Patent Publication Number: US-2011066372-A1

Title: Navigation device, navigation method, and mobile phone having navigation function

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a navigation device, a navigation method, and a mobile phone having a navigation function, which are suitable for, for example, a portable navigation device. 
     2. Description of the Related Art 
     Existing navigation devices receive position signals (hereinafter referred to as GPS signals) from a plurality of global positioning system (GPS) satellites and calculate the present position of a vehicle on the basis of the GPS signals. 
     However, when a vehicle in which the navigation device is placed is in a tunnel or an underground parking garage, it is difficult for the navigation device to receive GPS signals from GPS satellites and to calculate the present position on the basis of the GPS signals. 
     Even when it is difficult to receive GPS signals, some navigation devices calculate the velocity in the direction of travel of the vehicle on the basis of the acceleration in a horizontal direction perpendicular to the direction of travel and the angular velocity around the vertical axis perpendicular to the direction of travel when the vehicle is cornering, and thereby calculate the present position of the vehicle on the basis of the velocity in the direction of travel (see, for example, Japanese Unexamined Patent Application Publication No. 2008-76389). 
     Some navigation devices determine whether or not the present position of the vehicle is in a tunnel, and, if the present position is in a tunnel, highlights the tunnel on a map so as to indicate that the vehicle is passing through the tunnel and prevent a user to lose track of the present position (see, for example, Japanese Unexamined Patent Application Publication No. 6-317650). 
     SUMMARY OF THE INVENTION 
     The navigation device described in Japanese Unexamined Patent Application Publication No. 6-317650 only highlights the tunnel so as to indicate that the vehicle is passing through the tunnel, and it is difficult for the navigation device to accurately indicate the present position of the vehicle. 
     The present invention provides a navigation device, a navigation method, and a mobile phone having a navigation function, which can precisely indicate the present position of a moving body under conditions when it is difficult to receive GPS signals. 
     According to an embodiment of the present invention, there is provided a navigation device including position measuring means that measures a present position on the basis of satellite signals received from satellites; map displaying means that reads a local map including the present position from storage means and displays the local map on display means; present position notifying means that generates a mark and displays the mark on the local map, the mark representing the present position and having a predetermined shape; estimated present position acquiring means that acquires an estimated present position by estimating the present position in a communication environment in which the satellite signals are unreceivable; and control means that reads attribute information about a next link that is next to a present link including the present position and, if the control means determines that the next link is an area in which a reception sensitivity for the satellite signals is low, does not fix the mark and continuously displays the mark on the local map in accordance with the estimated present position instead of using the present position measured by the position measuring means after the present position has moved from the present link to the next link. 
     With the navigation device, if it is determined that the next link is an area in which the reception sensitivity for the satellite signals is low, after the present position has moved from the present link to the next link, the mark is not fixed and continues to be displayed on the local map in accordance with the estimated present position, whereby the present position of a moving body can be more accurately displayed than the case in which the mark is fixed and displayed. 
     According to an embodiment of the present invention, there is provided a navigation method including the steps of measuring a present position on the basis of satellite signals received from satellites by using predetermined position measuring means; reading a local map including the present position from storage means and displaying the local map on display means by using predetermined map reading means; generating and displaying a mark on the local map by using predetermined present position notifying means, the mark representing the present position and having a predetermined shape; acquiring an estimated present position by estimating the present position by using predetermined estimated present position acquiring means in a communication environment in which the satellite signals are unreceivable; and performing control, by using predetermined control means, so as to read attribute information about a next link next to a present link including the present position and, if the control means determines that the next link is an area in which a reception sensitivity for the satellite signals is low, so as not to fix the mark and so as to continuously display the mark on the local map in accordance with the estimated present position instead of using the present position measured by the position measuring means after the present position has moved from the present link to the next link. 
     With the method, if it is determined that the next link is an area in which the reception sensitivity for the satellite signals is low, after the present position has moved from the present link to the next link, the mark is not fixed and continues to be displayed on the local map in accordance with the estimated present position, whereby the present position of a moving body can be more accurately displayed than the case in which the mark is fixed and displayed. 
     According to an embodiment of the present invention, there is provided a mobile phone having a navigation function, the mobile phone including a mobile phone unit; and a navigation device including position measuring means that measures a present position on the basis of satellite signals received from satellites, map displaying means that reads a local map including the present position from storage means and displays the local map on display means, present position notifying means that generates a mark and displays the mark on the local map, the mark representing the present position and having a predetermined shape, estimated present position acquiring means that acquires an estimated present position by estimating the present position in a communication environment in which the satellite signals are unreceivable, and control means that reads attribute information about a next link that is next to a present link including the present position and, if the control means determines that the next link is an area in which a reception sensitivity for the satellite signals is low, does not fix the mark and continuously displays the mark on the local map in accordance with the estimated present position instead of using the present position measured by the position measuring means after the present position has moved from the present link to the next link. 
     With the mobile phone having the navigation function, if it is determined that the next link is an area in which the reception sensitivity for the satellite signals is low, after the present position has moved from the present link to the next link, the mark is not fixed and continues to be displayed on the local map in accordance with the estimated present position, whereby the present position of a moving body can be more accurately displayed than the case in which the mark is fixed and displayed. 
     The embodiments of the present invention realize a navigation device, a navigation method, and a mobile phone having a navigation function, with which, if it is determined that the next link is an area in which the reception sensitivity for the satellite signals is low, after the present position has moved from the present link to the next link, the mark is not fixed and continues to be displayed on the local map in accordance with the estimated present position, whereby the present position of a moving body can be more accurately displayed than the case in which the mark is fixed and displayed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating the overall structure of a PND; 
         FIG. 2  is a diagram illustrating the definition of the coordinate system associated with the PND; 
         FIG. 3A  is a diagram illustrating a vehicle traveling on a concave road surface, and  FIG. 3B  is a diagram illustrating the vehicle traveling on a convex road surface; 
         FIG. 4  is a diagram illustrating a vehicle traveling along a curve; 
         FIG. 5  is a diagram illustrating a method of calculating the present position using a velocity and an angle; 
         FIG. 6  is a diagram illustrating sensors included in the PND; 
         FIG. 7  is a block diagram illustrating of the circuit structure of the PND; 
         FIG. 8  is a block diagram illustrating the structure of a velocity calculator; 
         FIG. 9  is graph illustrating the relationship between a height and an angle; 
         FIGS. 10A and 10B  are graphs illustrating the angle of a road surface when a vehicle is traveling at a low velocity; 
         FIGS. 11A and 11B  are graphs illustrating the angle of a road surface when a vehicle is traveling at a high velocity; 
         FIG. 12  is a graph illustrating the angle of a road surface when a vehicle is traveling at a very low velocity; 
         FIG. 13  is a diagram illustrating a vibration due to a cradle; 
         FIG. 14  is a graph illustrating a total acceleration and a total angular velocity after being high pass filtered; 
         FIGS. 15A to 15H  are graphs illustrating the total angular velocity that has been Fourier transformed for every 4096 data points; 
         FIGS. 16A to 16H  are graphs illustrating the total acceleration that has been Fourier transformed for every 4096 data points; 
         FIGS. 17A to 17D  are graphs illustrating a comparison of low pass filtering performed on the total acceleration; 
         FIGS. 18A to 18D  are graphs illustrating a comparison of low pass filtering performed on the total angular velocity; 
         FIG. 19  is a graph illustrating the relationship between a front acceleration and a rear acceleration when the vehicle is traveling at a low velocity; 
         FIGS. 20A and 20B  are graphs illustrating the relationship between the front acceleration and the rear acceleration when the vehicle is traveling at a medium velocity and at a high velocity; 
         FIGS. 21A to 21F  are graphs illustrating a simulation result of the acceleration, the pitch rate, and the velocity when the PND is placed at three different positions; 
         FIG. 22  is a graph illustrating the relationship between the maximum value and the minimum value; 
         FIG. 23  is a graph illustrating the relationship between the velocity and the number of data points; 
         FIGS. 24A and 24B  are diagrams illustrating accelerations and pitch rates for arcs having different lengths; 
         FIG. 25  is a flowchart illustrating a process of calculating the present position using velocity calculation; 
         FIGS. 26A and 26B  are diagrams illustrating display control that fixes the present position mark in a tunnel; 
         FIGS. 27A and 27B  are diagrams illustrating display control that does not fix the present position mark in the tunnel; 
         FIG. 28  is a flowchart illustrating a process of controlling the display of the present position mark; and 
         FIG. 29  is a block diagram illustrating the circuit structure of a mobile phone having a navigation function according to another embodiment. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Hereinafter, embodiments for carrying out the present invention (hereinafter referred to as embodiments) will be described in the following order with reference to the drawings. 
     1. Embodiment 
     2. Other Embodiments 
     1. Embodiment 
     1-1. External Structure of PND 
       FIG. 1  illustrates a portable navigation device  1  (hereinafter referred to as the PND  1 ) according to an embodiment of the present invention. The PND  1  has a display  2  on a front surface thereof. The display  2  can display a map image corresponding to map data stored in, for example, a nonvolatile memory (not shown) of the PND  1 . 
     The PND  1  is supported by and is mechanically and electrically connected to a cradle  3  that is attached to a dashboard of a vehicle with a suction cup  3 A. 
     Thus, the PND  1  operates using electric power supplied by a battery of the vehicle through the cradle  3 . When the PND  1  is detached from the cradle  3 , the PND  1  operates using electric power supplied by an internal battery. 
     The PND  1  is disposed so that the display  2  extends perpendicular to the direction of travel of the vehicle.  FIG. 2  illustrates the coordinate system associated with the PND  1 . The X axis extends in the front-back direction of the vehicle, the Y axis extends in a horizontal direction perpendicular to the X axis, and the Z axis extends in the vertical direction. 
     In the coordinate system, the direction of travel of the vehicle is defined as the positive direction along the X axis, the rightward direction is defined as the positive direction along the Y axis, and the downward direction is defined as the positive direction along the Z axis. 
     1-2. Principle of Velocity Calculation 
     The fundamental principle used by the PND  1  to calculate the velocity of a vehicle on which the PND  1  is mounted will be described. 
     In practice, a road on which a vehicle travels is seldom flat, and is generally concave as illustrated in FIG.  3 A or generally convex as illustrated in  FIG. 3B . 
     In the coordinate system associated with the vehicle, the X axis extends in the front-back direction, the Y axis extends in a horizontal direction perpendicular to the X axis, and the Z axis extends in the vertical direction. 
     The PND  1  (not shown) is placed, for example, on the dashboard of the vehicle. When the vehicle travels on the concave road ( FIG. 3A ), a three-axis acceleration sensor of the PND  1  detects a downward acceleration α z  along the Z axis with a sampling frequency of, for example, 50 Hz. 
     A Y axis gyro sensor of the PND  1  detects an angular velocity ω y  around the Y axis (hereinafter referred to as a pitch rate) perpendicular to the direction of travel of the vehicle with a sampling frequency of, for example, 50 Hz. 
     For the PND  1 , the sign of the downward acceleration α z  along the Z axis is defined as positive. The sign of the pitch rate ω y  upwardly rotating, with respect to the direction of travel, along an imaginary circle that is formed along a concave road surface illustrated in  FIG. 3A  is defined as positive. 
     The PND  1  calculates the velocity of the vehicle in the direction of travel (hereinafter referred to as an autonomous velocity V) 50 times per second using the acceleration α z  detected by the three-axis acceleration sensor and the pitch rate ω y  detected by the Y axis gyro sensor in accordance with the following equation (1). 
     
