Patent Publication Number: US-7210235-B2

Title: Apparatus and method for detecting azimuth and inclination angle, program for detecting the same, and portable terminal device for detecting the same

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a technique for detecting azimuth and inclination angle of a center axis of a device of interest in a terrestrial coordinate system through detection of geomagnetism components and gravitational force components, and more particularly, to a technique for improving its detection accuracy. 
   2. Description of the Related Art 
   Recently, there have been developed portable terminal devices, such as a cellular phone, which include a magnetic sensor for detecting geomagnetism and an acceleration sensor for detecting inclination of the body of the device in order to measure azimuth, in accordance with the trend of their performance enhancement. Such a device is advantageous in that accuracy of azimuth detection can be improved by means of correction based on inclination of the device body. 
   Conventional techniques employing such correction are disclosed in Japanese Patent Application Laid-Open (kokai) Publication Nos. H10-185608 and 2003-172633. Both the techniques use a geomagnetism sensor and an acceleration sensor, and improve its detection accuracy through coordinated operation of these sensors. 
   However, when a detection apparatus as disclosed in the publications is incorporated in a portable terminal device such as a cellular phone, there arises a problem in that the acceleration sensor detects an acceleration component produced as a result of movement of the portable terminal device, and the detected inclination of the portable terminal device involves an error, whereby the azimuth correction amount involves an error, and the detection accuracy deteriorates. This problem cannot be solved by the techniques disclosed in the above-mentioned publications. 
   SUMMARY OF THE INVENTION 
   In view of the foregoing, an object of the present invention is to provide a technique for detecting an azimuth component of a center axis of a device of interest in a terrestrial coordinate system through detection of geomagnetism components and gravitational force components, in which influence of errors involved in the gravitational force components is reduced so as to improve detection accuracy in detecting the azimuth component of the center axis in the terrestrial coordinate system. 
   In order to achieve the above object, the present invention provides an apparatus, such as a portable terminal device, for detecting azimuth and inclination angle of a device, the apparatus having an azimuth sensor for detecting geomagnetism components in a coordinate system fixed to the device and an acceleration sensor for detecting gravitational force components in the coordinate system fixed to the device and adapted to generate final detection values of the azimuth and the inclination angle of the device in a terrestrial coordinate system by use of the geomagnetism components and the gravitational force components, the apparatus further comprising: first computation means for performing coordinate conversion of the geomagnetism components by use of the gravitational force components to thereby obtain the azimuth and the inclination angle to be used as reference data; geomagnetism-depression-angle obtaining means for obtaining a geomagnetism depression angle, which is an angle formed between a horizontal plane and a direction of geomagnetism; second computation means for solving simultaneous equations of the azimuth and the inclination angle (in the terrestrial coordinate system), the simultaneous equations being obtained on the basis of the relation between the geomagnetism components in the coordinate system fixed to the device and the geomagnetism components in the terrestrial coordinate system and being specified by the geomagnetism depression angle, to thereby obtain at least one set of computed values of the azimuth and the inclination angle to be used as candidates of the azimuth and the inclination angle; and selection means, operable when a plurality of sets of computed values are obtained, for selecting one set of the computed values among the candidates by referring to the reference data, the selected one set of computed values being used as the final detection values of the azimuth and the inclination angle. 
   In this apparatus, it is preferable that the second computation means, when only one set of the computed values is obtained by solving the simultaneous equations, outputs the one set of computed values of the azimuth and the inclination angle as the final detection values of the azimuth and the inclination angle. 
   It is also preferable that the selection means selects one set of the computed values containing the inclination angle which is closer to the inclination angle of the reference data than any other inclination angle(s) contained in remaining set(s) of the computed values and outputs the selected set of the computed values as the final detection values of the azimuth and the inclination angle. 
   In this case, it is preferable that the geomagnetism-depression-angle obtaining means includes: geomagnetism-depression-angle computation means for calculating a value corresponding to the geomagnetism depression angle by performing coordinate conversion of the detected geomagnetism components by use of the detected gravitational force components; and averaging means for accumulating the value corresponding to the geomagnetism depression angle and averaging the accumulated values to store the averaged value for use as the geomagnetism depression angle. 
   With this configuration, reliable computation can be performed by making use of the actually measured value of the geomagnetism depression angle at the present location (the current position). 
   The averaging means may include date and time data storing means for obtaining data of date and time when the value corresponding to the geomagnetism depression angle is obtained by the geomagnetism-depression-angle computation means and for storing the obtained data of date and time together with the value corresponding to the geomagnetism depression angle into a table; and data selecting means for selecting the stored values each corresponding to the geomagnetism depression angle in the table used for obtaining the averaged value by eliminating the stored value corresponding to the geomagnetism depression angle which was stored at the timing which is prior to the current date and time by a predetermined amount of time or more. 
   Alternatively, the averaging means may include position data storing means for obtaining position data of the apparatus when the value corresponding to the geomagnetism depression angle is obtained by the geomagnetism-depression-angle computation means and for storing the obtained position data together with the value corresponding to the geomagnetism depression angle into a table; and data selecting means for selecting the stored values each corresponding to the geomagnetism depression angle in the table used for obtaining the averaged value by eliminating the stored value corresponding to the geomagnetism depression angle which was stored at a position apart from the current position of the apparatus by a predetermined distance or longer. 
   In another embodiment, the geomagnetism-depression-angle obtaining means may include position data obtaining means for obtaining at least current latitude of the apparatus as current position data; and geomagnetism-depression-angle generation means for generating the geomagnetism depression angle from the current position data. 
   With this configuration, the geomagnetism depression angle can be obtained as a value which is not affected at all by errors stemming from the measured gravitational force components, whereby the detection accuracy can be improved. 
