Patent Publication Number: US-11046341-B2

Title: Satellite positioning apparatus and train control system capable of determining accurate and limited position range of moving object

Description:
TECHNICAL FIELD 
     The present invention relates to a satellite positioning apparatus that determines a position range of a moving object based on satellite positioning signals received from a plurality of positioning satellites, such as global positioning system (GPS) satellites. 
     BACKGROUND ART 
     Generally, an error of satellite positioning increases locally at locations under degraded receiving conditions of radio waves. Therefore, in order to apply a result of satellite positioning to moving object control systems, such as a train control system and an automobile control system, it is necessary to calculate a position range certainly including a measured position and a true value of a position of a moving object. 
     Patent Document 1 discloses a method of limiting an error area by obtaining a common area of error areas each calculated for a combination of four GPS satellites. 
     Patent Document 2 discloses a method of calculating a position range of a train by calculating, for each GPS satellite, a circle on the intersection of a sphere centered at a GPS satellite with radius of a distance of received signal, and the earth&#39;s surface, setting a common area of the circles as an error area of a GPS positioning result, and extracting a track included within the error area. 
     Non-Patent Document 1 discloses a method of calculating an error area formed by two perpendicular vector components, by using three GPS satellites satisfying a predetermined criterion. The size of such an error area is determined by magnification coefficients obtained from angles of the satellite&#39;s position with respect to the two vectors. At first, an error area is obtained, which is formed by a track vector component in a GPS measured position on the track, and a radial vector component of a tangent circle of the track at the measured position. Next, the track is approximated by the tangent circle at the measured position, and a length of the track is approximately calculated, which is included within the position range of the true value. A position range of the train is calculated based on the calculated length of the track and the measured position. 
     CITATION LIST 
     Patent Documents 
     
         
         PATENT DOCUMENT 1: Japanese Patent Laid-open Publication No. JP H06-011560 A 
         PATENT DOCUMENT 2: Japanese Patent No. JP 5373861132 
       
