Patent Publication Number: US-2023136318-A1

Title: Tire position determination system and revolving body position determination system

Description:
This nonprovisional application is based on Japanese Patent Applications Nos. 2021-177600 and 2022-138142 filed with the Japan Patent Office on Oct. 29, 2021 and Aug. 31, 2022, respectively, the entire contents of which are hereby incorporated by reference. 
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present disclosure relates to a tire position determination system and a revolving body position determination system. 
     Description of the Background Art 
     In a tire pressure monitoring system (TPMS) in a vehicle, a detector has conventionally been attached to each of a plurality of tires. The detector attached to each of the plurality of tires transmits pneumatic pressure information to a processing device such as an ECU attached to a vehicle body. 
     Some TPMS&#39;s are provided with an auto location function to automatically determine to which tire among a plurality of tires a detector is attached. 
     Japanese Patent Laying-Open No. 2019-48547 discloses a tire state information detection system that determines to which tire of double tires employed in a truck and the like a detector is attached. The tire state information detection system in Japanese Patent Laying-Open No. 2019-48547 performs the auto location function by detection of an acceleration in a revolution circumferential direction of the tire by each detector. 
     SUMMARY OF THE INVENTION 
     In general, however, tires are rotated not only between an inner side and an outer side of double tires attached to the same axle but also among tires attached to different axles. Even in an example where tires are rotated among the tires attached to the different axles, to which tire a detector is attached is desirably automatically determined with the auto location function. 
     The present disclosure was made to solve the problem described above, and an object thereof is to specify a tire attached to an axle with the use of a detector attached to each of an axle and a tire. 
     A tire position determination system according to one aspect of the present disclosure is a tire position determination system provided in a vehicle including a first revolving body that revolves in synchronization with any tire among a plurality of tires including a first tire. The tire position determination system includes a first tire detector, a revolving body detector, and a monitoring unit. The first tire detector is attached to the first tire and detects an acceleration in a direction intersecting with a revolution axis direction of the first tire. The revolving body detector is attached to the first revolving body and detects an acceleration in a direction intersecting with a revolution axis direction of the first revolving body. The monitoring unit is configured to receive information from the first tire detector and the revolving body detector. The monitoring unit obtains, during a first period, first correspondence representing relation between a first value based on a detection value from the first tire detector and a second value based on a detection value from the revolving body detector, obtains, during a second period, second correspondence representing relation between a third value based on a detection value from the first tire detector and a fourth value based on a detection value from the revolving body detector, and determines whether or not the first tire is revolving in synchronization with the first revolving body based on a result of comparison between the first correspondence and the second correspondence. 
     According to the aspect above, whether or not correspondence between an angle of revolution of the revolving body and an angle of revolution of the first tire in the first period has varied in the second period is determined. Thus, whether or not the first tire revolves in synchronization with the first revolving body can be determined and a tire attached to the revolving body can be determined. 
     A revolving body position determination system according to one aspect of the present disclosure is a revolving body position determination system provided in a vehicle including a third revolving body and a fourth revolving body that revolve in synchronization with any tire among a plurality of tires. The revolving body position determination system includes a third revolving body detector attached to the third revolving body, the third revolving body detector detecting an acceleration in a direction intersecting with a revolution axis direction of the third revolving body, a fourth revolving body detector attached to the fourth revolving body, the fourth revolving body detector detecting an acceleration in a direction intersecting with a revolution axis direction of the fourth revolving body, and a monitoring unit that receives information from the third revolving body detector and the fourth revolving body detector. The monitoring unit determines a position of attachment of the third revolving body detector based on an identifier received from the third revolving body detector, obtains, during a first period, first correspondence representing relation between a first value based on a detection value from the third revolving body detector and a second value based on a detection value from the fourth revolving body detector, obtains, during a second period, second correspondence representing relation between a third value based on a detection value from the third revolving body detector and a fourth value based on a detection value from the fourth revolving body detector, and determines whether or not the third revolving body and the fourth revolving body revolve in synchronization with each other based on a result of comparison between the first correspondence and the second correspondence. 