       
         
           
             
               
                 
                   V 
                   = 
                   
                     
                       α 
                       z 
                     
                     
                       ω 
                       y 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     When the vehicle travels on a convex road ( FIG. 3B ), the three-axis acceleration sensor of the PND  1  detects an upward acceleration α z′  along the Z axis with a sampling frequency of, for example, 50 Hz, and the Y axis gyro sensor of the PND  1  detects a pitch rate ω y′  around the Y axis with a sampling frequency of, for example, 50 Hz. 
     The PND  1  calculates the autonomous velocity V′ of the vehicle in the direction of travel 50 times per second using the acceleration α z′  detected by the three-axis acceleration sensor and the pitch rate ω y′  detected by the Y axis gyro sensor in accordance with the following equation (2). 
     
       
         
           
             
               
                 
                   
                     V 
                     ′ 
                   
                   = 
                   
                     
                       α 
                       z 
                       ′ 
                     
                     
                       ω 
                       y 
                       ′ 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     For convenience of description here, a negative acceleration is described as the acceleration α z′ . In practice, the three-axis acceleration sensor detects the acceleration α z′  as a negative value of the acceleration α z . Likewise, a negative pitch rate is described as the pitch rate ω y′ . In practice, the Y axis gyro sensor detects the pitch rate ω y′  as a negative value of the pitch rate ω y . Therefore, in practice, the autonomous velocity V′ is also calculated as the autonomous velocity V. 
     1-3. Principle of Calculating Present Position 
     Next, the principle of calculating the present position on the basis of the autonomous velocity V, which have been calculated by using the above principle of velocity calculation, and the angular velocity around the Z axis will be described. 
     Referring to  FIG. 4 , when the vehicle is, for example, turning to the left, a Z axis gyro sensor of the PND  1  detects an angular velocity around the Z axis (hereinafter referred to as a yaw rate) ω z  with a sampling frequency of, for example, 50 Hz. 
     Referring to  FIG. 5 , the PND  1  calculates the displacement from a previous position P 0  to a present position P 1  on the basis of the autonomous velocity V at the previous position P 0  and an angle θ that is calculated by multiplying the yaw rate ω z  detected by the gyro sensor by a sampling period (in this case, 0.02 s). The PND  1  calculates the present position P 1  by adding the displacement to the previous position P 0 . 
     1-4. Sensor Structure of PND 
     Referring to  FIG. 6 , the PND  1  includes a three-axis acceleration sensor  4 , a Y axis gyro sensor  5 , a Z axis gyro sensor  6 , and a barometric pressure sensor  7 . 
     The three-axis acceleration sensor  4  detects an acceleration α x  along the X-axis, an acceleration α y  along the Y-axis, and the acceleration α z  along the Z-axis respectively as voltages. 
     The Y axis gyro sensor  5 , the Z axis gyro sensor  6 , and the barometric pressure sensor  7  respectively detect the pitch rate ω y  around the Y axis, the yaw rate ω z  the around the Z axis, and an ambient pressure PR respectively as voltages. 
     1-5. Circuit Structure of PND 
     Referring to  FIG. 7 , a controller  11  of the PND  1 , which is a central processing unit (CPU), controls the PND  1  in accordance with an operating system that is read from a memory  12  that includes a nonvolatile memory. 
     In the PND  1 , the controller  11  performs velocity calculation and other processes described below in accordance with various application programs that are read from the memory  12 . 
     In order to perform the velocity calculation and other processes, the controller  11  includes, as functional blocks, a GPS processor  21 , a velocity calculator  22 , an angle calculator  23 , a height calculator  24 , a position calculator  25 , and a navigator  26 . 
     A GPS antenna ANT of the PND  1  receives GPS signals from GPS satellites, and the GPS signals are sent to the GPS processor  21  of the controller  11 . 
     The GPS processor  21  obtains present position data NPD 1  by accurately measuring the present position of the vehicle on the basis of orbit data obtained by demodulating the GPS signals and data on the distances between the GPS satellites and the vehicle, and sends the present position data NPD 1  to the navigator  26 . 
     The navigator  26  reads map data of a region including the present position of the vehicle from the memory  12  on the basis of the present position data NPD 1 , and generates a map image including the present position, outputs the map image to the display  2 , and thereby displays the map image. 
     The three-axis acceleration sensor  4  detects the accelerations α x , α y  and α z  with a sampling frequency of, for example, 50 Hz, and sends acceleration data AD that represents the acceleration α z  to the velocity calculator  22  of the controller  11 . 
     The Y axis gyro sensor  5  detects the pitch rate ω y  with a sampling frequency of, for example, 50 Hz, and sends pitch rate data PD that represents the pitch rate ω y  to the velocity calculator  22  of the controller  11 . 
     The velocity calculator  22  calculates the autonomous velocity V 50 times per second in accordance with equation (1) using of the acceleration α z , which corresponds to the acceleration data AD supplied by the three-axis acceleration sensor  4 , and the pitch rate ω y , which corresponds to the pitch rate data PD supplied by the Y axis gyro sensor  5 , and sends velocity data VD that represents the autonomous velocity V to the position calculator  25 . 
     The Z axis gyro sensor  6  detects the yaw rate ω z  at a sampling frequency of, for example, 50 Hz, and sends yaw rate data YD that represents the yaw rate ω z  to the angle calculator  23  of the controller  11 . 
     The angle calculator  23  calculates the angle θ with which the vehicle turns to the right or to the left by multiplying the yaw rate ω z , which corresponds to the yaw rate data YD supplied by the Z axis gyro sensor  6 , by a sampling period (in this case, 0.02 s), and sends angle data DD that represents the angle θ to the position calculator  25 . 
     The position calculator  25  calculates the displacement from the previous position P 0  to the present position P 1  illustrated in  FIG. 5  on the basis of the autonomous velocity V, which corresponds to the velocity data VD supplied by the velocity calculator  22 , and the angle θ, which corresponds to the angle data DD supplied by the angle calculator  23 . 
     The position calculator  25  calculates the present position P 1  by adding the displacement to the previous position P 0 , and sends present position data NPD 2 , which represents the present position P 1 , to the navigator  26 . 
     The barometric pressure sensor  7  detects the ambient pressure PR with a sampling frequency of, for example, 50 Hz, and sends barometric pressure data PRD that represents the barometric pressure PR to the height calculator  24 . 
     The height calculator  24  calculates the height of the vehicle on the basis of the barometric pressure PR, which corresponds to the barometric pressure data PRD supplied by the barometric pressure sensor  7 , and sends height data HD that represents the height of the vehicle to the navigator  26 . 
     The navigator  26  reads map data of a region including the present position of the vehicle from the memory  12  on the basis of the present position data NPD 2  supplied by the position calculator  25  and the height data HD supplied by the height calculator  24 , generates a map image including the present position, outputs the map image to the display  2 , and thereby displays the map image. 
     1-6. Autonomous Velocity Calculation Process 
     Next, an autonomous velocity calculation process performed by the velocity calculator  22  will be described in detail. In this process, the velocity calculator  22  calculates the autonomous velocity V on the basis of the acceleration α z , which corresponds to the acceleration data AD supplied by the three-axis acceleration sensor  4 , and the pitch rate ω y , which corresponds to the pitch rate data PD supplied by the Y axis gyro sensor  5 . 
     Referring to  FIG. 8 , in order to perform the autonomous velocity calculation, the velocity calculator  22  includes, as functional blocks, a data acquirer  31 , a high pass filter  32 , a low pass filter  33 , a velocity calculating section  34 , a smoother/noise filter  35 , and a velocity output section  36 . 
     The data acquirer  31  of the velocity calculator  22  acquires the acceleration data AD supplied by the three-axis acceleration sensor  4  and the pitch rate data PD supplied by the Y axis gyro sensor  5 , and sends the acceleration data AD and the pitch rate data PD to the high pass filter  32 . 