   The present invention also provides a method of detecting azimuth and inclination angle of a device in which geomagnetism components in a coordinate system fixed to the device and gravitational force components in the coordinate system fixed to the device are detected and final detection values of the azimuth and the inclination angle of the device in a terrestrial coordinate system are generated by use of the geomagnetism components and the gravitational force components, the method comprising steps of: performing coordinate conversion of the geomagnetism components by use of the gravitational force components to thereby compute the azimuth and the inclination angle, and storing the computed azimuth and inclination angle as reference data; obtaining a geomagnetism depression angle, which is an angle formed between a horizontal plane and a direction of geomagnetism; solving simultaneous equations of the azimuth and the inclination angle, the simultaneous equations being obtained on the basis of the relation between the geomagnetism components in the coordinate system fixed to the device and the geomagnetism components in the terrestrial coordinate system and being specified by the geomagnetism depression angle, to thereby obtain at least one set of computed values of the azimuth and the inclination angle to be used as candidates of the azimuth and the inclination angle; and selecting, when a plurality of sets of computed values are obtained, one set of computed values among the candidates by referring to the reference data, the selected one set of computed values being used as the final detection values of the azimuth and the inclination angle. 
   The present invention further provides a program for causing a computer to perform the steps of: detecting geomagnetism components in a coordinate system fixed to a device; detecting gravitational force components in the coordinate system fixed to the device; performing coordinate conversion of the geomagnetism components by use of the gravitational force components to thereby compute the azimuth and the inclination angle, and storing the computed azimuth and inclination angle as reference data; obtaining a geomagnetism depression angle, which is an angle formed between a horizontal plane and a direction of geomagnetism; solving simultaneous equations of the azimuth and the inclination angle, the simultaneous equations being obtained on the basis of the relation between the geomagnetism components in the coordinate system fixed to the device and the geomagnetism components in the terrestrial coordinate system and being specified by the geomagnetism depression angle, to thereby obtain at least one set of computed values of the azimuth and the inclination angle to be used as candidates of the azimuth and the inclination angle; and selecting, when a plurality of sets of computed values are obtained, one set of computed values among the candidates by referring to the reference data, the selected one set of computed values being used as final detection values of the azimuth and the inclination angle. 
   According to the present invention, since the azimuth and the inclination angle are obtained by solving simultaneous equations of the azimuth and the inclination angle defined (or specified) by the geomagnetism components, the final detection values which are not affected by errors of the gravitational force components can be obtained, whereby the detection accuracy is improved. In addition, the azimuth and the inclination angle are calculated from the geomagnetism components and the gravitational force components to be stored and used as reference data, and when a plurality of solutions exist, one solution is selected by making use of the reference data. This solves the problem which may arise when the simultaneous equations have a plurality of solutions. Because of the above-described advantages, the present invention can be effectively applied to a portable azimuth/inclination-angle detection device, particularly to an azimuth/inclination-angle detection device incorporated into a portable terminal device such as a cellular phone. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Various other objects, features and many of the attendant advantages of the present invention will be readily appreciated as the same becomes better understood by reference to the following detailed description of the preferred embodiments when considered in connection with the accompanying drawings, in which: 
       FIG. 1  is a block diagram showing the configuration of a cellular phone according to one embodiment of the present invention; 
       FIG. 2  is a front view of the cellular phone with the terminal units opened; 
       FIG. 3  is a block diagram showing functions realized by azimuth and inclination-angle detection processing; 
       FIG. 4  is a diagram showing data used in first and second computations and their coordinate systems; 
       FIG. 5  is a flowchart schematically showing the azimuth and inclination-angle detection processing; and 
       FIG. 6  is a flowchart showing an example of processing for acquiring geomagnetism depression angle. 
       FIG. 7  is an example of a geomagnetism depression angle table for storing (or accumulating) geomagnetism depression angles θ 0 . 
       FIG. 8  is another example of a geomagnetism depression angle table for storing (or accumulating) geomagnetism depression angles θ 0 . 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENT 
   An embodiment of the present invention will be described with reference to the drawings. 
     FIG. 1  is a block diagram showing the configuration of a cellular phone  1  according to the present embodiment. 
   As shown in  FIG. 1 , the cellular phone  1  is a foldable portable terminal device including two terminal units (housings)  1 - 1  and  1 - 2 . An antenna  201  is used for sending radio wave signals to an unillustrated radio base station and receiving radio wave signals therefrom. An RF (radio frequency) section  202  converts signals received by the antenna  201  to reception signals of an intermediate frequency, and outputs them to a modulation-demodulation section  203 . Further, the RF section  202  converts transmission signals sent from the modulation-demodulation section  203  to signals of a transmission frequency, and outputs them to the antenna  201  for transmission thereof. 
   The modulation-demodulation section  203  performs processing for demodulating reception signals sent from the RF section  202  and processing for modulating transmission signals sent from a CDMA (code division multiple access) section  204 . The CDMA section  204  performs processing for coding transmission signals and processing for decoding reception signals. A sound processing section  205  converts sound signals sent from a microphone  301  to digital signals and outputs them to the CDMA section  204 . Further, the sound processing section  205  receives digital sound signals from the CDMA section  204 , converts them to analog sound signals, and outputs the analog sound signals to a speaker  302  to produce sounds. 
   An antenna  401  is used for receiving radio wave signals from GPS (global positioning system) satellites. A GPS reception section  402  demodulates radio wave signals sent from the GPS satellites and calculates the position represented with latitude and longitude (and optionally altitude in the case of a three-dimensional mode) of the cellular phone  1  on the basis of the radio wave signals. 
   An acceleration sensor section  510  detects acceleration of the terminal unit  1 - 1 . The circuit components of the acceleration sensor section  510  are assembled in a single package and integrated into a single chip.  FIG. 2  shows a front view of the cellular phone  1  with the first and second terminal units  1 - 1  and  1 - 2  opened. The cellular phone  1  has three axes; X, Y, and Z axes. The Y axis is parallel to side surfaces of the first terminal unit  1 - 1 . The positive direction of the Y axis is a direction from the first terminal to the second terminal unit  1 - 2 . The X axis is located on the surface of the first terminal unit  1 - 1 , and extends perpendicular to the Y axis. The Z axis is perpendicular to a plane which include X axis and Y axis. The positive direction of the Z axis is a direction from the back side of the sheet of  FIG. 2  toward the front side thereof. Referring back to  FIG. 1 , the acceleration detected by the acceleration sensor section  510  is used for detecting motion and inclination of the terminal unit  1 — 1 . 
   A magnetic sensor section  520  includes magnetic sensors  521 - 1  to  521 - 3 , a temperature sensor  522 , and a magnetic sensor control section  523 , which are assembled in a single package and integrated into a single chip. The magnetic sensors  521 - 1  to  521 - 3  detect magnetism (magnetic field) in the X, Y, and Z axes, which perpendicularly intersect with respect to one another, respectively, and output them in the form of magnetic field data. Here, the magnetic sensors  521 - 1  to  521 - 3  are adjusted such that the X, Y, and Z axes coincide with those associated with the acceleration sensors. The temperature sensor  522  detects ambient temperature so as to perform temperature compensation for the magnetic sensors  521 - 1  to  521 - 3 . The magnetic sensor control section  523  performs predetermined data processing for the detection outputs of the magnetic sensors  521 - 1  to  521 - 3 , the temperature sensor  522 , and the acceleration sensor section  510 , and outputs resultant data. 