     According to the aspect above, whether or not correspondence between an angle of revolution of the third revolving body and an angle of revolution of the fourth revolving body in the first period has varied in the second period is determined. Thus, whether or not the third revolving body revolves in synchronization with the fourth revolving body can be determined and a position of the fourth revolving body can be detected based on the identifier received from the third revolving body. 
     The foregoing and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a diagram schematically showing a configuration of a vehicle  10  to which a tire position determination system according to the present embodiment is applied. 
         FIG.  2    is a block diagram showing a configuration of a tire detector. 
         FIG.  3    is an exploded perspective view of double tires. 
         FIG.  4    is a perspective view of an appearance of the tire detector attached to a wheel WH. 
         FIG.  5    is a transition diagram of arrangement of the tire detector when a tire on a vehicle inner side revolves. 
         FIG.  6    is a perspective view of an appearance of an axle detector attached to an axle. 
         FIG.  7    is a transition diagram of arrangement of the axle detector when the axle revolves. 
         FIG.  8    is a diagram showing relation between arrangement of an acceleration sensor and a detection value shown in  FIGS.  5  and  7   . 
         FIG.  9    is a diagram showing arrangement of double tires on a rear first-row right side and an axle when viewed on a side of a positive direction of a Y axis. 
         FIG.  10    is a diagram showing arrangement of double tires on a rear first-row left side and an axle when viewed on a side of a negative direction of the Y axis. 
         FIG.  11    is a diagram showing arrangement of the double tires on the rear first-row right side and the axle when viewed on the side of the positive direction of the Y axis during a first stop period. 
         FIG.  12    is a diagram showing arrangement of the double tires on the rear first-row left side and the axle when viewed on the side of the negative direction of the Y axis during the first stop period. 
         FIG.  13    shows a table in a storage where UHF signals received from a tire detector and an axle detector during the first stop period are collectively stored. 
         FIG.  14    shows a table of correspondence between angles of revolution during the first stop period. 
         FIG.  15    is a diagram showing arrangement of the double tires on the rear first-row right side and the axle when viewed on the side of the positive direction of the Y axis during a second stop period. 
         FIG.  16    is a diagram showing arrangement of the double tires on the rear first-row left side and the axle when viewed on the side of the negative direction of the Y axis during the second stop period. 
         FIG.  17    shows a table in the storage where UHF signals received from the tire detector and the axle detector during the second stop period are collectively stored. 
         FIG.  18    shows a table of correspondence between angles of revolution during the second stop period. 
         FIG.  19    is a flowchart showing tire position determination processing performed by a monitoring unit. 
         FIG.  20    shows a table in the storage where UHF signals received during the first stop period are stored when the axle detector and the tire detector are attached in advance in specific arrangement. 
         FIG.  21    shows a table in the storage where UHF signals received during the second stop period are stored when the axle detector and the tire detector are attached in advance in specific arrangement. 
         FIG.  22    is a perspective view of an appearance of the axle detector attached to the axle in a second modification. 
         FIG.  23    is a diagram showing a nut loosening detector attached to a nut. 
         FIG.  24    is a diagram for illustrating attachment of a plurality of nut loosening detectors to a single axle. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     An embodiment of the present disclosure will be described in detail below with reference to the drawings. The same or corresponding elements in the drawings have the same reference characters allotted and description thereof will not be repeated. 
     First Embodiment 
     &lt;Overall Configuration&gt; 
       FIG.  1    is a diagram schematically showing a configuration of a vehicle  10  to which a tire position determination system according to the present embodiment is applied. 
     Vehicle  10  according to the present embodiment is a vehicle including a single tire as a front wheel which is a steering wheel and double (twin or dual) tires as a rear wheel which is a non-steering wheel. The single tire refers to a form of attachment of a single tire at one tire attachment position. The double tires refer to a form of attachment of two tires of the same size coupled to each other at one tire attachment position. A direction FR shown in  FIG.  1    represents a direction of forward travel of vehicle  10 . 