     The high pass filter  32  removes direct-current components from the acceleration data AD and the pitch rate data PD, which are supplied by the data acquirer  31 , to generate acceleration data AD 1  and pitch rate data PD 1 , and sends the acceleration data AD 1  and the pitch rate data PD 1  to the low pass filter  33 . 
     The low pass filter  33  performs low pass filtering (described below) on the acceleration data AD 1  and the pitch rate data PD 1 , which are supplied by the high pass filter  32 , to generate acceleration data AD 2  and pitch rate data PD 2 , and sends the acceleration data AD 2  and the pitch rate data PD 2  to the velocity calculating section  34 . 
     The velocity calculating section  34  performs velocity calculation (described below) using the acceleration data AD 2  and the pitch rate data PD 2 , which are supplied by the low pass filter  33 , to generate velocity data VD 1 , and sends the velocity data VD 1  to the smoother/noise filter  35 . 
     The smoother/noise filter  35  performs smoothing and noise filtering (described below) on the velocity data VD 1 , which is supplied by the velocity calculating section  34 , to generate velocity data VD, and sends the velocity data VD to the velocity output section  36 . 
     The velocity output section  36  sends the velocity data VD, which is supplied by the smoother/noise filter  35  and represents the autonomous velocity V of the vehicle, to the position calculator  25 . 
     Thus, the velocity calculator  22  calculates the autonomous velocity V of the vehicle on the basis of the acceleration data AD supplied by the three-axis acceleration sensor  4  and the pitch rate data PD supplied by the Y axis gyro sensor  5 . 
     1-7. Low Pass Filtering 
     Next, low pass filtering, which is performed by the low pass filter  33  on the acceleration data AD 1  and the pitch rate data PD 1  supplied by the high pass filter  32 , will be described in detail. 
       FIG. 9  illustrates the relationship between a height H, which is based on the barometric pressure PR corresponding to the barometric pressure data PRD obtained by the barometric pressure sensor  7 , and an angle φ around the Y axis with respect to a horizontal direction, which is based on the pitch rate ω y  corresponding to the pitch rate data PD obtained by the Y axis gyro sensor  5 . Regarding the angle φ, the upward direction with respect to the direction of travel (the X axis) is defined as positive. 
     Referring to  FIG. 9 , there is a correlation between the height H and the angle φ as can be seen from the fact that when the height H sharply decreases from about the 12001st data point (240 s), i.e., when the vehicle travels downhill, the angle φ sharply decreases from about 0.5 deg to about −2.5 deg. 
     When the height H changes, the angle φ changes in accordance with the change in the height H. Thus, the PND  1  can detect the undulation of a road surface in the direction of travel of the vehicle using the Y axis gyro sensor  5 . 
       FIG. 10A  illustrates the angle φ of  FIG. 9 .  FIG. 10B  illustrates the angle φ of  FIG. 10A  from the 5001st data point to the 6001st data point. During this time, the vehicle travels at a low velocity that is lower than 20 km/h. As can be seen from  FIG. 10B , the angle φ oscillates once to twice per second. 
     Thus, when a vehicle is traveling at a low velocity lower than 20 km/h, the PND  1  mounted on the vehicle detects the angle φ, which is based on the pitch rate ω y  corresponding to the pitch rate data PD obtained by the Y axis gyro sensor  5 , as an oscillation having a frequency in the range of 1 to 2 Hz. 
     As with  FIG. 10A ,  FIG. 11A  illustrates the angle φ of  FIG. 9 .  FIG. 11B  illustrates the angle φ of  FIG. 11A  from the 22001st data point to the 23001st data point. During this time, the vehicle travels at a high velocity that is higher than 60 km/h. 
     As can be seen from  FIG. 11B , when the vehicle is traveling at a high velocity higher than 60 km/h, the PND  1  also detects the angle φ, which is based on the pitch rate ω y  corresponding to the pitch rate data PD obtained by the Y axis gyro sensor  5 , as an oscillation having a frequency in the range of 1 to 2 Hz. 
     Moreover, as illustrated in  FIG. 12 , when the vehicle is traveling at a very low velocity that is lower than 10 km/h, the PND  1  also detects the angle φ, which is based on the pitch rate ω y  corresponding to the pitch rate data PD obtained by the Y axis gyro sensor  5 , as an oscillation having a frequency in the range of 1 to 2 Hz. 
     Therefore, using the Y axis gyro sensor  5 , the PND  1  detects the pitch rate ω y  as an oscillation having a frequency in the range of 1 to 2 Hz irrespective of the velocity of the vehicle. 
     The PND  1  is supported by the cradle  3 , which is attached to the dashboard of the vehicle with the suction cup  3 A. Referring to  FIG. 13 , the cradle  3  includes a body  3 B, which is disposed on the suction cup  3 A, and a PND supporter  3 D. One end of the PND supporter  3 D is supported by the body  3 B at a support point  3 C that is located at a predetermined height, and the PND  1  is supported by the PND supporter  3 D at the other end of the PND supporter  3 D. 
     Therefore, when the vehicle vibrates due to the undulation of a road surface, the PND  1  vibrates up an down around the support point  3 C of the PND supporter  3 D with, for example, an acceleration α c  and an angular velocity ω c . 
     Therefore, in practice, the three-axis acceleration sensor  4  detects an acceleration (hereinafter referred to as a total acceleration) α cz  that is the sum of the acceleration α z  along the Z axis ( FIG. 1 ), which is generated by the vibration of the vehicle due to the undulation of the road surface, and the acceleration α c , which is generated by the vibration of the PND  1  around the support point  3 C of the PND supporter  3 D. 
     The Y axis gyro sensor  5  detects an angular velocity (hereinafter referred to as a total angular velocity) ω cy  that is the sum of the pitch rate ω y  around the Y axis ( FIG. 1 ), which is generated by the vibration of the vehicle due to the undulation of the road surface, and the angular velocity ω c , which is generated by the vibration of the PND  1  around the support point  3 C of the PND supporter  3 D. 
     Therefore, the low pass filter  33  acquires the acceleration data AD 1 , which represents the total angular velocity ω cy , and the pitch rate data PD 1 , which represents the total acceleration α cz , through the data acquirer  31  and the high pass filter  32 . 
       FIG. 14  illustrates the total acceleration α cz  and the total angular velocity ω cy , which respectively correspond to the acceleration data AD 1  and the pitch rate data PD 1  that have been high pass filtered by the high pass filter  32 .  FIGS. 15A to 15F  are graphs illustrating the total angular velocity ω cy  of  FIG. 14 , which has been Fourier transformed for every 4096 data points. 
     In particular,  FIG. 15A  is a graph of the total angular velocity ω cy  of  FIG. 14  from the 1st data point to the 4096th data point, which has been Fourier transformed. Likewise,  FIGS. 15B ,  15 C, and  15 D are graphs of the total angular velocity ω cy  of  FIG. 14  from the 4097th data point to the 8192nd data point, the 8193rd data point to the 12288th data point, and the 12289th data point to the 16384th data point, respectively, each of which has been Fourier transformed. 
       FIGS. 15E ,  15 F,  15 G, and  15 H, are graphs of the total angular velocity ω cy  of  FIG. 14  from the 16385th data point to the 20480th data point, the 20481st data point to the 24576th data point, the 24577th data point to the 28672nd data point, and the 28673rd data point to the 32768th data point, respectively, each of which has been Fourier transformed. 
     As can be clearly seen from  FIGS. 15C to 15H , a frequency component in the range of 1 to 2 Hz and a frequency component of about 15 Hz have large values. 
     That is, the Y axis gyro sensor  5  of the PND  1  detects the total angular velocity ω cy  that is the sum of the pitch rate ω y , which oscillates with a frequency in the range of 1 to 2 Hz due to the aforementioned undulation of the road surface, and the angular velocity ω x , which oscillates with a frequency of about 15 Hz due to the cradle  3  that supports the PND  1 . 
       FIGS. 16A to 16F  are graphs illustrating the total acceleration α cz  of  FIG. 14 , which has been Fourier transformed for every 4096 data points. 
     In particular,  FIG. 16A  is a graph of the total acceleration α cz  of  FIG. 14  from the 1st data point to the 4096th data point, which has been Fourier transformed. Likewise,  FIGS. 16B ,  16 C, and  16 D are graphs of the total acceleration α cz  of  FIG. 14  from the 4097th data point to the 8192nd data point, the 8193rd data point to the 12288th data point, and the 12289th data point to the 16384th data point, respectively, each of which has been Fourier transformed. 
       FIGS. 16E ,  16 F,  16 G, and  16 H, are graphs of the total acceleration α cz  of  FIG. 14  from the 16385th data point to the 20480th data point, the 20481st data point to the 24576th data point, the 24577th data point to the 28672nd data point, and the 28673rd data point to the 32768th data point, respectively, each of which has been Fourier transformed. 