   A main control section  601  performs main control of the cellular phone  1 , and is composed of a CPU (central processing unit). A ROM (read only memory)  602  and a RAM (random access memory)  603  serve as a main memory of the CPU. The ROM  602  stores programs to be executed by the CPU and various data. The RAM  603  provides a work region which the CPU uses to store data or the like in the course of its operation. 
   A signaling means  303  includes a speaker, a vibrator, a light-emitting diode, or the like, and informs an incoming call, reception of a mail, etc., to a user by means of sound, vibration, light, or the like. A clock section  304  is a clock function section used by the main control section  601 . A main operation section  305  receives instructions input by the user and feeds them to the main control section  601 . 
   An electronic photographing section  306  converts an image of an object to a digital signal, and outputs it to the main control section  601 . A display section  307  includes a liquid crystal display (LCD) for displaying images, characters, etc. on the basis of display signals sent from the main control section  601 . A touch panel  308  is built into the surface of the liquid crystal display of the display section  307 , and outputs to the main control section  601  a signal indicating an instruction, data, etc., which is input by the user through touching operation. An auxiliary operation section  309  is a push switch used for display changeover. 
   In the cellular phone  1  having the above-described configuration, the CPU of the main control section  601  starts a main program (upper level program) read from the ROM  602 , and selectively executes various applications with using the main program. When an executed application program requires azimuth data or inclination data, a measurement trigger is produced upon execution of this application program. In response to this measurement trigger, the main control section  601  starts processing for detecting azimuth and inclination angle of the center axis of the cellular phone  1  to thereby obtain an azimuth angle α and an elevation angle β in the terrestrial coordinate system. The azimuth angle α represents the azimuth in the terrestrial coordinate system. The elevation angle β represents the inclination angle of the center axis of the cellular phone  1  in the terrestrial coordinate system. 
     FIG. 3  is a block diagram showing functions realized by the above processing for detecting azimuth and inclination angle. As shown in  FIG. 3 , measurement trigger means  701  generates a measurement instruction. Measurement-data obtaining means  702  obtains measurement data sets g and h from the acceleration sensor section  510  and the magnetic sensor section  520 . First azimuth/inclination angle computation means  703  performs a first computation described later, to thereby obtain azimuth angle α, elevation angle β, twist angle γ, and geomagnetism depression angle θ from the measurement data sets g and h. The azimuth angle α, the elevation angle β, etc. will be described in later detail. Notably, the azimuth angle α and the elevation angle β calculated through the first computation are handled (treated) as reference values α 0  and β 0 , respectively, and the geomagnetism depression angle θ calculated through the first computation is handled (treated) as a rough value θ 0  involving an error. Averaging means  704  accumulates rough values θ 0  of the geomagnetism depression angle, and averages them so as to eliminate the error, to thereby obtain an accurate value of the geomagnetism depression angle θ. 
   Second azimuth/inclination angle computation means  705  performs a second computation described later, to thereby obtain azimuth angle α and elevation angle β from the measurement data set h and the geomagnetism depression angle θ (obtained by the averaging means  704 ). In the case where a plurality of solutions exist for the values of azimuth angle α and elevation angle β as a result of the second computation, the second azimuth/inclination angle computation means  705  outputs the respective solutions as candidate values (α 1 , β 1 ) and (α 2 , β 2 ), etc. Selection means  706  selects single values from the candidate values (α 1 , β 1 ) and (α 2 , β 2 ) and so on with reference to (i.e. by referring to) the reference values (α 0 , β 0 ) obtained by the first azimuth/inclination angle computation means  703 , and outputs the selected values as final detection values (α, β). 
     FIG. 4  is a diagram showing data used in the first and second computations and their coordinate systems. In  FIG. 4 , x, y, and z axes are orthogonal coordinate axes set on the cellular phone (see  FIG. 2 ), x 0 , y 0 , and z 0  axes are orthogonal coordinate axes, the x 0  and y 0  axes being located on a horizontal plane, and the y 0  axis being directed in the direction of magnetic north N. The z 0  axis extends upward from the horizontal plane along a direction perpendicular to the horizontal plane (that is, the positive direction of the z 0  axis is in a direction extending upward from the horizontal plane and perpendicular to the horizontal plane). Hereinafter, the coordinate system represented by the x 0 , y 0 , and z 0  axes will be referred to as the “terrestrial coordinate system”. A vector V represents the orientation of the center axis of the cellular phone  1 , and thus is parallel to the y axis. A vector V 0  is a projection vector obtained by projecting the vector V on the x 0 -y 0  plane (horizontal plane) from the upper side with respect to the z 0  axis, and thus is a vector on the x 0 -y 0  plane. The azimuth angle α corresponds to the angle formed between the y 0  axis and the vector V 0 . The elevation angle β corresponds to the angle formed between the vector V 0  and the vector V. The azimuth angle α and the elevation angle β determine the direction of the vector V. The twist angle γ is an angle at which the x-y plane is rotated about the y axis, and thus corresponds to the intersection angle between the y-z 0  plane and the y-z plane. A vector H represents the direction of geomagnetism, and is directed to the magnetic north N 0 . A geomagnetism depression angle θ is an angle formed between the horizontal plane and the direction of geomagnetism, and thus corresponds to an angle formed between the y 0  axis (magnetic north direction N) and the vector H (magnetic north N 0 ). 
     FIG. 5  is a flowchart schematically showing the processing for detection of azimuth and inclination angle. Referring to  FIG. 5  in combination with  FIG. 1 , the main control section  601  obtains a detected gravitational force g from the acceleration sensor section  510  and obtains a detected geomagnetism h from the magnetic sensor section  520  (S 101 ). As shown in Eq. 1, the detected gravitational force g is obtained in the form of gravitational force components (gx, gy, gz) in the coordinate system on the cellular phone  1  (the x, y, z coordinate system). Here, gx, gy, and gz correspond to the detection outputs of the acceleration sensors  510 - 1  to  510 - 3 , respectively.
   g =( gx, gy, gz )  Eq. 1 
   The main control section  601  firstly performs the first computation by use of the obtained detected gravitational force g and detected geomagnetism h (S 102 ). In this first computation, the main control section  601  performs a first angle computation so as to calculate the elevation angle β and the twist angle γ from (on the basis of) the detected gravitational force g, and then performs a second angle computation so as to calculate the azimuth angle α from (on the basis of) the detected gravitational force g, the calculated elevation angle β, and the calculated twist angle γ. 
   Prior to explanation of the first angle computation, the relation between the detected gravitational force g and the gravitational force G in the terrestrial coordinate system will be described. The gravitational force G in the terrestrial coordinate system can be represented by (Gx 0 , Gy 0 , Gz 0 ). Since Gx 0 =0 and Gy 0 =0, the gravitational force G can be represented as shown in Eq. 2. Notably, Gx 0 , Gy 0 , and Gz 0  are gravitational force components along the above-described x 0 , y 0 , and z 0  axes, respectively.
 