    
     Non-Patent Documents 
     
         
         NON-PATENT DOCUMENT1: T. Iwamoto, “Upper-bounding bias errors in satellite navigation”, IEEE Workshop on Statistical Signal Processing (SSP), 2014. 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     According to the method disclosed in Patent Document 1, since fixed magnitudes of error are given in advance for various factors of error, there is a problem of calculating an incorrect error area not including a true value of the position, when an unexpected error occurs, for example, unexpected multipath waves interfere a certain satellite. In addition, the method disclosed in Patent Document 2 has a problem that the calculated position range becomes too large, except for a special case in which the UPS satellite is at the zenith. In addition, according to the method disclosed in Non-Patent Document 1, since the track is approximated by the tangent circle when calculating the position range, there is a problem that the position range can not be accurately obtained when the train is moving along a track with a large change in curvature that can not be approximated by a circle. 
     An object of the present invention is to provide a satellite positioning apparatus capable of overcoming the above problems and determining an accurate and limited position range of a moving object based on satellite positioning signals received from a plurality of positioning satellites. 
     Solution to Problem 
     According to an aspect of the present invention, a satellite positioning apparatus is provided for determining a positional range of a moving object based on a plurality of satellite positioning signals received from a plurality of positioning satellites, respectively. The satellite positioning apparatus is provided with: a moving path memory, a signal receiver, a position calculator, an error area calculator, and a positional range determiner. The moving path memory stores, in advance, a moving path of the moving object. The signal receiver receives the satellite positioning signals through a receiving antenna mounted at a predetermined position on the moving object. The position calculator calculates measured positions and receiver clock errors, based on satellite positioning signals received from three positioning satellites having a predetermined relationship among their relative positions, and based on the moving path, the measured positions indicating results of positioning the moving object, and the receiver clock errors indicating errors among clocks of the positioning satellites and a clock of the satellite positioning apparatus. The error area calculator sets a plurality of vector pairs, each of the vector pairs consisting of arbitrary two vectors perpendicular to each other on a plane spanned by a tangent vector and a radial vector of a tangent circle of the moving path at the measured position, and calculates an error area for each of the vector pairs, based on the measured positions, the receiver clock errors, and positions of the three positioning satellites used for positioning the moving object, the error area indicating an area on the plane in which the moving object may be positioned, thus calculating a plurality of error areas corresponding to the plurality of vector pairs. The positional range determiner determines the positional range of the moving object based on the plurality of error areas and the moving path. 
     Each one error area of the plurality of error areas is a rectangular area having sides along two vectors of a vector pair corresponding to the one error area. Lengths of the sides of the one error area depend on angles among vectors toward the measured positions from the positions of the three positioning satellites used for positioning the moving object, and the two vectors of the vector pair corresponding to the one error area. The lengths of the sides of the one error area further depend on the receiver clock errors. Each of the plurality of vector pairs is set to minimize lengths of sides of an error area corresponding to the vector pair. 
     Advantageous Effects of Invention 
     According to the satellite positioning apparatus of the present invention, it is possible to determine an accurate and limited position range of the moving object based on the satellite positioning signals received from the plurality of positioning satellites. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a diagram showing a satellite positioning apparatus and main peripheral components mounted on a train, according to a first embodiment of the present invention. 
         FIG. 2  is a diagram showing a relationship between a train length and an installed position of a receiving antenna, in relation to the satellite positioning apparatus according to the first embodiment of the present invention. 
         FIG. 3  is a diagram showing a configuration of a signal receiver in the satellite positioning apparatus according to the first embodiment of the present invention. 
         FIG. 4  is a flowchart showing an operation of a position calculator according to the first embodiment of the present invention. 
         FIG. 5  is a diagram for illustrating an error area calculated by an error area calculator according to the first embodiment of the present invention. 
         FIG. 6  is a flowchart showing an operation of the error area calculator according to the first embodiment of the present invention. 
         FIG. 7A  is a graph showing a magnification coefficient in u′-direction calculated by the error area calculator according to the first embodiment of the present invention. 
         FIG. 7B  is a graph showing a magnification coefficient in v′-direction calculated by the error area calculator according to the first embodiment of the present invention. 
         FIG. 8  is a flowchart showing an operation of a position range extractor according to the first embodiment of the present invention. 
         FIG. 9  is a diagram showing a case in which a distance between an error area and a moving path is less than a threshold value, in relation to the position range extractor according to the first embodiment of the present invention. 
         FIG. 10  is a diagram showing a case in which the distance between the error area and the moving path exceeds the threshold value, in relation to the position range extractor according to the first embodiment of the present invention. 
         FIG. 11  is a diagram showing the error area, the moving path, and intersection points of the error area and the moving path, in relation to the position range extractor according to the first embodiment of the present invention. 
         FIG. 12  is a diagram showing a configuration of a satellite positioning apparatus according to a second embodiment of the present invention. 
         FIG. 13  is a diagram showing a configuration of a satellite positioning apparatus according to a third embodiment of the present invention. 
         FIG. 14  is a diagram showing a configuration of a satellite positioning apparatus according to a fourth embodiment of the present invention. 
         FIG. 15  is a diagram showing an exemplary installation of receiving antennas connected to the satellite positioning apparatus according to the fourth embodiment of the present invention. 
         FIG. 16  is a diagram showing an exemplary configuration of a position range calculator according to the fourth embodiment of the present invention. 
         FIG. 17  is a diagram showing another exemplary configuration of the position range calculator according to the fourth embodiment of the present invention. 
         FIG. 18  is a diagram showing an exemplary configuration of a train control system according to a fifth embodiment of the present invention. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     First Embodiment 
     The present invention is applied to a control system of a moving object that moves along a moving path provided with map information. Specifically, the present invention is applied to control systems of moving objects, such as a train moving along a track, and an automobile moving along a road. Hereinafter, in a first embodiment, a train will be described as an example. 
       FIG. 1  is a diagram showing a satellite positioning apparatus  20 A and main peripheral components mounted on a train  1 , according to the first embodiment of the present invention. 
     Referring to  FIG. 1 , the train  1  is provided with: a receiving antenna  10  configured to receive satellite positioning signals; the satellite positioning apparatus  20 A configured to calculate a position range of the train  1  based on the satellite positioning signals received through the receiving antenna  10 ; and a train control apparatus  30  configured to control a train speed and the like according to position range information. 
     Referring to  FIG. 1 , the receiving antenna  10  is installed at a predetermined position on the train  1 , for example, on the top of the train  1 , and receives radio waves of the satellite positioning signals emitted from positioning satellites S 1  to S n  in the sky, to convert the radio waves to high-frequency signals. 
     The positioning satellites to be used are satellites of any satellite navigation systems that allow positioning of a signal receiving point by emitting satellite positioning signals with time information and the satellites&#39; orbit information superimposed. The positioning satellites include, for example, GPS satellites, GLONASS satellites, Beidou satellites, QZSS satellites, and the like. From the viewpoint of improving availability of satellite positioning results and limiting a position range, the satellite positioning apparatus  20 A is preferably configured to receive satellite positioning signals from satellites of a plurality of satellite navigation systems. 
     Referring to  FIG. 1 , the satellite positioning apparatus  20 A determines the position range of the train  1 , based on the satellite positioning signals received from the plurality of positioning satellites S 1  to S n . The satellite positioning apparatus  20 A is provided with: a moving path memory  100 ; an antenna position memory  200 ; a signal receiver  300 ; a position calculator  400 ; an error area calculator  500 ; and a position range determiner  1100 . In addition, the position range determiner  1100  is provided with a position range extractor  600  and a position range restrictor  700 . 