     Considering the fact that the total angular velocity ω cy  ( FIGS. 15C to 15H ) has the frequency component in the range of 1 to 2 Hz and the frequency component of about 15 Hz, it is estimated that the total acceleration α cz  also has a frequency component in the range of 1 to 2 Hz and a frequency component of about 15 Hz. 
     That is, the three-axis acceleration sensor  4  of the PND  1  detects the total acceleration α cz , which is the sum of the acceleration α z , which oscillates with a frequency in the range of 1 to 2 Hz due to the aforementioned undulation of the road surface, and the acceleration α c , which oscillates with a frequency of about 15 Hz due to the cradle  3  that support the PND  1 . 
     Therefore, the low pass filter  33  performs low pass filtering on the acceleration data AD 1  and the pitch rate data PD 1 , which are supplied by the high pass filter  32 , so as to remove the frequency component of about 15 Hz, i.e., the acceleration α c  and the angular velocity ω c  that are generated due to the cradle  3  that supports the PND  1 . 
       FIG. 17A  is a graph of data that is the same as that of  FIG. 16H , which is plotted with a logarithmic vertical axis.  FIGS. 17B ,  17 C and  17 D are graphs of the total acceleration α cz  from the 28673rd data point to the 32768th data point, on which infinite impulse response (IIR) filtering with a cutoff frequency of 2 Hz has been performed twice, four times, and six times, respectively, and on which Fourier transformation has been performed. 
       FIG. 18A  is a graph of data that is the same as that of  FIG. 15H , which is plotted with a logarithmic vertical axis.  FIGS. 18B ,  18 C and  18 D are graphs of the total angular velocity ω cy  from the 28673rd data point to the 32768th data point, on which infinite impulse response (IIR) filtering with a cutoff frequency of 2 Hz is performed twice, four times, and six times, respectively, and on which Fourier transformation is performed. 
     As can be seen from  FIGS. 17B to 17D  and  FIGS. 18B to 18D , the PND  1  can remove the frequency component of about 15 Hz from the acceleration data AD 1  and the pitch rate data PD 1 , which are supplied by the high pass filter  32 , by performing the IIR filtering with a cutoff frequency of 2 Hz four times or more on the acceleration data AD 1  and the pitch rate data PD 1 . 
     Therefore, the low pass filter  33  according to the embodiment performs the IIR filtering with a cutoff frequency of 2 Hz four times on the acceleration data AD 1  and the pitch rate data PD 1 , which are supplied by the high pass filter  32 , to generate acceleration data AD 2  and pitch rate data PD 2 , and sends the acceleration data AD 2  and the pitch rate data PD 2  to the velocity calculating section  34 . 
     Thus, the low pass filter  33  removes the acceleration α c , which is generated due to the vibration of the PND supporter  3 D around the support point  3 C of the cradle  3 , from the total acceleration α cz , and thereby extracts only the acceleration α z , which is generated due to the undulation of the road surface. 
     Moreover, the low pass filter  33  removes the angular velocity ω c , which is generated due to the vibration of the PND supporter  3 D around the support point  3 C of the cradle  3 , from the total angular velocity ω cy , and thereby extracts only the pitch rate ω y , which is generated due to the undulation of the road surface. 
     1-8. Autonomous Velocity Calculation 
     Next, autonomous velocity calculation performed by the velocity calculating section  34  will be described in detail. The velocity calculating section  34  calculates the autonomous velocity V on the basis of the acceleration data AD 2  and the pitch rate data PD 2  supplied by the low pass filter  33 . 
       FIGS. 19 ,  20 A, and  20 B respectively illustrate the acceleration α z  corresponding to the acceleration data AD 2 , which is generated when the vehicle is traveling at a low velocity lower than 20 km/h, at a medium velocity equal to or higher than 20 km/h and lower than 60 km/h, and at a high velocity equal to or higher than 60 km/h. For each of the velocity ranges, a case in which the PND  1  is placed on the dashboard in a front part of the vehicle and a case in which the PND  1  is placed near to the rear window in a rear part of the vehicle are illustrated. 
     In  FIGS. 19 ,  20 A, and  20 B, the acceleration α z  that is detected by the PND  1  placed in the front part of the vehicle is referred to as the front acceleration and the acceleration α z  that is detected by the PND  1  placed in the rear part of the vehicle is referred to as the rear acceleration. 
     As can be seen from  FIGS. 19 ,  20 A, and  20 B, the phase of the rear acceleration is delayed with respect to the phase of the front acceleration irrespective of the velocity of the vehicle. This phase delay is approximately equal to the wheelbase divided by the velocity of the vehicle, the wheelbase being the distance between the front wheel axis and the rear wheel axis of the vehicle. 
       FIGS. 21A to 21C  respectively illustrate an example of a simulation result representing the relationship between the acceleration α z  corresponding to the acceleration data AD 2  and the pitch rate ω y  corresponding to the pitch rate data PD 2  when the PND  1  is placed on the dashboard (at a position away from the front wheel axis by 30% of the wheelbase), at the center, and at a position above the rear wheel axis of the vehicle.  FIGS. 21D to 21F  illustrate the autonomous velocity V calculated using equation (1) on the basis of the acceleration α z  and the pitch rate ω y  obtained from the simulation result illustrated in  FIGS. 21A to 21C . 
     In this simulation, it is assumed that a vehicle having a wheelbase of 2.5 m travels at a velocity of 5 m/s on a road surface having a sinusoidal undulation with an amplitude of 0.1 m and a wavelength of 20 m. 
     As can be seen from  FIGS. 21A to 21C , the phase of the acceleration α z  is delayed when the position of the PND  1  is moved toward the back of the vehicle. In contrast, the phase of the pitch rate ω y  is not delayed irrespective of the position of the PND  1  on the vehicle. 
     Therefore, as illustrated in  FIG. 21B , the phase difference between the acceleration α ,  and the pitch rate ω y  is negligible when the PND  1  is placed at the center of the vehicle. Thus, as illustrated in  FIG. 21E , the autonomous velocity V, which is calculated using equation (1), is substantially constant. 
     However, as illustrated in  FIGS. 21A and 21C , when the position of the PND  1  is moved forward or backward from the center of the vehicle, the phase difference between the acceleration α z  and the pitch rate ω y  increases. Therefore, as illustrated in  FIGS. 21D and 21F , due to the phase difference between the acceleration α z  and the pitch rate ω y , the autonomous velocity V calculated using equation (1) has a larger error than the autonomous velocity V calculated when the PND  1  is placed at the center of the vehicle ( FIG. 21E ). 
     In particular, when the autonomous velocity V of the vehicle is lower than 20 km/h, the phase difference between the acceleration α z  and the pitch rate ω y  is large, so that the calculation error of the autonomous velocity V increases. 
     Therefore, referring to  FIG. 22 , the velocity calculating section  34  extracts the maximum value and the minimum value of the acceleration α z , which corresponds to the acceleration data AD 2  supplied by the low pass filter  33 , from a range of 25 or 75 data points centered around a data point Pm that corresponds to the previous position P 0  ( FIG. 3 ). The maximum and minimum values will be referred to as the maximum acceleration α z,max  and the minimum acceleration α z,min , respectively. 
     Moreover, the velocity calculating section  34  extracts the maximum value and the minimum value of the pitch rate ω y , which corresponds to the pitch rate data PD 2  supplied by the low pass filter  33 , from a range of 25 or 75 data points centered around the data point Pm. The maximum and minimum values will be referred to as the maximum pitch rate ω y,max  and the minimum pitch rate ω y,min , respectively. 
     That is, the velocity calculating section  34  extracts the maximum and minimum accelerations α z,max  and α z,min  and the maximum and minimum pitch rates ω y,max  and ω y,min  from a range that is larger than the largest possible phase difference that may be generated between the acceleration α z  and the pitch rate ω y . 
     The velocity calculating section  34  calculates the autonomous velocity V in the direction of travel at the previous position P 0  ( FIG. 3 ) in accordance with the following equation (3), which is rewritten from equation (1), using the maximum and minimum accelerations α z,max  and α z,min , which are extracted from the acceleration data AD 2 , and the maximum and minimum pitch rates ω y,max  and ω y,min , which are extracted from pitch rate data PD 2 , to generate velocity data VD 1 , and sends the velocity data VD 1  to the smoother/noise filter  35 . 
     