 G =(0,0,  Gz   0 )  Eq. 2
 
   The relation between the gravitational force G and the detected gravitational force g can be represented by the following Eq. 3.
 
( Gx   0   , Gy   0   , Gz   0 ) BC =( gx, gy, gz )  Eq. 3
 
   In Eq. 3, B is a transformation formula for rotational transformation by the elevation angle β, and is represented by the matrix shown in Eq. 4. 
   
     
       
         
           
             
               
                 B 
                 = 
                 
                   [ 
                   
                     
                       
                         1 
                       
                       
                         0 
                       
                       
                         0 
                       
                     
                     
                       
                         0 
                       
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                         
                       
                       
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                         
                       
                     
                     
                       
                         0 
                       
                       
                         
                           
                             - 
                             sin 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                         
                       
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                         
                       
                     
                   
                   ] 
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 4 
               
             
           
         
       
     
   
   In Eq. 3, C is a transformation formula for rotational transformation by the twist angle γ, and is represented by the matrix shown in Eq. 5. 
   
     
       
         
           
             
               
                 C 
                 = 
                 
                   [ 
                   
                     
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           γ 
                         
                       
                       
                         0 
                       
                       
                         
                           
                             - 
                             sin 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           γ 
                         
                       
                     
                     
                       
                         0 
                       
                       
                         1 
                       
                       
                         0 
                       
                     
                     
                       
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           γ 
                         
                       
                       
                         0 
                       
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           γ 
                         
                       
                     
                   
                   ] 
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 5 
               
             
           
         
       
     
   
   According to Eqs. 4 and 5, the composite transformation formula BC for rotational transformation by the elevation angle β and the twist angle γ is represented by the matrix shown in Eq. 6. 
   
     
       
         
           
             
               
                 BC 
                 = 
                 
                   [ 
                   
                     
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           γ 
                         
                       
                       
                         0 
                       
                       
                         
                           
                             - 
                             sin 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           γ 
                         
                       
                     
                     
                       
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           γ 
                         
                       
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                         
                       
                       
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           γ 
                         
                       
                     
                     
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           γ 
                         
                       
                       
                         
                           
                             - 
                             sin 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                         
                       
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           γ 
                         
                       
                     
                   
                   ] 
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 6 
               
             
           
         
       
     
   
   When Eq. 6 and Eq. 2 are substituted in Eq. 3 and the resultant equation is simplified, the following Eq. 7 can be obtained. 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         ( 
                         
                           gx 
                           , 
                           gy 
                           , 
                           gz 
                         
                         ) 
                       
                       = 
                       
                         
                           ( 
                           
                             0 
                             , 
                             0 
                             , 
                             
                               Gz 
                               0 
                             
                           
                           ) 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 
                                   cos 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   γ 
                                 
                               
                               
                                 0 
                               
                               
                                 
                                   
                                     - 
                                     sin 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   γ 
                                 
                               
                             
                             
                               
                                 
                                   sin 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   β 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   sin 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   γ 
                                 
                               
                               
                                 
                                   cos 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   β 
                                 
                               
                               
                                 
                                   sin 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   β 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   cos 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   γ 
                                 
                               
                             
                             
                               
                                 
                                   cos 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   β 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   sin 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   γ 
                                 
                               
                               
                                 
                                   
                                     - 
                                     sin 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   β 
                                 
                               
                               
                                 
                                   cos 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   β 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   cos 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   γ 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
                 
                   
                     
                       = 
                       
                         
                           Gz 
                           0 
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               β 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               γ 
                             
                             , 
                             
                               
                                 - 
                                 sin 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               β 
                             
                             , 
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               β 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               γ 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 7 
               
             
           
         
       
     
   
   When Eq. 7 is simplified, the relation between the elevation angle β and the gravitational force components gx, gy, and gz is determined as shown in the following Eq. 8. 
   
