0\\ \frac{\partial <br><br>\mathrm{\varepsilon <br><br>}}{\partial <br><br>D}=2<br><br>\sum <br><br>\left(a_i+b_i<br><br>X<br><br><br><br>0+c_i<br><br>Y<br><br><br><br>0+d_i<br><br>Z<br><br><br><br>0+D\right)=0\end{array}\hspace{1em}<br><br>$

(5) obtaining the following simultaneous equations by effecting the above differentiating computation, where the variables X0, Y0, Z0 and D are treated as an independent variable of ε

for simplifying the computation;

$\left[\begin{array}{cccc}\left[b<br><br><br><br>b\right]& \left[b<br><br><br><br>c\right]& \left[b<br><br><br><br>d\right]& \left[b\right]\\ \left[b<br><br><br><br>c\right]& \left[c<br><br><br><br>c\right]& \left[c<br><br><br><br>d\right]& \left[c\right]\\ \left[b<br><br><br><br>d\right]& \left[c<br><br><br><br>d\right]& \left[d<br><br><br><br>d\right]& \left[d\right]\\ \left[b\right]& \left[c\right]& \left[d\right]& N\end{array}\right]<br><br>\left[\begin{array}{c}X<br><br><br><br>0\\ Y<br><br><br><br>0\\ Z<br><br><br><br>0\\ D\end{array}\right]=\left[\begin{array}{c}-\left[a<br><br><br><br>b\right]\\ -\left[a<br><br><br><br>c\right]\\ -\left[a<br><br><br><br>d\right]\\ -\left[a\right]\end{array}\right]$

where the operator [ ] used in the above equation represents;

$\left[m\right]=\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>m_i,\left[m,n\right]=\underset{t=1}{\overset{N}{\sum <br><br>}}<br><br>m_i<br><br>n_i$

(6) solving these simultaneous equations to derive the estimated offset (X0, Y0, Z0).

14. An azimuth detection method performed in a portable electronic apparatus which has a geomagnetic sensor and a foldable body handled by opening operation and closing operation, and which generates a leakage magnetic field, the method comprising the steps of:

using the geomagnetic sensor for measuring a geomagnetic field with an offset and outputting measurement data of the geomagnetic field such that the measurement data may contain an error due to the offset;

detecting an azimuth direction based on the measurement data from the geomagnetic sensor;

acquiring a plurality of the measurement data from the geomagnetic sensor, and estimating a value of the offset on the basis of the acquired measurement data for use in correcting the error contained in the measurement data during the detection of the azimuth direction;

detecting the opening operation of the foldable body;

computing a value of the leakage magnetic field generated by the portable electronic apparatus when the opening operation of the foldable body is detected; and

subtracting the computed value of the leakage magnetic field from the estimated value of the offset, thereby removing an influence of the leakage magnetic field from the estimated value of the offset.

15. An apparatus for measuring a magnetic offset of a geomagnetic sensor equipped in a portable information terminal, the geomagnetic sensor having a magnetic sensitivity to a geomagnetic field in a plurality of axes of a coordinate system, and being affected by magnetization to cause the magnetic offset, the apparatus comprising:

a data measurement section that measures an output of the geomagnetic sensor and that acquires a plurality of measurement data of the geomagnetic field, each measurement data being represented by a data point in the coordinate system;

an offset estimation section that estimates an offset value of the magnetic offset of the geomagnetic sensor from the plurality of the measurement data of the geomagnetic field, the offset value being represented by an offset point in the coordinate system;

a mean value calculation section that calculates distances between the offset point corresponding to the offset value and a plurality of the data points corresponding to the plurality of the measurement data used for estimating of the offset value, and further calculates a mean value of the calculated distances between the offset point and the plurality of the data points;

a standard deviation calculation section that calculates a standard deviation of the calculated distances with respect to the calculated mean value of the distances; and

a validity judgment section that judges validity of the estimated offset value on the basis of the calculated standard deviation.