       
         
           
             
               
                 
                   V 
                   = 
                   
                     
                       
                         α 
                         
                           z 
                           , 
                           max 
                         
                       
                       - 
                       
                         α 
                         
                           z 
                           , 
                           min 
                         
                       
                     
                     
                       
                         ω 
                         
                           y 
                           , 
                           max 
                         
                       
                       - 
                       
                         ω 
                         
                           y 
                           , 
                           min 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Thus, even when there is a phase difference between the acceleration α z  and the pitch rate ω y , the velocity calculating section  34  can calculate, by using equation (3), the autonomous velocity V from which the effect of the phase delay is removed. 
     Referring to  FIG. 23 , when calculating the autonomous velocity V in the direction of travel at the previous position P 0  while the vehicle is accelerating, the velocity calculating section  34  uses a range of 25 data points if the autonomous velocity V n-1  at the second previous position (not shown) (hereinafter referred to as a former velocity) is in the range of 0 km/h to 35 km/h, and the velocity calculating section  34  uses a range of 75 data points if the former velocity V n-1  is higher than 35 km/h. 
     When calculating the autonomous velocity V in the direction of travel at the previous position P 0  while the vehicle is decelerating, the velocity calculating section  34  uses a range of 75 data points if the former velocity V n-1  is equal to or higher than 25 km/h, and the velocity calculating section  34  uses a range of 25 data points if the former velocity V n-1  is lower than 25 km/h. 
     Thus, the velocity calculating section  34  switches the data range between 25 data points and 75 data points in accordance with the autonomous velocity V when extracting the maximum and minimum accelerations a α z,max  and α z,min  and the maximum and minimum pitch rates ω y,max  and ω y,min . 
     When the autonomous velocity V of the vehicle is equal to or lower than, for example, 25 km/h, the acceleration α z  and the pitch rate ω y  change sharply in response to a slight change in the road surface. Therefore, the velocity calculating section  34  uses a narrow data range in order to deal with a sharp change. 
     When the autonomous velocity of the vehicle is equal to or higher than 35 km/h, the influence of a suspension of the vehicle is large and the acceleration α z  and the pitch rate ω y  change slowly. Therefore, the velocity calculating section  34  sets a wide data range in order to deal with a slow change. 
     Thus, the velocity calculating section  34  changes the data range, from which the maximum and minimum accelerations α z,max  and α z,min  and the maximum and minimum pitch rates ω y,max  and ω y,min  are extracted, in accordance with the autonomous velocity V of the vehicle, so that the conditions of the road surface and the vehicle that change in accordance with the autonomous velocity V can be taken into account, whereby the autonomous velocity V can be calculated more precisely. 
     Moreover, when calculating the maximum and minimum accelerations α z,max  and α z,min  and the maximum and minimum pitch rates ω y,max  and ω y,min , the velocity calculating section  34  changes the data range with a hysteresis between the case when the vehicle is accelerating and the case when the vehicle is decelerating. 
     Thus, frequency of changing of the data range around a switching velocity is reduced as compared to a case in which the velocity calculating section  34  calculates the autonomous velocity V by changing the data range without a hysteresis. As a result, the velocity calculating section  34  can reduce the calculation error of the autonomous velocity V that may occur due to frequent switching of the data range, whereby the autonomous velocity V can be calculated more precisely. 
     1-9. Smoothing and Noise Filtering 
     Next, smoothing and noise filtering performed by the smoother/noise filter  35  on the velocity data VD 1 , which has been calculated by the velocity calculating section  34 , will be described in detail. 
     The smoother/noise filter  35  performs low pass filtering, which is first-order IIR with a variable cutoff frequency, on the velocity data VD 1  supplied by the velocity calculating section  34 . 
     To be specific, when calculating the autonomous velocity V in the direction of travel at the previous position P 0 , the smoother/noise filter  35  determines the cutoff frequency on the basis of the former velocity V. 
     When the velocity of the vehicle is equal to or higher than, for example, 60 km/h, the autonomous velocity V calculated by the velocity calculating section  34  of the PND  1  includes a large amount of noise, and thereby the autonomous velocity V considerably deviates. Therefore, the smoother/noise filter  35  uses a low pass filter having a low cutoff frequency when the former velocity V n-1  is equal to or higher than 60 km/h. 
     In contrast, the smoother/noise filter  35  uses a low pass filter having a high cutoff frequency when the former velocity V n-1  is lower than 60 km/h. 
     When the autonomous velocity V calculated by the velocity calculating section  34  is lower than, for example, 10 km/h, the pitch rate ω y , which is the denominator of equation (1) or (3), may be small, so that the autonomous velocity V calculated using the equation (1) or (3) may become considerably higher than the real value. 
     Therefore, the smoother/noise filter  35  acquires the acceleration data AD 2  and the pitch rate data PD 2 , which have been low pass filtered, from the low pass filter  33 . If the pitch rate ω y  corresponding to the pitch rate data PD 2  is lower than a predetermined threshold, the smoother/noise filter  35  determines that the autonomous velocity V is excessively high and sets the value of the autonomous velocity V, after being low pass filtered, at 0. 
     If an arc B 1  of the undulation of a road surface is larger than the wheelbase W of the vehicle as illustrated in  FIG. 24A , the PND  1  can accurately calculate the autonomous velocity V using the aforementioned fundamental principle. 
     However, if an arc B 2  of the undulation of a road surface is smaller than the wheelbase W of the vehicle as illustrated in  FIG. 24B , an acceleration α b  in a vertical direction of the vehicle and an angular velocity ω b  around the Y axis centered around the rear wheel of the vehicle are generated when the front wheel of the vehicle rolls over the undulation. 
     At this time, the three-axis acceleration sensor  4  and the Y axis gyro sensor  5  of the PND  1  detect the acceleration α b  and the angular velocity ω b  ( FIG. 24B ), instead of detecting the acceleration α z  and the pitch rate ω y  ( FIG. 24A ), which are generated by a vibration having a frequency in the range of 1 to 2 Hz due to the undulation of the road surface. 
     The acceleration α b  is larger than the acceleration α z , which is generated when the arc B 1  of the undulation of the road surface is larger than the wheelbase W of the vehicle. The angular velocity ω b  is higher than the pitch rate ω y , which is generated when the arc B 1  of the undulation of the road surface is larger than the wheelbase W of the vehicle. 
     A velocity V b  (hereinafter also referred to as a small-arc velocity) is calculated using equation (1) or (3) on the basis of the acceleration α b  and the angular velocity ω b , which are generated when the arc B 2  of the undulation of the road surface is smaller than the wheelbase W of the vehicle. 
     Because the acceleration α b  changes more than the angular velocity ω b  does, the velocity V b  is considerably higher than the autonomous velocity V, which is calculated using equation (1) or (3) on the basis of the acceleration α z  and the angular velocity ω y  generated when the arc B 1  of the undulation of the road surface is larger than the wheelbase W of the vehicle. 
     Therefore, when the arc B 2  of the undulation of the road surface is smaller than the wheelbase W of the vehicle, the velocity calculator  22  of the PND  1  calculates the small-arc velocity V b  using the acceleration α b  and the angular velocity ω b , which leads to calculating the autonomous velocity V as an excessively high value. 
     The smoother/noise filter  35  acquires, from the low pass filter  33 , the acceleration data AD 2  and the pitch rate data PD 2 , which have been low pass filtered, and determines whether or not the acceleration α z  corresponding to the acceleration data AD 2  and pitch rate ω y  corresponding to the pitch rate data PD 2  are higher than predetermined thresholds. 
     If the acceleration α z  corresponding to the acceleration data AD 2  and the pitch rate ω y  corresponding to the pitch rate data PD 2  are higher than the predetermined thresholds, the smoother/noise filter  35  determines that the autonomous velocity V is excessively high and uses the former velocity V n-1  instead of the autonomous velocity V that has been low pass filtered. That is, the smoother/noise filter  35  uses the former velocity V n-1  if the autonomous velocity V is excessively high when the velocity of the vehicle is not very low, because it is likely that the autonomous velocity V is not accurate in such a case. 
     Thus, if the autonomous velocity V that has been low pass filtered is excessively high, the smoother/noise filter  35  sets the autonomous velocity V at 0 when the velocity of the vehicle is very low and sets the autonomous velocity V at the former velocity V n-1  when the velocity of the vehicle is not very low, whereby the autonomous velocity V can be calculated more accurately. 
     1-10. Process of Position Calculation Using Autonomous Velocity Calculation 
     Referring to the flowchart of  FIG. 25 , a process of position calculation using the aforementioned autonomous velocity calculation, which is performed by the controller  11  of the PND  1 , will be described. 
     The controller  11  starts the process from a start step of a routine RT 1 . In step SP 1 , the data acquirer  31  of the velocity calculator  22  acquires the acceleration data AD detected by the three-axis acceleration sensor  4  and the pitch rate data PD detected by the Y axis gyro sensor  5 , and the controller  11  proceeds to step SP 2 . 
     In step SP 2 , the high pass filter  32  of the velocity calculator  22  of the controller  11  performs high pass filtering on the acceleration data AD and the pitch rate data PD, and the controller  11  proceeds to step SP 3 . 
     In step SP 3 , the low pass filter  33  of the velocity calculator  22  of the controller  11  performs low pass filtering, which is fourth-order IIR filtering with a cutoff frequency of, for example, 1 Hz, on the acceleration data AD 1  and the pitch rate data PD 1 , which have been high pass filtered, and the controller  11  proceeds to step SP 4 . 
     In step SP 4 , the velocity calculating section  34  of the velocity calculator  22  of the controller  11  calculates the autonomous velocity V using equation (3) on the basis of the acceleration α z  corresponding to the acceleration data AD 2  and the pitch rate ω y  corresponding to the pitch rate data PD 2 , which have been low pass filtered, and the controller  11  proceeds to step SP 5 . 
     In step SP 5 , the controller  11  performs smoothing and noise filtering on the velocity data VD representing the autonomous velocity V, which has been calculated in step SP 4 . 
     To be specific, the controller  11  performs low pass filtering having a variable cutoff frequency on the velocity data VD 1  representing the autonomous velocity V, which has been calculated in step SP 4 . 
     If the controller  11  determines that the autonomous velocity V that has been low pass filtered is excessively high, the controller  11  sets the autonomous velocity V at 0 when the velocity of the vehicle is lower than, for example, 10 km/h and sets the autonomous velocity V at the former velocity V n-1  when the velocity of the vehicle is equal to or higher than 10 km/h, and the controller  11  proceeds to step SP 6 . 
     In step SP 6 , the angle calculator  23  of the controller  11  acquires the yaw rate data YD detected by the Z axis gyro sensor  6 , and the controller  11  proceeds to step SP 7 . 
     In step SP 7 , the angle calculator  23  of the controller  11  calculates the angle data DD representing the angle θ by multiplying the yaw rate ω z  corresponding to the yaw rate data YD by the sampling period 0.02 s, and the controller  11  proceeds to step SP 8 . 