     In the description below, a vertical direction when vehicle  10  is arranged on the plane is defined as a “Z-axis direction,” a direction perpendicular to the Z-axis direction, in the direction of forward travel of vehicle  10 , is defined as a “positive direction along an X-axis direction,” and a direction perpendicular to the X-axis direction is defined as a “Y-axis direction.” Hereafter, a positive direction along a Z axis in each figure may be referred to as an upper side and a negative direction along the Z axis may be referred to as a lower side, the positive direction along an X axis may be referred to as a front side and a negative direction along the X axis may be referred to as a rear side, and a positive direction along a Y axis may be referred to as a right side and a negative direction along the Y axis may be referred to as a left side. 
     Vehicle  10  in the present embodiment includes front axles F 1  and F 2  and front tires  11  and  12  and rear axles R 1  to R 4  and rear double tires  21  to  24 . In vehicle  10 , two-axle double tires are adopted for rear wheels. The double tires are mainly adopted in a large-sized vehicle such as a truck or a bus. 
       FIG.  1    illustrates an example in which vehicle  10  is a rear-wheel drive type. Front tires  11  and  12  are attached to axle F 1  on a front left side and axle F 2  on a front right side, respectively. In other words, axle F 1  revolves as being integrated with tire  11 . Similarly, axle F 2  revolves as being integrated with tire  12 . 
     Rear double tires  21 ,  22 ,  23 , and  24  are attached to axle R 1  on the left side in a rear first row, axle R 2  on the right side in the rear first row, axle R 3  on the left side in a rear second row, and axle R 4  on the right side in the rear second row, respectively. In other words, axle R 1  to axle R 4  revolve as being integrated with double tires  21  to  24 , respectively. Vehicle  10  is not limited to the rear-wheel drive type but may be a front-wheel drive type or an all-wheel drive type. 
     In other words, axles F 1 , F 2 , and R 1  to R 4  revolve in synchronization with revolution of the tires attached thereto. Axles F 1 , F 2 , and R 1  to R 4  are collectively referred to as an “axle Ax” below. Axle Ax may correspond to the “first revolving body” in the present disclosure. 
     Double tires  21  include a tire  21   a  on a vehicle inner side and a tire  21   b  on a vehicle outer side. Double tires  22  include a tire  22   a  on the vehicle inner side and a tire  22   b  on the vehicle outer side. Double tires  23  include a tire  23   a  on the vehicle inner side and a tire  23   b  on the vehicle outer side. Double tires  24  include a tire  24   a  on the vehicle inner side and a tire  24   b  on the vehicle outer side. Tires  11 ,  12 , and  21   a  to  24   b  will collectively be referred to as a “tire Tr” below. 
     Vehicle  10  further includes a system that monitors a pneumatic pressure of each tire (TPMS). Specifically, vehicle  10  includes a plurality of tire detectors  13 ,  14 , and  31   a  and  31   b  to  34   a  and  34   b  each of which detects a tire pressure, a plurality of axle detectors  15   a ,  15   b ,  16   a ,  16   b ,  17   a , and  17   b  that detect an acceleration of gravity in a revolution diameter direction of axles F 1 , F 2 , and R 1  to R 4 , respectively, and a TPMS receiver  40 . Tire detectors  13  and  14  are attached to respective wheels of front tires  11  and  12 . Tire detectors  31   a  and  31   b  to  34   a  and  34   b  are attached to respective wheels of rear tires  21   a  to  24   b . Each of tire detectors  13 ,  14 , and  31   a  and  31   b  to  34   a  and  34   b  may be formed integrally with a valve for intake of air into each tire. 