16. An apparatus for measuring a magnetic offset of a geomagnetic sensor equipped in a portable information terminal, the geomagnetic sensor having a magnetic sensitivity to a geomagnetic field in a plurality of axes of a coordinate system and being affected by magnetization to cause the magnetic offset, the apparatus comprising:

a data measurement section that measures an output of the geomagnetic sensor, and successively provides a plurality of measurement data of the geomagnetic field including previous measurement data and current measurement data, each measurement data being represented by a data point in the coordinate system;

a distance determining section that calculates a distance between a current data point corresponding to the current measurement data and a previous data point corresponding to the previous measurement data which has been stored in the storage, and that determines whether the calculated distance between the current data point and the previous data point is greater than a predetermined distance;

a data storage that stores the current measurement data when the calculated distance is determined greater than the predetermined distance, thereby accumulating the measurement data; and

an offset estimation section that reads a plurality of the measurement data from the data storage and estimates an offset value of the magnetic offset from the plurality of the measurement data read out from the data storage.

17. An apparatus for measuring a magnetic offset of a geomagnetic sensor equipped in a portable information terminal having an inclination sensor, the geomagnetic sensor having a magnetic sensitivity to a geomagnetic field in two axes of a two dimensional coordinate system and being affected by magnetization to cause the magnetic offset, the inclination sensor sensing an inclination angle of the portable information terminal, the apparatus comprising:

a data measurement section that measures an output of the geomagnetic sensor, and successively provides a plurality of the measurement data of the geomagnetic field including preceding measurement data and succeeding measurement data;

an inclination measurement section that measures an output of the inclination sensor and successively provides a plurality of angle data which represent the inclination angles of the portable information terminal and which include preceding angle data measured concurrently with the preceding measurement data and succeeding angle data measured concurrently with the succeeding measurement data;

a data storage that stores the succeeding measurement data when a difference between a inclination angle of the portable information terminal denoted by the succeeding angle data and another inclination angle of the portable information terminal denoted by the preceding angle data is greater than a predetermined difference, thereby accumulating the measurement data by repeatedly operating the data measurement section and the inclination measurement section; and

an offset estimation section that reads out a plurality of the accumulated measurement data from the data storage and estimates the offset value of the magnetic offset from the plurality of the accumulated measurement data read out from the data storage.

18. An apparatus for measuring a magnetic offset of a geomagnetic sensor equipped in a portable information terminal, the geomagnetic sensor having a magnetic sensitivity to a geomagnetic field and being affected by magnetization to cause the magnetic offset, the apparatus comprising:

a data measurement section that measures an output of the geomagnetic sensor and successively provides measurement data of the geomagnetic field from the output of the geomagnetic sensor;

a data storage that stores the measurement data; and

an offset estimation section that reads out the measurement data from the data storage when a number of the measurement data stored in the data storage reaches a predetermined number, and that estimates an offset value of the magnetic offset based on the predetermined number of the measurement data read out from the data storage.

19. A portable electronic apparatus having a foldable body handled by opening operation and closing operation, comprising:

an azimuth detection section that has a geomagnetic sensor for measuring a geomagnetism with an offset and outputting measurement data of the geomagnetism such that the measurement data may contain an error due to the offset, and that detects an azimuth direction based on the measurement data from the geomagnetic sensor;

an open/close detection section that detects the opening operation or the closing operation of the foldable body; and

a control section that responds when either of the opening operation or the closing operation is detected for commencing acquisition of a series of the measurement data from the geomagnetic sensor, then that estimates a value of the offset on the basis of the acquired series of the measurement data, and that sets the estimated value of the offset for use in correcting the error contained in the measurement data during the detection of the azimuth direction.

20. The portable electronic apparatus according to claim 19, wherein the foldable body comprises a pair of units coupled to open and close with one another by the opening operation and the closing operation, and wherein the open/close detection section physically senses the opening and closing of the pair of the units for detecting the opening operation and the closing operation.