     The moving path memory  100  stores, in advance, three-dimensional information of a path through which the receiving antenna  10  travels as the moving path of the train  1  when the train  1  moves along the track. 
     The antenna position memory  200  stores, in advance, information on a size of the train  1  (in particular, a length from a head to a tail end), and an installed position of the receiving antenna  10  on the train  1 . 
     The signal receiver  300  demodulates the satellite positioning signals received through the receiving antenna  10 , and calculates navigation data and observation data. The signal receiver  300  outputs the navigation data and the observation data to the position calculator  400 . 
     The position calculator  400  calculates measured positions and receiver clock errors, based on the navigation data and the observation data of the three positioning satellites having a predetermined relationship among their relative positions, among the navigation data and the observation data of the received satellite positioning signals, and based on the three-dimensional information of the path stored in the moving path memory  100 . The measured positions indicate results of positioning the receiving antenna  10  as the position of the train  1 . The receiver clock errors indicate errors among clocks of the positioning satellites from which the satellite positioning signals have been received, and a clock of the satellite positioning apparatus  20 A. The position calculator  400  outputs the measured positions and the receiver clock errors to the error area calculator  500 . 
     The error area calculator  500  sets a plurality of vector pairs, each of the vector pairs consisting of arbitrary two vectors perpendicular to each other on a plane satisfying a predetermined criterion, and calculates an error area indicating an area where the receiving antenna  10  may exist, based on the vectors, the measured positions, the receiver clock errors, and positions of the three positioning satellites used for positioning. In addition, the error area calculator  500  calculates at least two or more error areas by setting at least two or more vector pairs. The error area calculator  500  outputs the error areas to the position range extractor  600 . 
     For each of the plurality of error areas corresponding to the plurality of vector pairs, the position range extractor  600  extracts a part of the moving path included in the error area, as a candidate position range corresponding to the error area. The position range extractor  600  extracts the candidate position ranges, based on the three-dimensional information of the path stored in the moving path memory  100 , and based on the size of the train  1  and the installed position of the receiving antenna  10 , that are stored in the antenna position memory  200 . The position range extractor  600  outputs the candidate position ranges to the position range restrictor  700 . 
     The position range restrictor  700  determines a common area of the plurality of candidate position ranges corresponding to the plurality of error areas, as the position range of the moving object. The position range restrictor  700  outputs the position range of the moving object, to the train control apparatus  30 . 
     Hereinafter, the satellite positioning apparatus  20 A according to the first embodiment will be described in more detail. 
     At first, the moving path memory  100  will be described. The three-dimensional information on the path through which the receiving antenna  10  travels when the train  1  moves along the track can be obtained, for example, by performing high precision positioning using a phase of a carrier wave of the positioning satellite, in advance. In addition, the three-dimensional information of the path can be obtained geometrically, for example, by using information on a series of coordinate of a pair of rails, and information on a height of the receiving antenna  10  with respect to the ground. Further, by applying an appropriate interpolation method, such as Lagrange interpolation, to the three-dimensional information of the path, the path can be represented by a curve C: r(t)=(x(t), y(t), z(t)), the curve C passing respective coordinate points. Further, the curve C can be represented by the curve C: r(s)=(x(s), y(s), z(s)), parameterized by a curve length “s” from the point 0 on the curve. In this case, by appropriately selecting a position of the point 0, it is possible to readily associate the position on the curve with a unit (kilometer) commonly used to represent a position along the track. 
     Next, the antenna position memory  200  will be described.  FIG. 2  is a diagram showing a relationship between a length of the train  1  and an installed position of the receiving antenna  10 , in relation to the satellite positioning apparatus  20 A according to the first embodiment of the present invention. 
     Referring to  FIG. 2 , l front  denotes a length from the installed position of the receiving antenna  10  to a head of the train  1 , and l backward  denotes a length from the installed position of the receiving antenna  10  to a tail end of the train  1 . 
     Next, the signal receiver  300  will be described.  FIG. 3  is a diagram showing a configuration of the signal receiver  300  in the satellite positioning apparatus  20 A according to the first embodiment of the present invention. The signal receiver  300  is connected to the receiving antenna  10 , and is provided with a high-frequency signal processor  310  and a baseband signal processor  320 . The high-frequency signal processor  310  performs processing of amplification, down-conversion, filtering, and analog/digital conversion on high-frequency signals outputted from the receiving antenna  10 , to convert into a signal format that can be processed by the baseband signal processor  320 . The baseband signal processor  320  performs signal acquisition processing, signal tracking processing, and navigation message demodulation processing on the signals outputted from the high-frequency signal processor  310 , to obtain navigation data and observation data of the positioning satellites associated with the received satellite positioning signals. The navigation data is data indicating orbital positions of the positioning satellites associated with the received satellite positioning signals. The observation data is data indicating pseudo-ranges l 1  to l n  between the positioning satellites associated with the received satellite positioning signals and the receiving antenna, and indicating a time t r  when the satellite positioning signals are received. The time or time period for measuring the pseudo-ranges may be arbitrarily set, for example, measuring every second. The signal receiver  300  outputs the calculated navigation data and observation data to the position calculator  400 . The position calculator  400  described later calculates the position of the receiving antenna  10  by using the satellite positioning signals received from at least three positioning satellites. Therefore, when only satellite positioning signals from two or less positioning satellites can be received, the signal receiver  300  outputs a signal indicating that the position range can not be measured, to the train control apparatus  30 . When the signal receiver  300  receives the satellite positioning signals from three or more positioning satellites, the position calculator  400  processes those satellite positioning signals. 
     In order to reduce an initial time required to calculate the navigation data, the satellite positioning apparatus  20 A may be configured to receive the latest navigation data from an external apparatus via a terrestrial wireless network. 
     Next, the position calculator  400  will be described. The position calculator  400  reads the curve r(s) of the moving path of the receiving antenna  10 , from the moving path memory  100 , and selects three positioning satellites satisfying a predetermined criterion, among the positioning satellites S 1  to S n  from which the signal receiver  300  has received the satellite positioning signals. The position calculator  400  calculates the measured positions and the receiver clock errors by performing calculation for positioning based on the read moving path r(s), positions of the selected three positioning satellites based on the navigation data of the positioning satellites, and the pseudo-ranges based on the observation data of the selected three positioning satellites. The position calculator  400  outputs the measured positions and the receiver clock errors to the error area calculator  500 . 
       FIG. 4  is a flowchart showing an operation of the position calculator  400  according to the first embodiment of the present invention. Hereinafter, the operation of the position calculator  400  will be described in accordance with the flowchart shown in  FIG. 4 . 
     At step S 1 , the position calculator  400  sets a trial count “t” as t=1. 
     At step S 2 , the position calculator  400  selects a set of arbitrary three positioning satellites, among the positioning satellites S 1  to S n  from which the signal receiver  300  has received the satellite positioning signals. The three positioning satellites are not limited to positioning satellites of the same satellite navigation system. For example, one may be selected from GPS satellites, one may be selected from GLONASS satellites, and one may be selected from Beidou satellites. Since three positioning satellites are selected from the n positioning satellites, the positioning satellites may be selected in N= n C 3  ways. 
     At step S 3 , the position calculator  400  performs positioning using the three positioning satellites selected at step S 2 , and the position calculator  400  calculates the measured positions and the receiver clock errors, under a constraint that a solution is on the curve r(s) of the moving path. 
     Hereinafter, a method of calculating the measured positions and the receiver clock errors will be described. (x k , y k , z k ) (k=1, 2, 3) denotes coordinates of the three positioning satellites S k , which are read from the navigation data, l 1 , l 2 , l 3  denotes the pseudo-ranges of the three positioning satellites, which are read from the observation data, and δb denotes the receiver clock error. In this case, an observation equation is represented by the following Mathematical Expressions 1 to 3.
 