     
       
         
           
             
               
                 β 
                 = 
                 
                   arctan 
                   ⁡ 
                   
                     ( 
                     
                       - 
                       
                         gy 
                         
                           
                             
                               gx 
                               2 
                             
                             + 
                             
                               gz 
                               2 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 8 
               
             
           
         
       
     
   
   Further, the relation between the twist angle γ and the gravitational force components gx, gy, and gz is determined as shown in the following Eq. 9. 
   
     
       
         
           
             
               
                 γ 
                 = 
                 
                   { 
                   
                     
                       
                         
                           arctan 
                           ⁡ 
                           
                             ( 
                             
                               gx 
                               gz 
                             
                             ) 
                           
                         
                       
                       
                         
                           gz 
                           ≥ 
                           0 
                         
                       
                     
                     
                       
                         
                           
                             180 
                             ⁢ 
                             
                               ( 
                               deg 
                               ) 
                             
                           
                           + 
                           
                             arctan 
                             ⁡ 
                             
                               ( 
                               
                                 gx 
                                 gz 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           gz 
                           &lt; 
                           0 
                         
                       
                     
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 9 
               
             
           
         
       
     
   
   In the first angle computation, the elevation angle β and the twist angle γ are computed (or calculated) based on the gravitational force components gx, gy, and gz by use of the relations of Eqs. 8 and 9. 
   Next, the second angle computation will be described. Here, the detected geomagnetism h is obtained in the form of geomagnetism components hx, hy, and hz in the coordinate system on the cellular phone  1  (x, y, z coordinate system) as shown in the following Eq. 10. Notably, hx, hy, and hz correspond to the detection outputs of the magnetic sensors  521 - 1  to  521 - 3 , respectively.
 
 h =( hx, hy, hz )  Eq. 10
 
   The geomagnetism H in the terrestrial coordinate system (x 0 , y 0 , z 0  coordinate system) can be represented by (Hx 0 , Hy 0 , Hz 0 ). Since Hx 0 =0, the geomagnetism H can be represented as shown in Eq. 11. Notably, Hx 0 , Hy 0 , and Hz 0  are geomagnetism components along the above-described x 0 , y 0 , and z 0  axes, respectively.
 
 H =(0, Hy   0   ,Hz   0 )  Eq. 11
 
   The relation between the geomagnetism H and the detected geomagnetism h can be presented by the following Eq. 12.
 
(0,  Hy   0   , Hz   0 ) ABC =( hx, hy, hz )  Eq. 12
 
   In Eq. 12, A is a transformation formula for rotational transformation by the azimuth angle α, and is represented by the matrix shown in Eq. 13. 
   
     
       
         
           
             
               
                 A 
                 = 
                 
                   [ 
                   
                     
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           α 
                         
                       
                       
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           α 
                         
                       
                       
                         0 
                       
                     
                     
                       
                         
                           
                             - 
                             sin 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           α 
                         
                       
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           α 
                         
                       
                       
                         0 
                       
                     
                     
                       
                         0 
                       
                       
                         0 
                       
                       
                         1 
                       
                     
                   
                   ] 
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 13 
               
             
           
         
       
     
   
   The following Eq. 14 is obtained through modification of Eq. 12. Eq. 14 is an identity of (hx 1 , hy 1 , hz 1 ). Here, hx 1 , hy 1 , and hz 1  represent geomagnetism components along the x 1 , y 1 , and z 1  axes (not shown) obtained through rotational transformation of the x 0 , y 0 , and z 0  axes by the azimuth angle α about the z 0  axis.
 
(0, Hy   0   ,Hz   0 ) A =( hx,hy,hz )C −1   B   −1 ≡( hx   1   ,hy   1   ,hz   1 )  Eq. 14
 
   The following Eq. 15 is obtained from Eq. 14.
 
( hx   1   ,hy   1   ,hz   1 )=(− Hy   0  sin α,  Hy   0  cos α,  Hz   0 )  Eq. 15
 
   The relation between the azimuth angle α and the geomagnetism components hx 1  and hy 1  is obtained from Eq. 15 as shown by the following Eq. 16. 
   
     
       
         
           
             
               
                 α 
                 = 
                 
                   { 
                   
                     
                       
                         
                           arctan 
                           ⁡ 
                           
                             ( 
                             
                               
                                 - 
                                 
                                   hx 
                                   1 
                                 
                               
                               / 
                               
                                 hy 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             
                                
                               
                                 hy 
                                 1 
                               
                                
                             
                             &gt; 
                             
                                
                               
                                 hx 
                                 1 
                               
                                
                             
                           
                           , 
                         
                       
                       
                         
                           
                             hy 
                             1 
                           
                           &gt; 
                           0 
                         
                       
                     
                     
                       
                         
                           
                             90 
                             ⁢ 
                             
                               ( 
                               deg 
                               ) 
                             
                           
                           - 
                           
                             arctan 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   - 
                                   
                                     hy 
                                     1 
                                   
                                 
                                 / 
                                 
                                   hx 
                                   1 
                                 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                                
                               
                                 hy 
                                 1 
                               
                                
                             
                             &lt; 
                             
                                
                               
                                 hx 
                                 1 
                               
                                
                             
                           
                           , 
                         
                       
                       
                         
                           
                             hx 
                             1 
                           
                           &gt; 
                           0 
                         
                       
                     
                     
                       
                         
                           