21. The portable electronic apparatus according to claim 20, wherein the pair of the units comprise a stationary unit which is generally held stationary in the opening operation and a movable unit which is moved relative to the stationary unit in response to the opening operation, and wherein the geomagnetic sensor is mounted in the movable unit.

22. The portable electronic apparatus according to claim 21, further comprising a display device that displays information associated with operations of the portable electronic apparatus and that is mounted in the movable unit.

23. The portable electronic apparatus according to claim 19, wherein the foldable body contains a magnetic source of generating a magnetism which may cause the offset in the geomagnetic sensor, and wherein the geomagnetic sensor is positioned in the foldable body remote from the magnetic source such a manner as to reduce a magnetic influence of the magnetic source.

24. The portable electronic apparatus according to claim 19, further comprising:

a validity judgment section that judges validity of the estimated value of the offset; and

a notification section that operates when the estimated value of the offset is judged invalid by the validity judgment section for prompting a user to perform again the opening operation or the closing operation.

25. The portable electronic apparatus according to claim 19, further comprising:

a validity judgment section that judges validity of the estimated value of the offset; and

a notification section that operates when the estimated value of the offset is judged invalid by the validity judgment section for prompting a user to further perform the opening operation and the closing operation while placing the foldable body in different orientations.

26. The portable electronic apparatus according to claim 19, wherein the foldable body is a revolver type having a part which revolves in the opening operation or the closing operation.

27. The portable electronic apparatus according to claim 26, wherein the geomagnetic sensor measures the geomagnetism in three axes orthogonal to each other, and wherein the foldable body of the revolver type comprises a pair of a stationary unit and a movable unit, which are coupled to open and close with one another by the opening operation and the closing operation, the stationary unit generally being held stationary in the opening operation and the movable unit being revolved to displace in directions of the three axes in response to the opening operation.

28. An apparatus for measuring a magnetic offset of a geomagnetic sensor which has a magnetic sensitivity to a geomagnetism in axes X, Y and Z of a coordinate system XYZ, and which is affected by magnetization to cause the magnetic offset, the apparatus comprising:

a data measurement section that measures an output of the geomagnetic sensor and acquires a plurality of measurement data (xi, yi, zi) (i=1, . . . , N) of the geomagnetism; and

an offset estimation section that estimates an offset value (X0, Y0, Z0) of the magnetic offset of the geomagnetic sensor from the plurality of the measurement data (xi, yi, zi) (i=1, . . . , N) of the geomagnetism,

wherein the offset value (X0, Y0, Z0) is estimated by the following computation algorithm (1) through (6);

(1) assuming a compass sphere of the geomagnetic sensor having a radius R in the coordinate system XYZ, and making an equation (xi−

X0)²+(yi−

Y0)²+(zi−

Z0)²=R² for each of the measurement data (xi, yi, zi) (i=1, N);

(2) defining a square error ε

for the above equations;

$\begin{array}{c}\mathrm{\varepsilon <br><br>}=<br><br>\sum <br><br>{\left\{{\left(x_i-X<br><br><br><br>0\right)}^2+{\left(y_i-Y<br><br><br><br>0\right)}^2+{\left(z_i-Z<br><br><br><br>0\right)}^2-R^2\right\}}^2\\ =<br><br>\sum <br><br>\{\left(x_i^2+y_i^2+z_i^2\right)-2<br><br>x_i<br><br>X<br><br><br><br>0-2<br><br>y_i<br><br>Y<br><br><br><br>0-2<br><br>z_i<br><br>Z<br><br><br><br>0+\\ {<br><br>\left(X<br><br><br><br>0^2+Y<br><br><br><br>0^2+Z<br><br><br><br>0^2\right)-R^2\}}^2\end{array}$

(3) shaping the square error ε

as follows;