     In step SP 8 , the controller  11  calculates the present position data NPD 2  on the basis of the velocity data VD, on which smoothing and noise filtering have been performed in step SP 5 , and the angle data DD, which has been calculated in step SP 7 , and the controller  11  proceeds to step SP 9 . 
     In step SP 9 , the controller  11  reads from the memory  12  a map data including the present position of the vehicle on the basis of the present position data NPD 2  supplied by the position calculator  25 , generates a map image including the present position, and outputs the map image to the display  2 , and the controller  11  proceeds to step SP 10  where the process finishes. 
     1-11. Existing Process of Controlling Display of Present Position Mark 
     Before describing the process of controlling display of a present position mark performed by PND  1  according to the embodiment of the present invention, the process of controlling display of a present position mark performed by an existing PND in accordance with autonomous present position data that is autonomously calculated by using outputs of a general acceleration sensor and a general gyro sensor (or a general barometric pressure sensor, or the like) will be described. 
     As illustrated in  FIG. 26A , when the existing PND is in an area before a tunnel TN, in which GPS signals can be received with high sensitivity (hereinafter referred to as a GPS measurement area AR 1 ), the existing PND measures GPS present position data and displays a present position mark PM on a map image in accordance with the GPS present position data. 
     Subsequently, when the vehicle enters the tunnel TN, which is an area in which it is difficult to receive GPS signals with high sensitivity (hereinafter referred to as a non-GPS measurement area AR 2 ), the existing PND displays the present position mark PM based on autonomous present position data switched from the GPS present position data. 
     The autonomous present position data of the existing PND has a large calculation error, and the present position mark PM that is displayed in accordance with the autonomous present position data in the non-GPS measurement area AR 2  becomes separated from the true present position. 
     As a result, with the existing PND, the present position marks PM just before the vehicle exits the tunnel TN and the present position mark PM just after the vehicle has exited the tunnel TN and moved to the GPS measurement area AR 3  (indicated by “?” in  FIG. 26A ) do not necessarily indicate the true present position. 
     In such a case, as illustrated in  FIG. 26B , if the existing PND continues to display the position mark PM in accordance with the autonomous present position data after the vehicle has entered the tunnel TN and moved to the non-GPS measurement area AR 2 , the present position mark PM overtakes the true present position. 
     Therefore, when the present position mark PM reaches a position near to the exit of the tunnel TN in accordance with the autonomous present position data, the present PND fixes the present position mark PM at the position so that the present position mark PM does not pass through the exit of the tunnel TN. 
     At this time, with the existing PND, the present position mark PM, which is fixed at a position near to the exit of the tunnel TN, becomes separated from the true present position at which the vehicle is traveling, so that the present position mark PM does not indicate the true present position. 
     1-12. Controlling Display of Present Position Mark According to Embodiment 
     The PND  1  according to the embodiment of the present invention controls display of a present position mark by using the present position data NPD 2 , which is calculated using the velocity data VD representing the autonomous velocity V calculated by the aforementioned calculation method and the angle data DD and which is more precise than the present position data used by the existing PND. 
     As described above, the controller  11  of the PND  1  can display the present position mark on a map image by using orbit data, which is obtained by demodulating GPS signals, and the present position data NPD 1 , which is measured on the basis of data on the distances between the GPS satellites and the vehicle. 
     When, for example, the vehicle is in a communication environment in which the GPS signals are unreceivable, such as a tunnel or an underground parking garage, the controller  11  of the PND  1  displays the present position mark on a map image by using the present position data NPD 2 , which is calculated on the basis of the aforementioned autonomous velocity V. 
     Thus, when the vehicle moves from a GPS measurement area to a non-GPS measurement area, the controller  11  of the PND  1  switches the present position data used for displaying the present position mark of the vehicle from the present position data NPD 1  to the present position data NPD 2 . 
     Conversely, when the vehicle moves from a non-GPS measurement area to a GPS measurement area, the controller  11  of the PND  1  switches the present position data used for displaying the present position mark of the vehicle from the present position data NPD 2  to the present position data NPD 1 . 
     Referring to  FIG. 27A , when the vehicle is in a GPS measurement area AR 10  before a tunnel TN 1 , the controller  11  of the PND  1  displays the present position mark PM on a map image in accordance with the present position data NPD 1 . 
     Then, the vehicle enters the tunnel TN 1  and moves from the GPS measurement area AR 10  to a non-GPS measurement area AR 11 . The present position mark PM is displayed in accordance with the present position data NPD 2 , which is autonomously obtained, and reaches a position near to the exit of the tunnel TN 1 . If the controller  11  of the PND  1  fixes the present position mark PM at the position at this time, the following problem arises. 
     If the vehicle exits the tunnel TN 1  and travels in a non-tunnel area that is shorter than, for example, 100 m, before entering the next tunnel TN 2 , it is difficult for the controller  11  of the PND  1  to receive GPS signals because the vehicle travels in the non-tunnel area for only a short time. 
     That is, for the PND  1 , the area including the tunnel TN 1 , the non-tunnel area, and the tunnel TN 2  is practically a non-GPS measurement area AR 11 , and the area beyond the exit of the tunnel TN 2  is a GPS measurement area AR 12 . 
     When the vehicle has passed through the tunnel TN 1 , the controller  11  of the PND  1  should display the present position mark PM by switching to the present position data NPD 1  measured on the basis of GPS signals. However, because the present position mark PM is fixed at the position near to the exit of the tunnel TN 1 , the present position mark PM becomes separated from the true present position (indicated by a broken line) by a large distance. 
     As illustrated in  FIG. 27B , when the vehicle enters the tunnel TN 1  and moves from the GPS measurement area AR 10  to the non-GPS measurement area AR 11 , the controller  11  of the PND  1  displays the present position mark PM while advancing the present position mark PM in the tunnel TN 1  in accordance with the present position data NPD 2 , which is autonomously obtained. 
     If a road between the exit of the tunnel TN 1  and the entrance of the next tunnel TN 2  is a non-tunnel area having a length equal to or shorter than 100 m, in which it is difficult to receive GPS signals, the controller  11  of the PND  1  performs display control in the following manner. 
     In the non-GPS measurement area AR 11  including the tunnels TN 1  and TN 2 , the controller  11  of the PND  1  dos not fix the present position mark PM at a position near to the exit of the tunnel TN 1  and displays the present position mark PM while advancing the present position mark PM in accordance with the present position data NPD 2 , which is autonomously obtained. 
     Subsequently, when the vehicle has passed through the non-GPS measurement area AR 11  including the tunnels TN 1  and TN 2  and moved to the GPS measurement area AR 12 , the controller  11  of the PND  1  switches the present position data that is used for displaying the present position mark PM from the present position data NPD 2 , which is autonomously obtained, to the present position data NPD 1 , which is measured on the basis of GPS signals. 
     In this case, the controller  11  of the PND  1  continuously displays the present position mark PM in the non-GPS measurement area AR 11  by using the present position data NPD 2 , which is autonomously calculated using the aforementioned autonomous velocity V and having a high precision. Therefore, the PND  1  can indicate to a user the present position mark PM having an extremely small error as compared with existing PNDs even when the vehicle is in the tunnels TN 1  and TN 2 . 
     1-13. Process of Controlling Display of Present Position Mark 
     Referring to  FIG. 28 , the controller  11  of the PND  1  starts the process of displaying a present position mark from the start step of a routine RT 2 . In step SP 11 , the controller  11  determines, on the basis of attribute information of the present link, whether or not the vehicle is in the GPS measurement area AR 10  and the present position is measurable using GPS signals. The term “link” refers to a unit area of a road that is divided by predetermined nodes. 
     If the determination is yes, the controller  11  enters a GPS travel mode (open air) that can display the present position mark PM in accordance with the present position data NPD 1  measured on the basis of GPS signals, and the controller  11  proceeds to step SP 13 . 
     In step SP 13 , the controller  11  of the PND  1  displays the present position mark PM while moving the present position mark PM in accordance with the present position data NPD 1  measured on the basis of GPS signals in the GPS measurement area AR 10 , and the controller  11  returns to step SP 11 . 
     If the determination in step SP 11  is no, which means that it is difficult to measure the present position using GPS signals, i.e., the vehicle is in the tunnel TN 1  and traveling in the non-GPS measurement area AR 11 , the controller  11  of the PND  1  proceeds to step SP 14 . 
     In step SP 14 , the controller  11  of the PND  1  enters an autonomous travel mode (tunnel) that can display the present position mark PM in accordance with the present position data NPD 2 , which is autonomously obtained, because the vehicle has entered the non-GPS measurement area AR 11  including the tunnels TN 1  and TN 2 , and the controller proceeds to step SP 15 . 
     In step SP 15 , the controller  11  of the PND  1  displays the present position mark PM on a map in accordance with the present position data NPD 2 , which is precisely calculated using the autonomous velocity V, and the controller  11  proceeds to step SP 16 . 
     In step SP 16 , the controller  11  of the PND  1  displays the present position mark PM on the map while advancing the present position mark PM in the non-GPS measurement area AR 11  in accordance with the present position data NPD 2 , which is periodically calculated, and the controller proceeds to step SP 17 . 
     In step SP 17 , the controller  11  of the PND  1  reads attribute information about a link of the road that is next to the present link on which the vehicle is traveling and determines whether or not the attribute of the next link of the road is a tunnel. 
     If the determination is yes, which means that the next link of the road continues to be the tunnel TN 1 , the controller  11  of the PND  1  proceeds to step SP 18 . 
     In step SP 18 , the controller  11  of the PND  1  displays the present position mark PM on the map while advancing the present position mark in accordance with the present position data NPD 2  because the road ahead continues to be the tunnel TN 1 , and the controller  11  returns to step SP 11 . 
     If the determination in step SP 17  is no, which means that the road ahead is not the tunnel TN 1 , the controller  11  of the PND  1  proceeds to step SP 19 . 
     In step SP 19 , the controller  11  of the PND  1  determines whether or not the next tunnel TN 2  is within 100 m from the tunnel TN 1 . 
     If the determination is no, which means that the next tunnel TN 2  is more than 100 m away, the controller  11  of the PND  1  proceeds to step SP 20 . 
     In step SP 20 , the controller  11  of the PND  1  displays the present position mark PM while advancing the present position mark PM in accordance with the present position data NPD 2 . When the present position mark PM reaches a position near to the exit of the tunnel TN 1 , the controller  11  of the PND  1  fixes the present position mark PM at the position, and the controller returns to step SP 11 . 
     In this case, the controller  11  of the PND  1  can appropriately receive GPS signals in a non-tunnel area between the tunnels TN 1  and TN 2 , which has a length larger than 100 m. Therefore, the non-tunnel area is a GPS measurement area, and the controller  11  of the PND  1  can display the present position mark PM while advancing the present position mark PM in accordance with the present position data NPD 1 . 