                             180 
                             ⁢ 
                             
                               ( 
                               deg 
                               ) 
                             
                           
                           + 
                           
                             arctan 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   - 
                                   
                                     hx 
                                     1 
                                   
                                 
                                 / 
                                 
                                   hy 
                                   1 
                                 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                                
                               
                                 hy 
                                 1 
                               
                                
                             
                             &gt; 
                             
                                
                               
                                 hx 
                                 1 
                               
                                
                             
                           
                           , 
                         
                       
                       
                         
                           
                             hy 
                             1 
                           
                           &lt; 
                           0 
                         
                       
                     
                     
                       
                         
                           
                             270 
                             ⁢ 
                             
                               ( 
                               deg 
                               ) 
                             
                           
                           - 
                           
                             arctan 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   - 
                                   
                                     hy 
                                     1 
                                   
                                 
                                 / 
                                 
                                   hx 
                                   1 
                                 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                                
                               
                                 hy 
                                 1 
                               
                                
                             
                             &lt; 
                             
                                
                               
                                 hx 
                                 1 
                               
                                
                             
                           
                           , 
                         
                       
                       
                         
                           
                             
                               hx 
                               ⁢ 
                               
                                   
                               
                             
                             1 
                           
                           &lt; 
                           0 
                         
                       
                     
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 16 
               
             
           
         
       
     
   
   Similarly, the relation between the geomagnetism depression angle θ and the geomagnetism components hx 1 , hy 1 , and hz 1  can be presented by the following Eq. 17. 
   
     
       
         
           
             
               
                 θ 
                 = 
                 
                   arctan 
                   ⁢ 
                   
                     
                       hz 
                       1 
                     
                     
                       
                         
                           hx 
                           1 
                           2 
                         
                         + 
                         
                           hy 
                           1 
                           2 
                         
                       
                     
                   
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 17 
               
             
           
         
       
     
   
   In the second angle computation, the azimuth angle α is computed from the geomagnetism components hx, hy, and hz by use of the relations of Eqs. 14 and 16. 
   In this manner, the main control section  601  obtains the azimuth angle α and the elevation angle β by performing the first and second angle computations. However, the azimuth angle α thus obtained and the elevation angle β thus obtained are values which are calculated on the basis of the detected gravitational force g, and therefore, they are low in accuracy because of influence of errors produced as a result of movement of the cellular phone  1 . Accordingly, the main control section  601  stores the thus-obtained azimuth angle α and elevation angle β as reference values (α 0 , β 0 ), and ends step S 102 . Notably, in the case where the calculated twist angle γ falls within the range of −10 degree to +10 degrees, the values (α 0 , β 0 ) may be stored as final detection values, and step S 102  and subsequent steps may be omitted. 
   Next, the main control section  601  performs the second computation (S 103 ). In this second computation, the main control section  601  obtains the azimuth angle α and the elevation angle β from the detected geomagnetism h obtained in step S 101  and the separately obtained geomagnetism depression angle θ. 
   Prior to explanation of the second computation, the horizontal component Hy 0  and the vertical component Hz 0  of the geomagnetism H can be represented by the following Eq. 18 by use of the geomagnetic intensity Hg and the geomagnetism depression angle θ.
 
 H =(0,  Hy   0   , Hz   0 )= Hg (0, cos θ, sin θ)  Eq. 18
 
   The relation between the geomagnetism H and the detected geomagnetism h can be represented by the following Eq. 19.
 
(0,  Hy   0   , Hz   0 ) AB =( hx, hy, hz )  Eq. 19
 
   In Eq. 19, AB is a composite transformation formula for conversion between the x, y, z coordinate system and the x 0 , y 0 , z 0  coordinate system, and is represented by the matrix of Eq. 20, which is obtained from Eqs. 4 and 13. 
   
     
       
         
           
             
               
                 AB 
                 = 
                 
                   [ 
                   
                     
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           α 
                         
                       
                       
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           α 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                         
                       
                       
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           α 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                         
                       
                     
                     
                       
                         
                           
                             - 
                             sin 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           α 
                         
                       
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           α 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                         
                       
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           α 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                         
                       
                     
                     
                       
                         0 
                       
                       
                         
                           
                             - 
                             sin 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                         
                       
                       
                         
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           β 
                         
                       
                     
                   
                   ] 
                 
               
             
             
               
                 Eq 
                 . 
                 
                     
                 
                 ⁢ 
                 20 
               
             
           
         
       
     
   
   The following Eq. 21 is derived from Eqs. 18 and 19.
 