     Axle detectors  15   a  to  17   b  are attached to respective axles F 1 , F 2 , and R 1  to R 4 . Portions of attachment of axle detectors  15   a  to  17   b  are not limited to the axles. For example, axle detectors  15   a  to  17   b  may be attached to a hub, a knuckle, or the like that revolves in synchronization with revolution of the tire. Axle detectors  15   a  to  17   b  may correspond to the “revolving body detector” in the present disclosure. 
     Each of tire detectors  13 ,  14 , and  31   a  and  31   b  to  34   a  and  34   b  and axle detectors  15   a  to  17   b  is activated when a prescribed activation condition is satisfied, and detects a pneumatic pressure of each tire and outputs a radio signal in an ultra high frequency (UHF) band (which is also simply referred to as a “UHF signal” below) that includes a result of detection. The “prescribed activation condition” is set in advance to be satisfied regularly or irregularly. Tire detectors  13 ,  14 , and  31   a  and  31   b  to  34   a  and  34   b  and axle detectors  15   a  to  17   b  can thus intermittently be activated at timings different from one another and transmit UHF signals. The radio signal transmitted from each of tire detectors  13 ,  14 , and  31   a  and  31   b  to  34   a  and  34   b  and axle detectors  15   a  to  17   b  is not limited to a radio signal in the UHF band and may be a radio signal at another frequency. 
     The UHF signal outputted from each of tire detectors  13 ,  14 , and  31   a  and  31   b  to  34   a  and  34   b  and axle detectors  15   a  to  17   b  includes information indicating a specific ID number for specifying at least each of tire detectors  13 ,  14 , and  31   a  and  31   b  to  34   a  and  34   b  and axle detectors  15   a  to  17   b . The UHF signal outputted from each of tire detectors  13 ,  14 , and  31   a  and  31   b  to  34   a  and  34   b  includes information indicating a tire pressure. As TPMS receiver  40  receives the UHF signal outputted from each of tire detectors  13 ,  14 , and  31   a  and  31   b  to  34   a  and  34   b , it monitors a pneumatic pressure of each tire. 
     Tires identical in specifications and construction are employed as front tires  11  and rear tires  21   a  to  24   b  for allowing tire rotation. Therefore, tire detectors identical in configuration are adopted also for tire detectors  13 ,  14 , and  31   a  and  31   b  to  34   a  and  34   b . When tire detectors  13 ,  14 , and  31   a  and  31   b  to  34   a  and  34   b  do not have to be described as being distinguished from one another, tire detectors  13 ,  14 , and  31   a  and  31   b  to  34   a  and  34   b  are also simply denoted to as a “tire detector  30 ” below without being distinguished from one another. Axle detectors identical in configuration are adopted also for axle detectors  15   a  to  17   b . When axle detectors  15   a  to  17   b  do not have to be described as being distinguished from one another, axle detectors  15   a  to  17   b  are also simply denoted to as an “axle detector  15 ” below without being distinguished from one another. 
     TPMS receiver  40  is provided on a vehicle body side of vehicle  10 . TPMS receiver  40  includes a monitoring unit  45  that monitors a pneumatic pressure of each tire. Monitoring unit  45  includes a storage  46 , a processing unit  47 , and an antenna A 1 . Antenna A 1  is configured to receive UHF signals transmitted from tire detector  30  and axle detector  15 . Monitoring unit  45  receives the UHF signal received by antenna A 1 . 
     Processing unit  47  includes a processor such as a not-shown central processing unit (CPU), a memory, and an input and output buffer. The memory includes a read only memory (ROM) and a random access memory (RAM). The processor develops a program stored in the ROM on the RAM and executes the same. Various types of processing performed by processing unit  47  are described in the program stored in the ROM. 