ε

=Σ

(a_i+b_iX0+c_iY0+d_iZ0+D)²

where, a_i=xi²+yi²+zi², b_i=−

2xi, c_i=−

2yi, d_i=−

2zi and D=(X0²+Y0²+Z0²)−

R²;

(4) differentiating E with the variables X0, Y0, Z0, and D as follows for setting the square error ε

to the minimum;

$\{\begin{array}{c}\frac{\partial <br><br>\mathrm{\varepsilon <br><br>}}{\partial <br><br>X<br><br><br><br>0}=2<br><br>\sum <br><br>\left(a_i+b_i<br><br>X<br><br><br><br>0+c_i<br><br>Y<br><br><br><br>0+d_i<br><br>Z<br><br><br><br>0+D\right)<br><br>b_i=0\\ \frac{\partial <br><br>\mathrm{\varepsilon <br><br>}}{\partial <br><br>Y<br><br><br><br>0}=2<br><br>\sum <br><br>\left(a_i+b_i<br><br>X<br><br><br><br>0+c_i<br><br>Y<br><br><br><br>0+d_i<br><br>Z<br><br><br><br>0+D\right)<br><br>c_i=0\\ \frac{\partial <br><br>\mathrm{\varepsilon <br><br>}}{\partial <br><br>Z<br><br><br><br>0}=2<br><br>\sum <br><br>\left(a_i+b_i<br><br>X<br><br><br><br>0+c_i<br><br>Y<br><br><br><br>0+d_i<br><br>Z<br><br><br><br>0+D\right)<br><br>d_i=0\\ <br><br>\frac{\partial <br><br>\mathrm{\varepsilon <br><br>}}{\partial <br><br>D}=2<br><br>\sum <br><br>\left(a_i+b_i<br><br>X<br><br><br><br>0+c_i<br><br>Y<br><br><br><br>0+d_i<br><br>Z<br><br><br><br>0+D\right)=0\end{array}\hspace{1em}<br><br>$

(5) obtaining the following simultaneous equations by effecting the above differentiating computation, where the variables X0, Y0, Z0 and D are treated as an independent variable of ε

for simplifying the computation;

$\left[\begin{array}{cccc}\left[\mathrm{bb}\right]& \left[\mathrm{bc}\right]& \left[\mathrm{bd}\right]& \left[b\right]\\ \left[\mathrm{bc}\right]& \left[\mathrm{cc}\right]& \left[c<br><br><br><br>d\right]& \left[c\right]\\ \left[\mathrm{bd}\right]& \left[c<br><br><br><br>d\right]& \left[\mathrm{dd}\right]& \left[d\right]\\ \left[b\right]& \left[c\right]& \left[d\right]& N\end{array}\right]<br><br>\left[\begin{array}{c}X<br><br><br><br>0\\ Y<br><br><br><br>0\\ Z<br><br><br><br>0\\ D\end{array}\right]=\left[\begin{array}{c}-\left[\mathrm{ab}\right]\\ -\left[a<br><br><br><br>c\right]\\ -\left[\mathrm{ad}\right]\\ -\left[a\right]\end{array}\right]$

where the operator [ ] used in the above equation represents;

$\left[m\right]=\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>m_i,\left[m,n\right]=\underset{t=1}{\overset{N}{\sum <br><br>}}<br><br>m_i<br><br>n_i$

(6) solving these simultaneous equations to derive the estimated offset (X0, Y0, Z0).

29. A portable electronic apparatus having a foldable body handled by opening operation and closing operation, and generating a leakage magnetic field, comprising;

an azimuth detection section that has a geomagnetic sensor for measuring a geomagnetic field with an offset and outputting measurement data of the geomagnetic field such that the measurement data may contain an error due to the offset, and that detects an azimuth direction based on the measurement data from the geomagnetic sensor;

an offset estimation section that acquires a plurality of the measurement data from the geomagnetic sensor, and that estimates a value of the offset on the basis of the acquired measurement data for use in correcting the error contained in the measurement data during the detection of the azimuth direction;

an operation detection section that detects the opening operation of the foldable body; and

a leakage magnetic field removal section that operates when the opening operation of the foldable body is detected for computing a value of the leakage magnetic field generated in the foldable body and that subtracts the computed value of the leakage magnetic field from the estimated value of the offset, thereby removing an influence of the leakage magnetic field from the estimated value of the offset.