 l   1 =√{square root over (( x   1   −x ( s )) 2 +( y   1   −y ( s )) 2 +( z   1   −z ( s )) 2 )}+δ b   [Mathematical Expression 1]
 
 l   2 =√{square root over (( x   2   −x ( s )) 2 +( y   2   −y ( s )) 2 +( z   2   −z ( s )) 2 )}+δ b   [Mathematical Expression 2]
 
 l   3 =√{square root over (( x   3   −x ( s )) 2 +( y   3   −y ( s )) 2 +( z   3   −z ( s )) 2 )}+δ b   [Mathematical Expression 3]
 
     By solving Mathematical Expressions 1 to 3 for unknowns “s” and “δb” using the least-squares method, measured position P (x(s), y(s), z(s)) and the receiver clock error δb are obtained. 
     At step S 4 , the position calculator  400  determines whether or not the set of three positioning satellites selected at step S 2  satisfy a predetermined positioning criterion. Hereinafter, the positioning criterion to be satisfied by the set of three positioning satellites will be described. This positioning criterion is a criterion on the constellation of three positioning satellites, which should be satisfied when the error area calculator  500  calculates the error area. When the criterion is not satisfied, the error area can not be calculated. “u” denotes a unit vector in a tangential direction of the moving path r(s) at the measured position P, “v” denotes a unit vector in a radial direction of a tangent circle of the moving path r(s) at the measured position P, “g k ” denotes a unit direction vector in a direction in which the measured position P is seen from each positioning satellite S k  (k=1, 2, 3), and “i” denotes an imaginary unit. In this case, variables f k , h k , and z k  are defined as follows.
 
 f   k   :=g   k   ·u  
 
 h   k   :=g   k   ·v  
 
 z   k   :=f   k   +ih   k  
 
     In this case, using z 1 =z 4 , the positioning criterion is given as follows.
 
 Im ( z   k   *z   k+1 )= f   k   h   k+1   −f   k+1   h   k &gt;0
 
     This positioning criterion indicates that when straight lines from the measured position P toward the three satellites are projected onto a plane “α” spanned by the vectors “u” and “v”, the three satellites are not positioned only on one side of an arbitrary straight line on the plane “α”, passing through the measured position P. 
     If the set of three positioning satellites satisfy this positioning criterion, the process proceeds to step S 5 , and if not, the process proceeds to step S 6 . 
     At step S 5 , the position calculator  400  outputs the measured position P and the receiver clock error δb that are calculated at step S 3 , to the error area calculator  500 , and terminates the processing of the position calculator. In this case, next, the error area calculator  500  performs its processing. 
     At step S 6 , the position calculator  400  increments the trial count “t” by one. 
     At step S 7 , the position calculator  400  determines whether or not the trial count “t” is smaller than a number N of combinations of the positioning satellites. That is, for all combinations of three positioning satellites selected from the n positioning satellites from which the satellite positioning signals have been received, it is determined whether or not the calculation of the measured positions and the receiver clock errors, and the determination of the positioning criterion have been done. If t&gt;N, the process returns to step S 2 , and arbitrary three positioning satellites are reselected. In this case, the positioning satellites are to be selected so as not to reselect the previously selected combinations. If t=N, it is considered that the satellite positioning signals received at time t r  does not satisfy the positioning criterion for all combinations of the positioning satellites. In this case, the process proceeds to step S 8 , and the position calculator  400  outputs a signal indicating that the position range can not be measured, to the train control apparatus  30 , and terminates the processing of the position calculator  400 . 
     Next, the error area calculator  500  will be described. The error area calculator  500  sets a plurality of vector pairs, each vector pair consisting of arbitrary two vectors perpendicular to each other on the plane “α” spanned by the vectors “u” and “v”, and the error area calculator  500  calculates an error area for each of the plurality of vector pairs, based on the two vectors of the vector pair, the measured positions, the receiver clock errors, and the positions of the three positioning satellites used for positioning. Let (u′, v′) be a vector pair including arbitrary two vectors perpendicular to each other on the plane “α”, variables f k ′ and h k ′ are defined as follows.
 
 f   k   ′:=g   k   ·u′ 
 
 h   k   ′:=g   k   ·v′ 
 
     Then, assuming that a true value Q of a coordinate of the receiving antenna  10  exists on the plane “α”, δu′ denotes a component of a positioning error in u′-direction, and δv′ denotes a component of the positioning error in v′-direction. In this case, a magnification coefficient M u′  in u′-direction and a magnification coefficient M v′  in v′-direction are defined by the following Mathematical Expressions 4 and 5. 
     
       
         
           
             
                 
             
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     Two error inequalities in u′-direction and v′-direction hold as follows.
 