     When the present position mark PM has reached the position near to the exit of the tunnel TN 1 , the controller  11  of the PND  1  fixes the present position mark PM at the position and displays the present position mark PM. Because the present position mark PM is displayed in accordance with the present position data NPD 2  having a high precision, the present position that has only a negligible error with respect to the true present position can be displayed. 
     In the non-tunnel area between the tunnel TN 1  and the tunnel TN 2 , which is a GPS measurement area in which GPS signals can be received, the controller  11  of the PND  1  can display the present position mark PM in accordance with the present position data NPD 1  measured on the basis of GPS signals, whereby the present position mark PM having a small error with respect to the true present position can be displayed. 
     Thus, when the vehicle is in the tunnel TN 1 , the controller  11  of the PND  1  can display the present position mark PM having a small error in accordance with the precise present position data NPD 2 , which is autonomously obtained. When the vehicle has passed through the tunnel TN 1  to the non-tunnel area (GPS measurement area), the controller  11  of the PND  1  can display the present position mark PM having a small error in accordance with the present position data NPD 1 , which is obtained on the basis of the GPS signals. 
     If the determination in step SP 19  is yes, which means that the tunnel TN 2  is within 100 m from the TN 1 , the controller  11  of the PND  1  proceeds to step SP 18 . 
     In step SP 18 , the controller  11  of the PND  1  determines that the vehicle is in the non-GPS measurement area AR 11  including the tunnels TN 1  and TN 2  and a non-tunnel area therebetween, because the non-tunnel area between the tunnel TN 1  and the tunnel TN 2  is shorter than 100 m and it is difficult to appropriately receive GPS signals. 
     For the controller  11  of the PND  1 , the non-GPS measurement area AR 11  includes the tunnels TN 1  and TN 2  and the non-tunnel area therebetween, and a road beyond the tunnel TN 2  is the GPS measurement area AR 12 . Therefore, in the non-GPS measurement area AR 11 , the controller  11  of the PND  1  continuously displays the present position mark PM while advancing the present position mark in accordance with the present position data NPD 2 , which is autonomously obtained, without fixing the present position mark PM at a position near to the exit of the tunnel TN 1 , and the controller returns to step SP 11 . 
     In step SP 11 , the controller  11  of the PND  1  repeats the process after step SP 11 . Thus, even when the vehicle travels in a communication environment such as the GPS measurement area AR 10 , the non-GPS measurement area AR 11 , and the GPS measurement area AR 12 , the controller  11  of the PND  1  can display the present position mark PM having only a negligible error with respect to the true present position. 
     1-14. Operation and Effect 
     In the PND  1  having the structure described above, the three-axis acceleration sensor  4  detects the acceleration α z  along the Z axis perpendicular to direction of travel of the vehicle, which is generated due to the undulation of a road surface, and the Y axis gyro sensor  5  detects the pitch rate ω y  around the Y axis perpendicular to the direction of travel of the vehicle, which is generated due to the undulation of a road surface. 
     The PND  1  calculates the autonomous velocity V using equation (1) or (3) on the basis of the acceleration α z  detected by the three-axis acceleration sensor  4  and the pitch rate ω y  detected by the Y axis gyro sensor  5 . 
     Thus, the PND  1 , which has a simple structure including the three-axis acceleration sensor  4  and the Y axis gyro sensor  5 , can accurately calculate the autonomous velocity V of the vehicle even when it is difficult for the PND  1  to receive GPS signals, and can precisely calculate the present position data NPD 2  representing the present position of the vehicle on the basis of the autonomous velocity V and the yaw rate ω z  around the Z axis under all road conditions. 
     Moreover, when the vehicle enters the tunnel TN 1  ( FIG. 27B ) and moves from the GPS measurement area AR 10  to the non-GPS measurement area AR 11 , the PND  1  displays the present position mark PM while advancing the present position mark PM in the tunnel TN 1  in accordance with the present position data NPD 2 , which is autonomously obtained. 
     When the area between the tunnel TN 1  and the next tunnel TN 2  is a non-tunnel area that is shorter than 100 m and in which it is difficult to receive GPS signals, the controller  11  of the PND  1  performs display control in the following manner. 
     That is, the controller  11  of the PND  1  dos not fix the present position mark PM in a position near to the exit of the tunnel TN 1  in the non-GPS measurement area AR 11 . Instead, the controller  11  of the PND  1  displays the present position mark PM while advancing the present position mark PM in accordance with the present position data NPD 2 , which is autonomously obtained. 
     Subsequently, when the vehicle has passed through the non-GPS measurement area AR 11  and moved to the GPS measurement area AR 12 , the controller  11  of the PND  1  switches the present position data that is used for displaying the present position mark PM from the present position data NPD 2 , which is autonomously obtained, to the present position data NPD 1 , which is measured on the basis of GPS signals. 
     Thus, the controller  11  of the PND  1  continuously displays the present position mark in the non-GPS measurement area AR 11  by using the present position data NPD 2 , which is autonomously calculated using the aforementioned autonomous velocity V and has a high precision, so that the PND  1  can indicate to a user the present position mark PM having an extremely small error as compared with existing PNDs even when the vehicle is in the tunnels TN 1  and TN 2 . 
     When the distance between the tunnel TN 1  and the tunnel TN 2  is shorter than 100 m and it is difficult to receive GPS signals when the vehicle is traveling at a high velocity, the controller  11  of the PND  1  does not switch the present position data from the present position data NPD 2 , which is autonomously obtained, to the present position data NPD 1 , which is obtained on the basis of GPS signals, and continuously displays the present position data PM in accordance with the present position data NPD 2 . 
     Thus, when the vehicle is the non-GPS measurement area AR 11  including the tunnel TN 1 , the non-tunnel area, and the tunnel TN 2 , the controller  11  of the PND  1  can continuously and precisely display the present position data PM in accordance with the present position data NPD 2 , which is autonomously obtained, whereby the PND  1  can display the present position of the vehicle more precisely than existing PNDs. 
     With the above structure, the PND  1  can precisely display the present position of the vehicle with the present position mark PM in a communication environment in which GPS signals are unreceivable, such as the tunnels TN 1  and TN 2 , or an environment in which it is difficult to receive GPS signals when the vehicle is traveling at a high velocity, such as an area that is between the tunnels TN 1  and TN 2  and shorter than 100 m. 
     2. Other Embodiments 
     In the above embodiment, the autonomous velocity V is calculated using equation (3) on the basis of the maximum and minimum accelerations α z,min  and a α z,max , which are extracted from the acceleration α z  corresponding to the acceleration data AD 2 , and the maximum and minimum angular velocities ω y,max  and ω y,min , which are extracted from the pitch rate ω y  corresponding to the angular velocity data DD 2 . 
     However, the present invention is not limited thereto. The velocity calculating section  34  may calculate the variances of the acceleration α z  corresponding to the acceleration data AD 2  and the pitch rate ω y  corresponding to the pitch rate data PD 2 , which are supplied by the low pass filter  33 , for, for example, a range of 25 data points or 75 data points around the data point P m  corresponding to the previous position P 0 . Then, the velocity calculating section  34  may calculate the autonomous velocity V by dividing the variance of the acceleration α z  by the variance of the pitch rate ω y . 
     Alternatively, the velocity calculating section  34  may calculate the deviations of the acceleration α z  corresponding to the acceleration data AD 2  and the pitch rate ω y  corresponding to the pitch rate data PD 2 , which are supplied by the low pass filter  33 , for, for example, a range of 25 data points or 75 data points around the data point P m  corresponding to the previous position P 0 . Then, the velocity calculating section  34  may calculate the autonomous velocity V by dividing the variance of the acceleration α z  by the variance of the pitch rate ω y . 
     In the above embodiment, the three-axis acceleration sensor  4 , the Y axis gyro sensor  5 , and the Z axis gyro sensor  6  respectively measure the accelerations α x , α y , α z , the pitch rates ω y , and the yaw rate ω z  with a sampling frequency of 50 Hz. However, the present invention is not limited thereto. The three-axis acceleration sensor  4 , the Y axis gyro sensor  5 , and the Z axis gyro sensor  6  may respectively measure the accelerations α x , α y , α z , the pitch rates ω y , and the yaw rate ω z  with a sampling frequency of, for example, 10 Hz instead of 50 Hz. 
     In the above embodiment, the autonomous velocity V is calculated using the acceleration α z  and the pitch rate ω y  that are detected with a sampling frequency of 50 Hz. However, the present invention is not limited thereto. The velocity calculator  22  of the PND  1  may calculate the averages of the acceleration α z  and the pitch rate ω y , which are detected with a sampling frequency of 50 Hz, for, for example, every 25 data points, and may calculate the autonomous velocity V from the averages of the acceleration α z  and the pitch rate ω y . 
     In this case, the velocity calculator  22  of the PND  1  calculates the averages of the acceleration α z  and pitch rate ω y , which are detected with a sampling frequency of 50 Hz, for, for example, every 25 data points, thereby calculating the autonomous velocity V twice per second. Thus, a processing load for the controller  11  of the PND  1  due to autonomous velocity calculation can be reduced. 
     In the above embodiment, the high pass filter  32  and the low pass filter  33  perform high pass filtering and low pass filtering on the acceleration data AD and the pitch rate data PD, which have been detected by the three-axis acceleration sensor  4  and the Y axis gyro sensor  5 . However, the present invention is not limited thereto. The PND  1  may perform, in addition to the high pass filtering and low pass filtering, moving average filtering on the acceleration data AD and the pitch rate data PD. The PND  1  may perform filtering that is an appropriate combination of high pass filtering, low pass filtering, and moving average filtering on the acceleration data AD and the pitch rate data PD. 
     In the embodiment described above, when calculating the autonomous velocity V at, for example, the previous position P 0  using the acceleration α z  and the pitch rate ω y , if it is determined that the autonomous velocity V at the previous position P 0  is excessively high, the autonomous velocity V at the previous position P 0  is set at the former velocity V n-1 . However, the present invention is not limited thereto. When it is determined that the autonomous velocity at the previous position P 0  is excessively high, the velocity calculator  22  of the PND  1  may set the autonomous velocity V at a value that equals the former velocity V n-1  at the previous position P 0  plus a velocity that will be increased by acceleration of the vehicle. 
     When the autonomous velocity V at the previous position P 0  is lower than the former velocity V n-1  by a predetermined threshold, the velocity calculator  22  of the PND  1  may set the autonomous velocity V at the previous position P 0  at a value that equals the former velocity V n-1  minus a velocity that will be decreased by deceleration of the vehicle. 
     In the embodiment described above, the autonomous velocity V is calculated on the basis of the acceleration α z  and the pitch rate ω y  using equation (3). 
     However, the present invention is not limited thereto. The controller  11  of the PND  1  may compare the autonomous velocity V, which is calculated on the basis of the acceleration α z  and the pitch rate ω y  using equation (3), with the GPS velocity V g , which is calculated on the basis of GPS signals. 
     When the autonomous velocity V has an error with respect to the GPS velocity V g , the controller  11  of the PND  1  may calculate, for example, a correction factor for correcting the autonomous velocity V by using a linear function or a polynomial function of a second or a higher degree so as to minimize the error, and stores the correction factor in the memory  12 . 