 Hg (0, cos θ, sin θ) AB =( hx,hy,hz )  Eq. 21
 
   That is, when the geomagnetism depression angle θ and the geomagnetism components hx, hy, and hz are given, simultaneous equations of the azimuth angle α and the elevation angle β can be obtained from Eqs. 20 and 21. 
   In the second computation, the main control section  601  utilizes the simultaneous equations of the azimuth angle α and the elevation angle β using the geomagnetism depression angle θ (obtained at step  202 ) and the geomagnetism components hx, hy, and hz (obtained at S 201 ) to obtain (calculate) the azimuth angle α and the elevation angle β by solving the simultaneous equations. However, solutions of the simultaneous equations are not necessarily unique, and in some cases, two or more sets of solutions are obtained. 
   When two or more sets of solutions are obtained, the main control section  601  stores the solutions as candidate values (α 1 , β 1 ), (α 2 , β 2 ) and soon to end the step S 103 . When the result of the second computation shows that only one set of solutions is obtained (S 104 : No), the solutions are stored as detection values α and β (i.e., final detection values α and β to be output), and the operation ends. When two or more sets of solutions are obtained (S 104 : Yes), the main control section  601  performs comparison and selection processing (S 105 ). 
   In this comparison and selection processing, the main control section  601  compares the above-described reference values (α 0 , β 0 ) and the candidate values (α 1 , β 1 ), (α 2 , β 2 ) and so on, and it selects one set of candidate values containing an elevation angle which is closer to the elevation angle β 0  of the reference values than an elevation angle contained in the other set(s). That is, the selected values contain the elevation angle which is closest to the elevation angle β 0  of the reference values among the other elevation angle(s) of the candidate values. The main control section  601  stores the thus selected candidate value set as detection values (α, β) (i.e., the final detection values α and β to be output). Since the thus obtained-values α and β (through the second computation) are based on the geomagnetism depression angle θ and the geomagnetism components hx, hy, and hz, they do not involve errors stemming from movement of the cellular phone  1 . Accordingly, the thus-obtained (detection) values α and β are highly accurate. 
   Next, processing for obtaining the geomagnetism depression angle θ will be described. 
     FIG. 6  is a flowchart showing an example of processing for obtaining the geomagnetism depression angle θ. The processing will be described with reference to  FIGS. 1 and 6 . The main control section  601  starts the processing for obtaining the geomagnetism depression angle θ in response to a trigger which is appropriately set. In this processing, as in the above-described processing for detecting azimuth and inclination angle, the main control section  601  obtains the detected gravitational force g from the acceleration sensor section  510  and obtains the detected geomagnetism h from the magnetic sensor section  520  (S 201 ). Subsequently, the main control section  601  obtains the geomagnetism depression angle θ from (on the basis of) the gravitational force components gx, gy, and gz and the geomagnetism components hx, hy, and hz, by use of the relations represented by Eqs. 8 and 9 as well as the relations represented by Eqs. 14 and 17 (S 202 ). This step corresponds to geomagnetism-depression-angle computation means for calculating a value corresponding to the geomagnetism depression angle θ by performing coordinate conversion of the detected geomagnetism components h by use of the detected gravitational force components g. The main control section  601  stores and keeps (or accumulates) the obtained geomagnetism depression angle θ as a rough value θ 0  of the geomagnetism depression angle, which value involves errors stemming from the acceleration sensors  510 - 1  to  510 - 3  (S 203 ). 
   After that, the main control section  601  performs average calculation processing (S 205 ) in response to a trigger generated when, for instance, the data of value θ 0  is accumulated by a predetermined amount (that is, an amount of the data of value θ 0  becomes equal to a predetermined amount) (S 204 ). In this average calculation processing, the main control section  601  calculates the mean value of the accumulated (stored) values θ 0  of the geomagnetism depression angle so as to eliminate errors stemming from the acceleration sensors  510 - 1  to  510 - 3  caused by movement of the cellular phone  1  (S 205 ) in order to obtain the geomagnetism depression angle θ to be used at the step of S 103  described before. The steps of S 203 , S 204  and S 205  corresponds to averaging means for accumulating the value corresponding to the geomagnetism depression angle and averaging the accumulated values to store the averaged value for use as the geomagnetism depression angle. 
   At this time, the main control section  601  may select only the values θ 0  within a predetermined deviation range with respect to the current average value θ, and use only the selected values θ 0  as data to undergo the average calculation (e.g., the main control section  601  may calculate a new average value θ based on the thus-selected values θ 0 ). In this case, values θ 0  involving significant errors stemming from the acceleration sensors  510 - 1  to  510 - 3  can be eliminated, so that a more accurate value of the geomagnetism depression angle θ can be obtained. 
   One of examples for accumulating (or storing) the geomagnetism depression angle θ (the rough value θ 0 ) is described, hereinafter. When the main control section  601  stores the obtained geomagnetism depression angle θ as a rough value θ 0 , it simultaneously obtains data representing current date and time (data of date and time) from the clock section  304  and stores the obtained data of date and time together with the value θ 0  into a table (a geomagnetism depression angle table). This operation corresponds to date and time data storing means for obtaining data of date and time when the value corresponding to the geomagnetism depression angle is obtained by the geomagnetism-depression-angle computation means and for storing the obtained data of date and time together with the value corresponding to the geomagnetism depression angle into a table. 
     FIG. 7  shows an example of the geomagnetism depression angle table for storing (or accumulating) the geomagnetism depression angle θ 0  and the data of date and time. When the number of the data stored in the geomagnetism depression angle table reaches a predetermined number n, the main control section  601  again obtains data representing current date and time (date and time of the present timing) from the clock section  304 . 
   Subsequently, the main control section  601  compares data representing current date and time with the data of date and time stored together with the value θ 0  in the geomagnetism depression angle table to determine whether or not the geomagnetism depression angle table contains data (i.e., the value θ 0 ) stored at the timing which is prior to the current date and time by a predetermined amount of time or more. If there is no data (i.e., the value θ 0 ) stored at the timing which is prior to the current date and time by the predetermined amount of time or more in the table, the main control section  601  performs the average calculation processing of step S 205 . 
   On the other hand, if there is data (i.e., the value θ 0 ) stored at the timing which is prior to the current date and time by the predetermined amount of time or more in the table, the main control section  601  deletes (or eliminates) such data including the value θ 0  from the table, and then returns to step S 201  to continue to obtain the data. 
   It should be noted that the above described processing may be referred to as the “determination processing for selecting data”. The determination processing for selecting data corresponds to data selecting means for selecting the stored values corresponding to the geomagnetism depression angle in the table used for obtaining (or calculating) the averaged value by eliminating the stored value corresponding to the geomagnetism depression angle which was stored at the timing which is prior to the current date and time by a predetermined amount of time or more. 
   It should also be noted that the main control section  601  does not clear (or delete) the selected data stored in the geomagnetism depression angle table when performing the average calculation processing of step S 205 , and can thereby validly utilize the geomagnetism depression angle θ 0  obtained in the past. Further, the main control section  601  can utilize only the data including the value θ 0  stored within the predetermined amount of time from the current date and time, by performing the determination processing for selecting data in which the main control section  601  uses the above-described data of date and time. Thus, accuracy of the geomagnetism depression angle θ can be improved. 
   Another example for accumulating (or storing) the geomagnetism depression angle θ (the rough value θ 0 ) is described, hereinafter. 
   The main control section  601  may obtain current position data (latitude and longitude, or φ and λ) from the GPS reception section  402  and store the currently obtained geomagnetism depression angle θ as a rough value θ 0  together with the current position data (and more preferably, together with the data of current date and time) into the geomagnetism depression angle table. This operation corresponds to position data storing means for obtaining position data when the value corresponding to the geomagnetism depression angle is obtained by the geomagnetism-depression-angle computation means and for storing the obtained position data together with the value corresponding to the geomagnetism depression angle into a table. 
   In this example, as the way of the determination processing for selecting data described above, the main control section  601  obtains current position data and compares the current position data with the position data stored together with the value θ 0  in the geomagnetism depression angle table to delete the data including the value θ 0  from the geomagnetism depression angle table (or not to utilize such data in the average calculation processing of step S 205 ), the data indicating that the value θ 0  corresponding to the data was stored at a position apart from the current position by a predetermined distance or longer. This operation corresponds to data selecting means for selecting the stored values corresponding to the geomagnetism depression angle in the table used for obtaining the averaged value by eliminating the stored value corresponding to the geomagnetism depression angle which was stored at a position apart from the current position by a predetermined distance or longer.  FIG. 8  shows an example of the geomagnetism depression angle table for storing (or accumulating) the geomagnetism depression angle θ 0  and the position data together with the data of date and time. 
   Next, another processing for obtaining the geomagnetism depression angle θ will be described with reference to  FIG. 1 . 
   The main control section  601  performs the processing for obtaining the geomagnetism depression angle θ, for example, at the beginning of step S 103  (see  FIG. 5 ) of the processing for detecting azimuth and inclination angle. In this obtaining processing, the main control section  601  firstly obtains current position data φ and λ from the GPS receiver  402 . Notably, φ represents the latitude and λ represent the longitude. The main control section  601  then computes the geomagnetism depression angle θ from the position data φ and λ by use of the following Eq. 22.
 