|δ u′|≤M   u′   |δb| 
 
|δ v′|≤M   v′   |δb| 
 
     The right sides of these error inequalities are referred to as “upper limit error values”. 
       FIG. 5  is a diagram for illustrating an error area calculated by the error area calculator  500  according to the first embodiment of the present invention. The error area is a rectangular area centered at the measured position P and having sides along two vectors u′ and v′ of a vector pair corresponding to the error area. As can be seen from the definitions of the variables f k ′ and h k ′, lengths of the sides of the error area depend on angles among vectors g k  toward the measured position P from the positions of the three positioning satellites used for positioning of the receiving antenna  10 , and the two vectors u′ and v′ of the vector pair corresponding to the error area. The lengths of the sides of the error area also depend on the receiver clock error δb. The length of one side of the error area is twice as large as the upper limit error value. 
       FIG. 6  is a flowchart showing an operation of the error area calculator  500  according to the first embodiment of the present invention. Next, the operation of the error area calculator  500  will be described in accordance with the flowchart shown in  FIG. 6 . 
     At step S 11 , when M is an integer of 2 or more, the error area calculator  500  selects M vector pairs, each of the vector pairs consisting of two vectors perpendicular to each other on the plane “α”. 
     There is no restriction on a method of selecting perpendicular vector pairs, but from the viewpoint of limiting the error area, for example, a pair providing the smallest magnification coefficients may be selected. Hereinafter, a specific example will be explained. The plane “α” is assumed to be a ground plane at a point of latitude 34.759 degrees and longitude 135.42 degrees. From the GPS satellites in the sky at 15:00 on Jul. 16, 2015 (Japan time), three positioning satellites of satellite numbers PRN 19, PRN 30, and PRN 32 are selected. For these positioning satellites,  FIGS. 7A and 7B  respectively show changes of the magnification coefficient l in u′-direction and the magnification coefficient M v′  in v′-direction, when rotating the vector pair (u′, v′) consisting of two vectors perpendicular to each other on the plane “α”. A horizontal axis of each graph indicates a rotation angle of the vector pair. Referring to  FIG. 7A , the magnification coefficient M u′  in u′-direction is minimized at a rotation angle A. Referring to  FIG. 7B , the magnification coefficient M v′  in v′-direction is minimized at a rotation angle B. Each of the plurality of vector pairs may be selected such that the magnification coefficients M u′  and M v′  become the minimum value or its neighborhood, and thus, such that the lengths of the sides of the error area corresponding to the vector pair becomes the minimum value or its neighborhood. In addition, when sufficient calculation resources are available, for example, vector pairs at constant angle intervals may be automatically selected. 
     Each of the selected M vector pairs is referred to as an m-th (m=1, 2, . . . , M) vector pair. In addition, a set of magnification coefficients obtained for the m-th vector pair is referred to as m-th magnification coefficients. 
     At step S 12 , the error area calculator  500  calculates an m-th upper limit error value for the m-th vector pair selected at step S 11 , by multiplying the m-th magnification coefficients by an absolute value |δb| of the receiver clock error. 
     At step S 13 , the error area calculator  500  calculates an m-th error area from the measured positions and the m-th upper limit error value, and terminates the processing of the error area calculator  500 . 
     Next, the position range extractor  600  will be described. The position range extractor  600  reads the moving path r(s) from the moving path memory  100 , and calculates an m-th candidate position range for the m-th error area calculated by the error area calculator  500 . 
       FIG. 8  is a flowchart showing an operation of the position range extractor according to the first embodiment of the present invention. Hereinafter, the operation of the position range extractor  600  will be described in accordance with the flowchart shown in  FIG. 8 . 
     At step S 21 , the position range extractor  600  sets the trial count t=1. 
     At step S 22 , the position range extractor  600  determines whether or not a distance between a t-th error area and the moving path r(s) is less than a threshold value. A determination method at step S 22  is described as follows. A perpendicular line AB to the plane “α” is given, the perpendicular line AB passing through an arbitrary point A on the moving path r(s), and a point B existing within the t-th error area. The perpendicular line AB has a length “h”. For any such points A and B, the length “h” of the perpendicular line AB is compared with a predetermined threshold value K. 
       FIG. 9  shows a case in which a distance between the error area and the moving path is less than a threshold value. In the range of the error area, the moving path r(s) exists on the plane “α”. In this case, since the true value Q of the position of the receiving antenna  10  can be considered to exist on the plane “α”, the t-th error area is determined to be reliable, and a t-th candidate position range is calculated at steps S 23  and S 24 . 
       FIG. 10  shows a case in which the distance between the error area and the moving path exceeds the threshold value. In the range of the error area, the moving path r(s) protrudes from the plane “α”. In this case, since there is a possibility that the true value Q of the position of the receiving antenna  10  does not exist on the plane “α”, a t-th upper limit error value is determined not to be reliable, and the process proceeds to step S 25 . 
     At step S 23 , the position range extractor  600  extracts the moving path r(s) existing within the t-th error area, and calculates an intersection point s=ls m  on the tail end of the train  1 , and an intersection point s=lg m  on the head of the train  1 .  FIG. 11  is a diagram showing the error area, the moving path r(s), an intersection point C on the tail end of the train  1 , and an intersection point D on the head of the train  1 . 
     At step S 24 , the position range extractor  600  calculates the t-th candidate position range based on the intersection points calculated at step S 23 , and based on the installed position of the receiving antenna  10  read out from the antenna position memory  200 . In this case, the candidate position range can be determined with a start point of “ls m −l backward ”, and an end point of “lg m +l backward ”. 
     At step S 25 , the position range extractor  600  increments the trial count “t” by one. 
     At step S 26 , the position range extractor  600  determines whether or not the trial count “t” is larger than the number M of vector pairs selected by the error area calculator  500 . That is, it is determined whether or not the candidate position ranges have been extracted for all the error areas. If t&lt;M, the process returns to step S 22 . If t=M, the position range extractor  600  outputs results at step S 27 . 
     A method of outputting the extracted results of the candidate position ranges will be described. If no candidate position range has not been calculated, that is, if all the distances between the error areas and the moving path r(s) are equal to or larger than the threshold value at step S 22 , the position range extractor  600  outputs a signal indicating that the position range can not be measured, to the train control apparatus  30 . If at least one candidate position range has been calculated, the position range extractor  600  outputs the results to the position range restrictor  700 . 
     Next, an operation of the position range restrictor  700  will be described. The position range restrictor  700  extracts a common area of all candidate position ranges that have been outputted by the position range extractor  600 , and outputs the common area as the position range of the receiving antenna  10 , to the train control apparatus  30 . When the position range extractor outputs only one candidate position range, the position range restrictor  700  simply outputs the extracted candidate position range as the position range of the receiving antenna  10 , to the train control apparatus  30 . 