     Therefore, the velocity calculator  22  of the PND  1  may calculate the autonomous velocity V on the basis of the acceleration α z  and the pitch rate ω y  respectively detected by the three-axis acceleration sensor  4  and the Y axis gyro sensor  5  using equation (3), read the correction factor from the memory  12 , and correct the autonomous velocity V using the correction factor and a linear function or a polynomial function of a second or a higher degree. 
     In this case, the PND  1  can more precisely calculate the autonomous velocity V by learning beforehand the correction factor for correcting the autonomous velocity V on the basis of the GPS velocity V g  calculated on the basis of GPS signals. 
     When calculating the correction factor used to correct the autonomous velocity V with respect to the GPS velocity V g , the controller  11  of the PND  1  may divide the range of the autonomous velocity V into a plurality of velocity regions, such as a super low velocity region, a low velocity region, a medium velocity region, and a high velocity region, and may calculate a correction factor for each of the velocity regions. 
     When calculating the correction factor used to correct the autonomous velocity V with respect to the GPS velocity V g , the controller  11  of the PND  1  may calculate the correction factor only when the vehicle is traveling at a high velocity that is equal to or higher than a predetermined value, such as 60 km/h. 
     In the above embodiment, the PND  1  performs navigation while the PND  1  is supplied with electric power. However, the present invention is not limited thereto. When the power button (not shown) is pressed and the PND  1  is powered off, the PND  1  may store, in the memory  12 , the present position, the height, and the like at the moment when the power button is pressed. When the power button is pressed again and the PND  1  is powered on, the PND  1  may read the present position, the height, and the like from the memory  12 , and may perform navigation on the basis of the present position, the height, and the like in accordance with the process of calculating the present position. 
     In the above embodiment, the PND  1  calculates the autonomous velocity V while the PND  1  is supported on the cradle  3  placed on the dashboard of the vehicle. However, the present invention is not limited thereto. When it is detected that the PND  1  is mechanically or electrically disconnected from the cradle  3 , the autonomous velocity V may be set at 0 or maintained at the former velocity V n-1 . 
     In the above embodiment, the three-axis acceleration sensor  4 , the Y axis gyro sensor  5 , the Z axis gyro sensor  6 , and the barometric pressure sensor  7  are disposed inside the PND  1 . However, the present invention is not limited thereto. The three-axis acceleration sensor  4 , the Y axis gyro sensor  5 , the Z axis gyro sensor  6 , and the barometric pressure sensor  7  may be disposed outside the PND  1 . 
     The PND  1  may include an adjustment mechanism disposed on a side thereof so that a user can adjust the attachment angles of the three-axis acceleration sensor  4 , the Y axis gyro sensor  5 , the Z axis gyro sensor  6 , and the barometric pressure sensor  7 . 
     In this case, the PND  1  allows a user to adjust the adjustment mechanism so that, for example, the rotation axis of the Y axis gyro sensor  5  is aligned in the vertical direction with respect to the vehicle even when the display  2  is not substantially perpendicular to the direction of travel of the vehicle. 
     In the above embodiment, the autonomous velocity V is determined as excessively high if the pitch rate ω y  corresponding to the pitch rate data PD 2  is lower than a predetermined threshold and if the acceleration α z  corresponding to the acceleration data AD 2  and the pitch rate ω y  corresponding to the pitch rate data PD 2  are higher than predetermined thresholds. However, the present invention is not limited thereto. The controller  11  may determine that the autonomous velocity V is excessively high if the autonomous velocity V calculated by the velocity calculating section  34  is higher than the former velocity V n-1  by a predetermined value. 
     In this case, the smoother/noise filter  35  may set the autonomous velocity V at 0 when the autonomous velocity V calculated by the velocity calculating section  34  is higher than the former velocity V n-1  by a predetermined value and when the former velocity is at a low velocity lower than, for example, 10 km/h. The smoother/noise filter  35  may set the autonomous velocity V at the former velocity V n-1  when the autonomous velocity V calculated by the velocity calculating section  34  is higher than the former velocity V n-1  by a predetermined value and the former velocity is equal to or higher than, for example, 10 km/h. 
     In the above embodiment, the controller  11  of the PND  1  performs the process of calculating the present position of the routine RT 1  and the process of display control of the present position mark of the routine RT 2  in accordance with application programs stored in the memory  12 . However, the present invention is not limited thereto. The controller  11  of the PND  1  may perform the process of calculating the present position and the process of controlling display of the present position in accordance with application programs that are installed from storage media, downloaded from the Internet, or installed by using other methods. 
     In the embodiment described above, when the vehicle is traveling in the tunnel TN 1  and TN 2 , the controller  11  of the PND  1  may recognize that the vehicle is in the non-GPS measurement area AR 11  and continuously and precisely display the present position mark PM in accordance with the present position data NPD 2 , which is autonomously obtained. However, the present invention is not limited thereto. When the vehicle is traveling near to a position under an elevated highway or in an underground parking garage, the controller  11  of the PND  1  may realize that the vehicle is in the non-GPS measurement area AR 11  on the basis of attribute information about the road that indicates a low reception sensitivity for GPS signals, and continuously and precisely display the present position mark PM in accordance with the present position data NPD 2 , which is autonomously obtained. 
     In the embodiment described above, in step SP 20 , the controller  11  of the PND  1  displays the present position mark PM while advancing the present position mark PM in accordance with the present position data NPD 2  and, when the present position mark PM reaches a position near to the exit of the tunnel TN 1 , fixes the present position mark PM at the position. However, the present invention is not limited thereto. Because the present position data NPD 2 , which is autonomously measured, is more precise than that of existing NPDs, the controller  11  of the PND  1  may continuously display the present position mark PM in accordance with the present position data NPD 2  without fixing the present position mark PM at the position near to the exit of the tunnel TN 1 . 
     In the description above, a navigation device according to an embodiment of the present invention is applied to the PND  1 . However, the present invention is not limited thereto, and a navigation device according to an embodiment of the present invention may be applied to a mobile phone. 
     Referring to  FIG. 29 , a mobile phone  100  includes an integrated controller  101  and a mobile phone unit  102 . The integrated controller  101  has a CPU structure and controls the function of the mobile phone unit  102  as a mobile phone. 
     The mobile phone  100  includes a navigation unit  106  that includes the controller  11 , the three-axis acceleration sensor  4 , the Y axis gyro sensor  5 , the Z axis gyro sensor  6 , and the barometric pressure sensor  7 , which are illustrated in  FIG. 7  and realize the navigation function of the PND  1 . The integrated controller  101  controls the navigation unit  106 . Description of the structure of the controller  11 , which is the same as described above, is omitted. 
     The mobile phone  100  includes a memory  103 , which is a semiconductor memory for storing various data, a display  104 , which is a liquid crystal display (LCD) for displaying various information, and an operation section  105  having input buttons and the like. 
     In a normal mode, the mobile phone  100  uses the mobile phone unit  102  to perform a phone function and an email function. In practice, the mobile phone unit  102  of the mobile phone  100  receives a signal with an antenna  110  and sends the received signal to a transmitter/receiver  111 . 
     The transmitter/receiver  111  includes a transmitter/receiver section that converts the received signal to a received data by demodulating the received signal, and sends the received data to a decoder  112 . The decoder  112  reproduces the voice data of a person at the other end by decoding the received data under the control of a mobile phone controller  114  having a microcomputer structure, and outputs the voice data to a speaker  113 . The speaker  113  outputs the voice of the person at the other end on the basis of the voice data. 
     The mobile phone unit  102  sends a voice signal collected by the microphone  115  to an encoder  116 . The encoder  116  converts the voice signal to digital voice data and encodes the digital voice data by using a predetermined method under the control by the mobile phone controller  114 , and sends the digital voice data to the transmitter/receiver  111 . 
     The transmitter/receiver  111  modulates the digital voice data by using a predetermined method, and wirelessly transmits the modulated data from the antenna  110 . 
     The mobile phone controller  114  of the mobile phone unit  102  displays the phone number of the person at the other end, the signal strength, and the like in accordance with an operation command sent from the operation section  105 . 
     If the received data supplied by the transmitter/receiver  111  to the decoder  112  is an email, the mobile phone controller  114  of the mobile phone unit  102  send email data, which has been reproduced by decoding the received data, to the display  104  so as to display the email, and stores the email data in the memory  103 . 
     When email data that is input through the operation section  105  is supplied, the mobile phone controller  114  of the mobile phone unit  102  encodes the email data using the encoder  116 , and wirelessly sends the email data using the transmitter/receiver  111  and the antenna  110 . 
     When the mobile phone  100  is in a navigation mode, the integrated controller  101  controls the navigation unit  106  and perform the process of controlling display of the present position mark display described above ( FIG. 28 ). 
     In the embodiment described above, the present position mark PM is displayed by using the present position data NPD 2 , which is more precise than present position data used in existing PNDs. The NPD 2  is calculated by using the velocity data VD representing the autonomous velocity V, which is calculated in accordance with the method of calculating the autonomous velocity, and the angle data DD. However, the present invention is not limited thereto. The present position mark PM may be displayed by using present position data that is autonomously calculated by using an appropriate method, as long as the present position data is as precise as the present position data NPD 2 . An example of the method is to calculate the present position by using the acceleration of the vehicle in a direction perpendicular to the direction of travel and an angular velocity around a vertical axis that is perpendicular to the direction of travel. 
     In the embodiment described above, the PND  1 , which corresponds to a navigation device according to the present invention, includes the GPS processor  21  corresponding to position measuring means, the navigator  26  corresponding to map displaying means and present position notifying means, the velocity calculator  22  and the position calculator  25  corresponding to estimated present position acquiring means, and the navigator  26  corresponding to control means. However, the present invention is not limited thereto. A navigation device according to the present invention may include position measuring means, map displaying means, present position notifying means, estimated present position acquiring means, and control means, which have different structures. 
     The present application contains subject matter related to that disclosed in Japanese Priority Patent Application JP 2009-213448 filed in the Japan Patent Office on Sep. 15, 2009, the entire content of which is hereby incorporated by reference. 
     It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and alterations may occur depending on design requirements and other factors insofar as they are within the scope of the appended claims or the equivalents thereof.