     Information indicating a position of a tire where each tire detector  30  is attached and information indicating a tire pressure are stored in storage  46  as being brought in correspondence with an ID number of each tire detector  30 . In the present embodiment, ten tire positions (a front left side, a front right side, a rear first-row left inner side, a rear first-row left outer side, a rear first-row right inner side, a rear first-row right outer side, a rear second-row left inner side, a rear second-row left outer side, a rear second-row right inner side, and a rear second-row right outer side) in total are set in advance and an ID number of each tire detector  30  is brought in correspondence with any one tire position. For example, the tire position “front left side” is brought in correspondence with the ID number of tire detector  13 , and the tire position “rear first-row right inner side” is brought in correspondence with the ID number of tire detector  32   a.    
     Information indicating a position of an axle where each axle detector  15  is attached is stored in storage  46  as being brought in correspondence with the ID number of each axle detector  15 . In the present embodiment, six axle positions (the front left side, the front right side, the rear first-row left side, the rear first-row right side, the rear second-row left side, and the rear second-row right side) in total are set in advance, and the ID number of each axle detector  15  is brought in correspondence with any one tire position. For example, the tire position “front left side” is brought in correspondence with the ID number of axle detector  15   a  and the tire position “rear first-row right side” is brought in correspondence with the ID number of axle detector  16   b.    
     When monitoring unit  45  receives a UHF signal from each tire detector  30 , it determines the tire position corresponding to the ID number included in the UHF signal by referring to the information stored in storage  46 . Monitoring unit  45  updates the pneumatic pressure at the specified tire position with the tire pressure included in the UHF signal. 
     When monitoring unit  45  receives a UHF signal including the ID number of tire detector  32   a , it refers to correspondence between the ID number and the tire position stored in storage  46 . Monitoring unit  45  thus specifies the tire position corresponding to the ID number included in the UHF signal as the “rear first-row right inner side.” Monitoring unit  45  updates the pneumatic pressure at the specified “rear first-row right inner side” with the tire pressure included in the UHF signal. 
     TPMS receiver  40  can have information on correspondence between the tire position and the tire pressure stored in storage  46  shown on a display  52 . Display  52  is arranged at a position where a driver can visually recognize the same. Display  52  is arranged, for example, in an instrument panel within the vehicle. 
     TPMS receiver  40  accepts various types of information provided by a user through an input unit  53 . Input unit  53  includes, for example, a button and a touch screen. Input unit  53  is arranged, for example, in the instrument panel within the vehicle similarly to display  52 . 
     When the tire pressure included in the received UHF signal is equal to or lower than a low-pressure threshold value, monitoring unit  45  has the tire position where the tire pressure is at the low-pressure threshold value shown on display  52  together with a warning. TPMS receiver  40  performs processing for determining the tire pressure for each received UHF signal and monitors each pneumatic pressure of each tire. The driver can thus recognize in real time the position of the tire the tire pressure of which has become equal to or lower than the low-pressure threshold value. 
     &lt;Configuration of Tire Detector  30 &gt; 
       FIG.  2    is a block diagram showing a configuration of tire detector  30 . Tire detector  30  includes a controller  35 , a pressure sensor  38 , an acceleration sensor (G sensor)  39 , an antenna A 2 , and a transmission circuit CT. 
     Controller  35  includes a storage  36  and a processing unit  37 . Processing unit  37  includes a processor such as a not-shown CPU, a memory, and an input and output buffer. The memory includes a ROM and a RAM. The processor develops a program stored in the ROM on the RAM and executes the same. Various types of processing performed by processing unit  37  are described in the program stored in the ROM. 
     In storage  36 , an ID number specific for each tire detector  30  shown in  FIG.  1    is stored. In storage  36  included in tire detector  13  in  FIG.  1   , “01” is stored as the ID number, and in storage  36  included in tire detector  14 , “02” is stored as the ID number. 
     In double tires  21 , in storage  36  included in tire detector  31   b, “ 03” is stored as the ID number, and in storage  36  included in tire detector  31   a, “ 04” is stored as the ID number. In double tires  22 , in storage  36  included in tire detector  32   a, “ 05” is stored as the ID number, and in storage  36  included in tire detector  32   b, “ 06” is stored as the ID number. Thus, in storage  36  within each tire detector  30 , the ID number specific to each tire detector  30  is stored. 