     A modified embodiment of the satellite positioning apparatus  20 A according to the first embodiment will be described. In the above description, the position calculator  400  of the satellite positioning apparatus  20 A determines measured positions and receiver clock errors for a set of positioning satellites satisfying the positioning criterion, and performs subsequent processing based on only such measured positions and receiver clock errors. However, the position calculator  400  may determines a plurality sets of measured positions and receiver clock errors for a plurality sets of positioning satellites satisfying the positioning criterion, respectively, and performs subsequent processing based on the plurality sets of measured positions and receiver clock errors. 
     An operation in this case will be described. At first, the position calculator  400  sets a plurality of sets of positioning satellites, each set including three positioning satellites satisfying the positioning criterion, and each set being referred to as a f-th combination of positioning satellites (f=1, 2, . . . , N). The position calculator  400  outputs measured positions and receiver clock errors for the first to N-th combinations of positioning satellites, respectively. The error area calculator  500  outputs first to M-th error areas for the first to N-th combinations of positioning satellites. The position range extractor  600  outputs first to M-th candidate position ranges for the first to the N-th combinations of positioning satellites. The position range restrictor  700  extracts a common area of all candidate position ranges outputted by the position range extractor  600 , and outputs the common area as the position range of the receiving antenna  10 , to the train control apparatus  30 . 
     According to the satellite positioning apparatus  20 A of the first embodiment described above, the satellite positioning apparatus  20 A is configured as follows. The moving path memory  100  stores the moving path of the train  1  in advance. The signal receiver  300  receives the satellite positioning signals through the receiving antenna  10  mounted at a predetermined position on the train  1 . The position calculator  400  calculates measured positions and receiver clock errors, based on satellite positioning signals received from three positioning satellites having a predetermined relationship among their relative positions, and based on the moving path, the measured positions indicating results of positioning the train  1 , and the receiver clock errors indicating errors among clocks of the positioning satellites and a clock of the satellite positioning apparatus. The error area calculator  500  sets a plurality of vector pairs, each of the vector pairs consisting of arbitrary two vectors perpendicular to each other on a plane spanned by a tangent vector and a radial vector of a tangent circle of the moving path at the measured positions. Then, for each of the plurality of vector pairs, the error area calculator  500  calculates an error area indicating an area on the plane in which the train  1  may exist, based on the measured positions, the receiver clock errors, and positions of the three positioning satellites used for positioning the train  1 . Thus, the error area calculator  500  calculates a plurality of error areas corresponding to the plurality of vector pairs. For each of the plurality of error areas corresponding to the plurality of vector pairs, the position range extractor  600  extracts a part of the moving path included in the error area, as a candidate position range corresponding to the error area. Thus, the position range extractor  600  extracts a plurality of candidate position ranges corresponding to the plurality of error areas. The position range restrictor  700  determines a common area of the plurality of candidate position ranges corresponding to the plurality of error areas, as the position range of the train  1 . 
     According to the satellite positioning apparatus  20 A of the first embodiment, it is possible to determine an accurate and limited position range of a moving object based on the satellite positioning signals received from the plurality of positioning satellites. 
     The error area calculator  500  does not use predetermined magnitudes of error for various factors of error, but calculates the error area every time. Therefore, even when an unexpected multipath wave occurs, it is possible to calculate an error area certainly including a true value of the position. 
     Therefore, the satellite positioning apparatus  20 A according to the first embodiment can accurately determine the position range, even when the train is moving along a path with a large change in curvature that can not be approximated by a circle. 
     Since the position range extractor  600  determines that the distance between the error area and the moving path is less than a predetermined threshold value, there is an advantageous effect of increasing reliability of the position range. 
     Since the position range restrictor  700  limits the position range of the train  1 , it is possible to more frequently run the trains  1 . 
     Further, according to the satellite positioning apparatus  20 A of the first embodiment, the error area calculator  500  sets a vector pair consisting of arbitrary two vectors perpendicular to each other, without being limited to a pair of vectors in a tangential direction and a radial direction of a tangent circle at the measured positions. Therefore, it is possible to limit the error area regardless of the constellation of the positioning satellites. 
     According to the conventional method described in Non-Patent Document 1, since the track is approximated by the tangent circle when calculating the position range, there is a problem that the position range can not be accurately obtained when moving along a track with a large change in curvature that can not be approximated by a circle. On the other hand, according to the satellite positioning apparatus  20 A of the first embodiment, it is possible to limit the error area regardless of the constellation of the positioning satellites. 
     According to the satellite positioning apparatus  20 A of the first embodiment, the position range determiner  1100  is configured to include the position range extractor  600  and the position range restrictor  700 , but not limited thereto. The position range determiner  1100  may determine the position range of the moving object based on the plurality of error areas and the moving path. The position range determiner  1100  may be configured to determine a common area of the plurality of error areas and moving path as the position range of the moving object, by extracting the common area of the plurality of error areas, and then determining a part of the moving path included in the extracted common area, as the position range. 
     Second Embodiment 
     The satellite positioning apparatus  20 A of the first embodiment is configured to calculate the position range of the train  1  based on only the received satellite positioning signals. On the other hand, a satellite positioning apparatus  20 B according to a second embodiment is configured to further use a device for measuring a moving distance of the train, thus being capable of reliably calculating a position range of a train  1 , even under a degraded receiving environment of satellite positioning signals, e.g., when the train is running through a tunnel. 
       FIG. 12  is a diagram showing a configuration of the satellite positioning apparatus  20 B according to the second embodiment of the present invention. The satellite positioning apparatus  20 B of the second embodiment and the satellite positioning apparatus  20 A of the first embodiment shown in  FIG. 1  are different in the following two points. A first difference is that the satellite positioning apparatus  20 B according to the second embodiment is provided with a moving distance measurement device  800 . A second difference is that the satellite positioning apparatus  20 B of the second embodiment is provided with a position range estimator  1000 . Hereinafter, the same reference numerals are given to similar components to those of the satellite positioning apparatus  20 A shown in  FIG. 1 , and their description will be omitted. 
     At first, the moving distance measurement device  800  will be described. The moving distance measurement device  800  calculates a distance L that the train  1  has moved from a reference time t ref  to a current time t now , as follows.
 