θ=51°03′.804+73′.745Δφ−9′.472Δλ−0′.771Δφ 2 −0′.459ΔφΔλ+0′.359Δλ 2    Eq. 22
 
   Notably, this equation is for the year 2000, and Δφ and Δλ can be obtained as follows:
 
Δφ=φ−37°  N 
 
Δλ=λ−138°  E. 
 
   Eq. 22 is an approximated quadratic equation for representing distribution of geomagnetism depression angle θ with respect to the latitude and the longitude. Since the coefficients of the terms of Eq. 22 change with movement of the magnetic poles, accuracy is maintained through, for example, updating at regular intervals, such as once a year. For instance, data of the coefficients can be downloaded to portable terminal device (or the cellular phone  1 ) from a server for the update. Further, depending on the accuracy required for obtaining the geomagnetism depression angle θ, the third and subsequent terms of Eq. 22 may be omitted; i.e., there may be used an approximated linear equation for representing the geomagnetism depression angle θ by the longitude φ. 
   Alternatively, it is preferable that a conversion table for converting the position data φ and λ to the geomagnetism depression angle θ be previously prepared on the basis of Eq. 22 and stored in the ROM  602 , and the main control section  601  obtain the geomagnetism depression angle θ based on the obtained position data φ and λ with reference to the conversion table. In this case, since the main control section  601  can obtain the geomagnetism depression angle θ without use of the detected gravitational force g from the magnetic sensor section  520 , the main control section  601  can perform accurate computation which does not involve errors stemming from the acceleration sensors  510 - 1  to  510 - 3 . Further, with this configuration, the geomagnetism depression angle θ can be obtained through simple computation. 
   Various embodiments of the present invention have been described in detail above. However, the present invention is not limited to the embodiments, and the present invention may include modifications without departing from the scope of the present invention. For example, in the case where the present invention is applied to a cellular phone or a like device which has a function of communicating with a relay station, a server, or the like, the relay station, the server, or the like may be designed to have a function of sending the position data φ and λ or the geomagnetism depression angle θ and send the data to the cellular phone in response to a request from the cellular phone. This configuration is advantageous in that each terminal (i.e., each of the cellular phone) can obtain accurate values of the geomagnetism depression angle θ particularly in the narrow band radio communication system such as PHS (Personal Handyphone System (registered trademark)). 
   In the above-described embodiment, the main control section  601  is a control section using a CPU. However, the main control section  601  may be formed by use of a BBP (base band processor) or a combination of a BBP (as a main processor) and a DSP (digital signal processor; as a sub processor) which performs modulation and demodulation of communication signals and the like. 
   Programs to be incorporated into the BBP and/or the DSP may be recorded on a computer-readable recording medium for distribution. The programs may be distributed in a form which realizes a portion of the above-described functions. For example, the program may be distributed in the form of application software which utilizes the basic functions provided by an operation system (OS). Moreover, the program may be distributed in the form of a so-called differential program which realizes predetermined functions through combination with programs of existing systems already stored in computer systems. 
   The term “computer-readable recording medium” encompasses not only recording media such as transportable magnetic disks and magneto-optical disks, but also storage apparatuses such as hard disk drives and other nonvolatile storage apparatuses. Moreover, the above-mentioned programs may be provided from other computer systems via an arbitrary transmission medium such as the Internet or other types of networks. In this case, the term “computer-readable recording medium” encompasses a device which holds programs on the transmission medium for a certain period of time; such as a volatile memory in a computer system which serves as a host or a client on a network. 
   The configuration in which the control section is formed by a co-processor scheme by use of a BBP and/or a DSP has been described; however, it may be the case that at least a portion of the processors are formed by hardware circuits such as FPGA (field programmable gate alley). As in the case of the above-described programs, data of circuit programs to be incorporated into the FPGA can be distributed in various manners.