     Pressure sensor  38  detects a tire pressure and outputs a result of detection (which is also referred to as a “tire pressure P” below) to controller  35 . Acceleration sensor  39  detects an acceleration in a uniaxial direction generated in tire detector  30  and outputs a result of detection (which is also referred to as an “acceleration G” below) to controller  35 . Tire detector  30  may further include a temperature sensor that detects a tire temperature in addition to pressure sensor  38  and acceleration sensor  39 . 
     Controller  35  controls transmission circuit CT to output a UHF signal from antenna A 2 . The transmitted UHF signal includes information indicating acceleration G and time information indicating time of detection of acceleration G, in addition to an ID number stored in storage  36  and information indicating tire pressure P. 
     As described above, tire detector  30  is activated and outputs the UHF signal at timing when a prescribed activation condition is satisfied. Tire detector  30  is provided with a not-shown battery, and operates with electric power supplied from the battery. This battery is constructed not to readily externally be charged. Therefore, in tire detector  30  in a first embodiment, desirably, operating time is minimized to suppress power consumption by tire detector  30 . 
     From this point of view, the “prescribed activation condition” is set in advance to suppress a frequency of activation of tire detector  30  as much as possible. For example, the prescribed activation condition may include such a timer-based activation condition that a not-shown timer has counted lapse of prescribed timer time since previous stop and such an acceleration-based activation condition that acceleration G detected by acceleration sensor  39  has attained to a specific value (for example, a maximum value or a minimum value). 
     The “timer time” used as the timer-based activation condition described above may be set to a fixed value or a variable value that varies with acceleration G. For example, controller  35  may determine whether or not a tire is revolving based on acceleration G which represents the result of detection by acceleration sensor  39  and change the set timer time. 
     More specifically, controller  35  may set the timer time to a relatively long time period (for example, approximately several minutes or approximately several hours which are further longer) in a stop state in which tires are not revolving, and may set the timer time to a relatively short time period (for example, approximately several seconds or approximately several milliseconds which are further shorter) in a traveling state in which tires are revolving. One active time period (a time period from activation until next stop) of tire detector  30  may be restricted to a relatively short time period (for example, approximately several milliseconds). 
     &lt;Configuration of Axle Detector  15 &gt; 
     Axle detector  15  is in such a configuration that pressure sensor  38  is removed from the configuration of tire detector  30  shown in  FIG.  2    by way of example. Description of the configuration of axle detector  15  identical to that of tire detector  30  will not be repeated. 
     An ID number specific for each axle detector  15  shown in  FIG.  1    is stored in storage  36  in axle detector  15 . For example, in storage  36  included in axle detector  15   a  in  FIG.  1   , “11” is stored as the ID number, and in storage  36  included in axle detector  15   b, “ 12” is stored as the ID number. In storage  36  included in axle detector  16   a, “ 13” is stored as the ID number, and in storage  36  included in axle detector  16   b, “ 14” is stored as the ID number. Furthermore, in storage  36  included in axle detector  17   a, “ 15” is stored as the ID number, and in storage  36  included in axle detector  17   b, “ 16” is stored as the ID number. 
     &lt;Construction of Double Tires&gt; 
     Vehicle  10  according to the present embodiment includes double tires  21  to  24  as rear wheels which are non-steering wheels as described above.  FIG.  3    is an exploded perspective view of double tires  22 . An exemplary construction of double tire  22  will be described with reference to  FIG.  3   . Double tires  21 ,  23 , and  24  are also similar in construction to double tires  22 . 
     Double tires  22  include tire  22   a  on the vehicle inner side and tire  22   b  on the vehicle outer side. A wheel WH of each of tires  22   a  and  22   b  includes a flat portion FP. Flat portion FP protrudes on the outer side relative to a side surface portion (a sidewall portion) of each tire. Tire  22   a  on the vehicle inner side and tire  22   b  on the vehicle outer side are coupled back-to-back. In other words, tires  22   a  and  22   b  are fixed with flat portions FP of wheels WH thereof face each other. 