 L=∫   t     ref     t     now     v (τ)· dτ±d   [Mathematical Expression 6]
 
     Where, v(τ) denotes a speed of the train  1  obtained without relying on satellite positioning signals, and “d” denotes a magnitude of error to be added to a distance measurement result. The speed of the train is measured using, for example, a tachogenerator (not shown) attached to an axle. The speed of the train is calculated by obtaining a wheel&#39;s rotation speed by the tachogenerator, and multiplying the wheel&#39;s rotation speed by a circumference of the wheel. The reference time t ref  is a time calculated by the position range estimator  1000  to be described later. In addition, the moving distance measurement device  800  stores a reference position P ref , i.e., a reference for the moving distance. The reference position P ref  is a position calculated by the position range estimator  1000  to be described later. The moving distance measurement device  800  outputs the distance L that the train  1  has moved, to the position range estimator  1000 . 
     In addition, the position range restrictor  700  outputs the position range of the train  1  calculated from the satellite positioning signals in a manner similar to that of the first embodiment, to the position range estimator  1000 . 
     The position range estimator  1000  compares the position range of the train  1  calculated from the satellite positioning signals, with a predetermined threshold value. When a size of the position range of the train  1  calculated from the satellite positioning signals exceeds the threshold value (that is, when a sufficiently accurate position range of the train  1  is not calculated from the satellite positioning signals), the position range estimator  1000  calculates the position range of the train  1  based on the distance L outputted from the moving distance measurement device  800 . In this case, a section from a start point “P ref +L−d” to an end point “P ref +L+d” is calculated as the position range of the train  1 . The position range estimator  1000  outputs the position range of the train  1  calculated from the distance L, to the train control apparatus  30 . On the other hand, when the size of the position range of the train  1  calculated from the satellite positioning signals is equal to or less than the threshold value (that is, when a sufficiently accurate position range of the train  1  is calculated from the satellite positioning signals), the position range estimator  1000  outputs the position range of the train  1  calculated from the satellite positioning signals, to the train control apparatus  30 . Then, the position range estimator  1000  updates the reference time t ref  with a current time, and updates the reference position P ref  with a point within the current position range, to output them to the moving distance measurement device  800 . 
     According to the satellite positioning apparatus  20 B of the second embodiment described above, the moving distance measurement device  800  measures a distance that the train  1  has moved from the reference time t ref  to the current time t now . In addition, the position range estimator  1000  outputs one of the position range of the train  1  calculated from the satellite positioning signals, and the position range of the train  1  calculated from the distance L, to the train control apparatus  30 . Therefore, even under a degraded receiving environment of satellite positioning signals, e.g., when the train is running through a tunnel, it is possible to reliably calculate the position range of the train  1 . In addition, the satellite positioning apparatus  20 B according to the second embodiment also has similar advantageous effects to those described in the first embodiment. 
     Third Embodiment 
     The satellite positioning apparatus  20 B of the second embodiment is configured to determine, as the position range of the train  1 , one of the position range of the train  1  calculated from satellite positioning signals, and the position range of the train  1  calculated from the distance L. On the other hand, a satellite positioning apparatus  20 C of a third embodiment is configured to determine, as the position range of the train  1 , an overlapping portion of a position range of the train  1  calculated from the satellite positioning signals, and a position range of the train  1  calculated from the distance L, thus being capable of further limiting the position range of a train  1 . 
       FIG. 13  is a diagram showing a configuration of the satellite positioning apparatus  20 C according to the third embodiment of the present invention. The satellite positioning apparatus  20 C of the third embodiment and the satellite positioning apparatus  20 B of the second embodiment shown in  FIG. 12  are different in the following four points. A first difference is that the satellite positioning apparatus  20 C of the third embodiment is provided with a position range memory  900 . A second difference is that, instead of the position range determiner  1100  shown in  FIG. 12 , there is provided a position range determiner  1101  including the position range extractor  600  and a position range restrictor  701 , and an operation of the position range restrictor  701  shown in  FIG. 13  is different from the operation of the position range restrictor  700  shown in  FIG. 12 . A third difference is that an operation of a moving distance measurement device  801  shown in  FIG. 13  is different from the operation of the moving distance measurement device  800  shown in  FIG. 12 . A fourth difference is that an operation of a position range estimator  1001  shown in  FIG. 13  is different from the operation of the position range estimator  1000  shown in  FIG. 12 . Hereinafter, the same reference numerals are given to similar components to those of the satellite positioning apparatus  20 B shown in  FIG. 12 , and their description will be omitted. 
     At first, the moving distance measurement device  801  will be described. The moving distance measurement device  801  calculates a distance L that the train  1  has moved from a first time t before  when satellite positioning signals are received, to a second time t now  when satellite positioning signals are received after the first time, as follows.
 
 L=∫   t     before     t     now     v (τ)· dτ±d   [Mathematical Expression 7]
 