30. The portable electronic apparatus according to claim 29, wherein the foldable body comprises a pair of units coupled to open and close with one another by the opening operation and the closing operation, and wherein the operation detection section physically senses the opening of the pair of the units for detecting the opening operation.

31. The portable electronic apparatus according to claim 29, wherein the leakage magnetic field removal section operates when the opening operation of the foldable body is detected for acquiring a series of the measurement data from the geomagnetic sensor, and computes the value of the leakage magnetic field based on the acquired measurement data.

32. The portable electronic apparatus according to claim 29, wherein the operation detection section further detects the closing operation of the foldable body, and wherein the offset estimation section operates when the closing operation is detected for commencing acquisition of a series of the measurement data from the geomagnetic sensor, and estimates the value of the offset on the basis of the acquired series of the measurement data.

33. A magnetic sensor device equipped in a portable electronic apparatus which has a foldable body handled by opening operation and closing operation, and which generates a leakage magnetic field, the magnetic sensor device comprising:

an azimuth detection section that has a geomagnetic sensor for measuring a geomagnetic field with an offset and outputting measurement data of the geomagnetic field such that the measurement data may contain an error due to the offset, and that detects an azimuth direction based on the measurement data from the geomagnetic sensor;

an offset estimation section that acquires a plurality of the measurement data from the geomagnetic sensor, and that estimates a value of the offset on the basis of the acquired measurement data for use in correcting the error contained in the measurement data during the detection of the azimuth direction; and

a leakage magnetic field removal section that responds to the opening operation of the foldable body for computing a value of the leakage magnetic field generated in the foldable body and that subtracts the computed value of the leakage magnetic field from the estimated value of the offset, thereby removing an influence of the leakage magnetic field from the estimated value of the offset.

34. A machine readable medium for use in a portable information terminal apparatus having a CPU and geomagnetic sensor which has a magnetic sensitivity to a geomagnetic field in a plurality of axes of a coordinate system and which is affected by magnetization to cause an magnetic offset, the medium containing program instructions executable by the CPU for causing the portable information terminal apparatus to perform a method of measuring the magnetic offset of the geomagnetic sensor, wherein the method comprises:

a data measurement step of measuring an output of the geomagnetic sensor and acquiring a plurality of measurement data of the geomagnetic field, each measurement data being represented by a data point in the coordinate system;

an offset estimation step of estimating an offset value of the magnetic offset of the geomagnetic sensor from the plurality of the measurement data of the geomagnetic field, the offset value being represented by an offset point in the coordinate system;

a mean value calculation step of calculating distances between the offset point corresponding to the offset value and a plurality of the data points corresponding to the plurality of the measurement data used for estimating of the offset value, and further calculating a mean value of the calculated distances between the offset point and the plurality of the data points;

a standard deviation calculation step of calculating a standard deviation of the calculated distances with respect to the calculated mean value of the distances; and

a validity judgment step of judging validity of the estimated offset value on the basis of the calculated standard deviation.

35. A machine readable medium for use in a portable information terminal apparatus having a CPU, a storage and a geomagnetic sensor which has a magnetic sensitivity to a geomagnetic field in a plurality of axes of a coordinate system and which is affected by magnetization to cause an magnetic offset, the medium containing program instructions executable by the CPU for causing the portable information terminal apparatus to perform a method of measuring the magnetic offset of the geomagnetic sensor, wherein the method comprises:

a data measurement step of measuring an output of the geomagnetic sensor, and successively providing a plurality of measurement data of the geomagnetic field including previous measurement data and current measurement data, each measurement data being represented by a data point in the coordinate system;

a distance determining step of calculating a distance between a current data point corresponding to the current measurement data and a previous data point corresponding to the previous measurement data which has been stored in the storage, and determining whether the calculated distance between the current data point and the previous data point is greater than a predetermined distance;

a data storing step of storing the current measurement data in the storage when the calculated distance is determined greater than the predetermined distance, thereby accumulating the measurement data in the storage; and

an offset estimation step of reading a plurality of the measurement data from the storage and estimating an offset value of the magnetic offset from the plurality of the measurement data read out from the storage.

36. A machine readable medium for use in a portable information terminal apparatus having a CPU, a storage, a geomagnetic sensor and an inclination sensor, the geomagnetic sensor having a magnetic sensitivity to a geomagnetic field in two axes of a two dimensional coordinate system and being affected by magnetization to cause a magnetic offset, the inclination sensor sensing an inclination angle of the portable information terminal apparatus, the medium containing program instructions executable by the CPU for causing the portable information terminal apparatus to perform a method of measuring the magnetic offset of the geomagnetic sensor, wherein the method comprises:

a data measurement step of measuring an output of the geomagnetic sensor, and successively providing a plurality of the measurement data of the geomagnetic field including preceding measurement data and succeeding measurement data;

an inclination measurement step of measuring an output of the inclination sensor and successively providing a plurality of angle data which represent the inclination angles of the portable information terminal apparatus and which include preceding angle data measured concurrently with the preceding measurement data and succeeding angle data measured concurrently with the succeeding measurement data;

a data storing step of storing the succeeding measurement data in the storage when a difference between a inclination angle of the portable information terminal apparatus denoted by the succeeding angle data and another inclination angle of the portable information terminal apparatus denoted by the preceding angle data is greater than a predetermined difference, thereby accumulating the measurement data in the storage by repeating a routine of the data measurement step, the inclination measurement step and the data storing step; and

an offset estimation step of reading out a plurality of the accumulated measurement data from the storage and estimating the offset value of the magnetic offset from the plurality of the accumulated measurement data read out from the storage.

37. A machine readable medium for use in a portable information terminal apparatus having a CPU, a storage and a geomagnetic sensor which has a magnetic sensitivity to a geomagnetic field and which is affected by magnetization to cause an magnetic offset, the medium containing program instructions executable by the CPU for causing the portable information terminal apparatus to perform a method of measuring the magnetic offset of the geomagnetic sensor, wherein the method comprises:

a data measurement step of measuring an output of the geomagnetic sensor and successively providing measurement data of the geomagnetic field from the output of the geomagnetic sensor;

a data storing step of storing the measurement data into the storage; and

an offset estimation step of reading out the measurement data from the storage when a number of the measurement data stored in the storage reaches a predetermined number, and estimating an offset value of the magnetic offset based on the predetermined number of the measurement data read out from the storage.

38. A machine readable medium for use in a portable electronic apparatus having a CPU, a geomagnetic sensor and a foldable body which is handled by opening operation and closing operation and which generates a leakage magnetic field, the machine readable medium containing an azimuth measurement program executable by the CPU for causing the portable electronic apparatus to perform an azimuth measurement process comprising the steps of:

operating the geomagnetic sensor for measuring a geomagnetic field with a certain offset and outputting measurement data of the geomagnetic field such that the measurement data may contain an error due to the offset;

detecting an azimuth direction based on the measurement data from the geomagnetic sensor;

acquiring a plurality of the measurement data from the geomagnetic sensor, and estimating a value of the offset on the basis of the acquired measurement data for use in correcting the error contained in the measurement data during the detection of the azimuth direction;

detecting the opening operation of the foldable body;

computing a value of the leakage magnetic field generated from the foldable body when the opening operation of the foldable body is detected; and

subtracting the computed value of the leakage magnetic field from the estimated value of the offset, thereby removing an influence of the leakage magnetic field from the estimated value of the offset.