     Where, v(τ) denotes a speed of the train  1  obtained without relying on satellite positioning signals, and “d” denotes a magnitude of error to be added to a distance measurement result. 
     The first time t before  is not necessarily an immediately preceding time of receiving the satellite positioning signals. For example, when the signal receiver  300  calculates pseudo-ranges every second, the first time t before  may be a time before the second time t now  by five or ten seconds. 
     Next, the position range memory  900  will be described. The position range memory  900  stores the position range of the train.  1  calculated from the satellite positioning signals after the first time t before  and outputted by the position range restrictor  701 . 
     Next, the position range estimator  1001  will be described. The position range estimator  1001  calculates an estimated position range of the train  1  at the second time t now , by reading the position range of the train  1  at the first time t before , from the position range memory  900 , and adding the moving distance outputted by the moving distance measurement device  801 . The position range estimator  1001  outputs the estimated position range to the position range restrictor  701 . For example, the position range of the train  1  at the first time t before  is represented by a start point s=l st  and an end point s=l go . Let a moving distance from the first time t before  to the second time t now  to be “l±d”. In this case, the calculated estimated position range is represented by a start point “l st +l−d” and an end point “l go +l+d”. 
     Finally, the position range restrictor  701  will be described. The position range restrictor  701  extracts a common area of all candidate position ranges outputted by the position range extractor  600 , and the estimated position range outputted by the position range estimator  1001 , to determine the common area as the position range of the train  1 . The position range restrictor  701  outputs the position range of the train  1  to the train control apparatus  30 . When the signal receiver  300 , the position calculator  400 , or the position range extractor  600  outputs a signal indicating that the position range can not be measured, the position range restrictor  701  simply outputs the estimated position range to the train control apparatus  30 . 
     According to the satellite positioning apparatus  20 C of the third embodiment described above, the moving distance measurement device  801  measures a distance that the train  1  has moved between the first time t before  and the second time t now . In addition, the position range memory  900  stores the position range after the first time t before . In addition, the position range estimator  1001  calculates the estimated position range, by reading the position range at the first time t before  from the position range memory  900 , and adding the moving distance of the train  1  from the time t before  to the time t now , which has been measured by the moving distance measurement device  801 . 
     Therefore, according to the third embodiment, it is possible to further limit the position range of the train  1  as compared with the case of the first and second embodiments. In addition, the satellite positioning apparatus  20 C according to the third embodiment also has similar advantageous effects to those described in the first embodiment and the second embodiment. 
     Fourth Embodiment 
     The satellite positioning apparatus  20 A of the first embodiment, the satellite positioning apparatus  20 B of the second embodiment, and the satellite positioning apparatus  20 C of the third embodiment are configured to calculate the position range of the train  1  based on the satellite positioning signals received through one receiving antenna  10  mounted on the train  1 . On the other hand, a satellite positioning apparatus  20 D of a fourth embodiment calculates a position range of a train according to signals from a plurality of receiving antennas mounted on the train, thus further limiting a position range. 
       FIG. 14  is a diagram showing a configuration of a satellite positioning apparatus according to the fourth embodiment of the present invention. Referring to  FIG. 14 , the satellite positioning apparatus  20 D is provided with: two existing range calculators, i.e., a first position range calculator  40 A and a second position range calculator  40 B; and one position range restrictor  702 . In addition, referring to  FIG. 14 , the first position range calculator  40 A is connected to a first receiving antenna  10 A, and the second position range calculator  40 B is connected to a second receiving antenna  10 B. In addition, both the first position range calculator  40 A and the second position range calculator  40 B operate according to a common clock (not shown), and output data of satellite positioning signals received at the same time t r . The position range restrictor  702  outputs, as the position range of the satellite positioning apparatus  20 D, a common area among all candidate position ranges outputted by the first position range calculator  40 A, and candidate position ranges outputted by the second position range calculator  40 B. 
       FIG. 15  is a diagram showing an exemplary installation of the receiving antennas connected to the satellite positioning apparatus according to the fourth embodiment of the present invention. From the viewpoint of further limiting the position range of a train  1 , it is desirable to receive radio waves of different conditions by installing the first receiving antenna  10 A and the second receiving antenna  10 B on the train  1  at positions as far as possible from each other. Referring to  FIG. 15 , the first receiving antenna  10 A and the second receiving antenna  10 B are installed at a leading vehicle and a tail vehicle of the train  1  consisting of three vehicles, respectively. The train  1  of  FIG. 15  is provided with the two receiving antennas, i.e., the first receiving antenna  10 A and the second receiving antenna  10 B, but not limited thereto, and three or more receiving antennas may be provided to a plurality of predetermined different positions on the train  1 , respectively. In this case, the number of position range calculators increases depending on the number of the receiving antennas. 
       FIG. 16  is a diagram showing an exemplary configuration of the position range calculator  40 A. The position range calculator  40 A shown in  FIG. 16  is configured by omitting the position range restrictor  700  from the satellite positioning apparatus  20 A shown in  FIG. 1 . In addition,  FIG. 17  is a diagram showing another exemplary configuration of the position range calculator  40 A. The position range calculator  40 A shown in  FIG. 17  is configured by omitting the position range restrictor  701  from the satellite positioning apparatus  20 C shown in  FIG. 13 . It should be noted that the same reference numerals are given to similar components to those shown in  FIG. 1  or  FIG. 12 , and their description will be omitted. The second position range calculator  40 B also has a similar configuration to that of the first position range calculator  40 A. 
     According to the satellite positioning apparatus  20 D of the fourth embodiment, candidate position ranges are calculated for each receiving antenna. Therefore, for example, even when one receiving antenna is in an environment of receiving a multipath wave, the other receiving antenna may be in an environment of not receiving a multipath wave, and therefore, it is possible to limit the position range by calculating the position range of the train  1  based on the received results of the latter receiving antenna. In addition, the satellite positioning apparatus  20 D according to the fourth embodiment also has similar advantageous effects to those described in the first embodiment, the second embodiment, and the third embodiment. 
     Although a train has been described as an example of a moving object in the first to fourth embodiments, the above-described principle can be applied to a moving object that moves along a predetermined path, not limited to a train. The above-described principle can also be applied to, for example, an automobile that moves along a road. 
     Fifth Embodiment 
       FIG. 18  is a diagram showing an exemplary configuration of a train control system according to a fifth embodiment of the present invention. The train control system in  FIG. 18  includes a plurality of satellite positioning apparatuses provided to a plurality of trains  1 - 1  and  1 - 2 , respectively. Each satellite positioning apparatus is configured according to any one of the first to fourth embodiments. The trains  1 - 1  and  1 - 2  are running in the same direction. The train control apparatus  30  of the train  1 - 2  calculates a virtual train interval d interval , which is a difference between a front end of a position range of the train  1 - 2 , and a rear end of a position range of the train  1 - 1  running in front of the train  1 - 2 , based on the respective position ranges of the train  1 - 1  and  1 - 2  determined using the satellite positioning apparatuses. The train control apparatus  30  of the train  1 - 2  controls a speed of the train  1 - 2  based on the virtual train interval and a braking distance of the train  1 - 2  (in particular, a braking distance with which the train can safely stop). 
     With such a configuration, it is possible to control the train while satisfying safety required for a security apparatus. Information on the respective position ranges calculated by the trains may be exchanged via an external control apparatus  50  installed outside a track, or may be directly exchanged between the trains  1 - 1  and  1 - 2 . 
     REFERENCE SIGNS LIST 
     
         
         
           
               1 ,  1 - 1 ,  1 - 2 : TRAIN, 
               10 : RECEIVING ANTENNA, 
               10 A: FIRST RECEIVING ANTENNA, 
               10 B: SECOND RECEIVING ANTENNA, 
               20 A,  20 B,  20 C: SATELLITE POSITIONING APPARATUS, 
               30 : TRAIN CONTROL APPARATUS, 
               40 A: FIRST POSITION RANGE CALCULATOR, 
               40 B: SECOND POSITION RANGE CALCULATOR, 
               50 : EXTERNAL CONTROL APPARATUS, 
               100 : MOVING PATH MEMORY, 
               200 : ANTENNA POSITION MEMORY, 
               300 : SIGNAL RECEIVER, 
               310 : HIGH-FREQUENCY SIGNAL PROCESSOR, 
               320 : BASEBAND SIGNAL PROCESSOR, 
               400 : POSITION CALCULATOR, 
               500 : ERROR AREA CALCULATOR, 
               600 : POSITION RANGE EXTRACTOR, 
               700 ,  701 ,  702 : POSITION RANGE RESTRICTOR, 
               800 : MOVING DISTANCE MEASUREMENT DEVICE, 
               900 : POSITION RANGE MEMORY, 
               1000 ,  1001 : POSITION RANGE ESTIMATOR, 
               1100 ,  1101 : POSITION RANGE DETERMINER, 
             S 1  to S n : POSITIONING SATELLITE.