     Tire  22   a  on the vehicle inner side is fixed to axle R 2  by being fastened by an inner nut NIN by insertion of a bolt BT of a hub H 2  of axle R 2  into a hole provided in flat portion FP of wheel WH. A tip end side (vehicle outer side) of inner nut MN is threaded. In a wheel of a large-sized vehicle such as a truck, in conformity with JIS, inner nut NIN as shown in  FIG.  3    is attached. In conformity with ISO, on the other hand, inner not NIN is not attached. Wheel WH in the present embodiment may be a wheel in conformity with any of JIS and ISO. 
     Tire  22   b  on the vehicle outer side is fixed to tire  22   a  on the vehicle inner side by being fastened by a wheel nut NW by insertion of the thread on the tip end side of inner nut NIN into the hole provided in flat portion FP of wheel WH. Tire  22   a  and tire  22   b  are thus connected to the same axle R 2  as being coupled to each other. 
     Tire  22   a  is fixed such that a revolution axis of axle R 2  and a revolution axis of tire  22   a  are coaxial with each other. Similarly, tire  22   b  is fixed such that the revolution axis of axle R 2  and a revolution axis of tire  22   b  are coaxial with each other. Tire Tr including double tires  22  is fixed such that a revolution axis of axle Ax to which tire Tr is attached and a revolution axis of tire Tr are coaxial with each other. 
     &lt;Diagram of Appearance of Tire Detector  30 &gt; 
       FIG.  4    is a perspective view of an appearance of tire detector  30  attached to wheel WH. Tire detector  30  is supported as being fixed to wheel WH.  FIG.  4    shows a revolution axis direction D 1 , a revolution circumferential direction D 2 , and a revolution diameter direction D 3  of wheel WH when tire Tr revolves. Acceleration sensor  39  of tire detector  30  in the present embodiment is a uniaxial acceleration sensor having revolution diameter direction D 3  as a detection direction. The direction of detection by acceleration sensor  39  of tire detector  30  is not limited to revolution diameter direction D 3 , but it should only be a direction orthogonal to revolution axis direction D 1 . In other words, the direction of detection by acceleration sensor  39  of tire detector  30  may be revolution circumferential direction D 2 . 
     &lt;Detection Value from Acceleration Sensor  39  in Tire Detector  32   a&gt;   
       FIG.  5    is a transition diagram of arrangement of tire detector  32   a  when tire  22   a  on the vehicle inner side revolves.  FIG.  5    shows transition of arrangement of tire detector  32   a  when tire  22   a  is viewed from the side of the positive direction (outer side of vehicle  100 ) in the Y-axis direction. In other words,  FIG.  5    shows transition of arrangement of tire detector  32   a  when tire  22   a  is viewed on a side of flat portion FP in wheel WH of tire  22   a.    
       FIG.  5    shows arrangements  1   h  to  12   h  as twelve patterns of exemplary arrangement of tire detector  32   a . Arrangement  12   h  of tire detector  32   a  is such an arrangement that tire detector  32   a  is located in revolution diameter direction D 3  extending from a central point CP 1  of tire  22   a  in the positive direction along the Z-axis. Arrangement  12   h  is referred to as arrangement at “θ degree” or “+360 degrees” below. 
     Arrangement  1   h  represents arrangement of tire detector  32   a  when tire  22   a  revolves by θ degrees clockwise from the state of arrangement  12   h . θ degrees in  FIG.  7    is set to thirty degrees. Arrangement  1   h  is referred to as arrangement at “+30 degrees” below. Arrangement  2   h  represents arrangement of tire detector  32   a  when tire  22   a  revolves by θ degrees clockwise from the state of arrangement  1   h . Arrangement  2   h  is referred to as arrangement at “+60 degrees” below. 
     Arrangement  3   h  represents arrangement of tire detector  32   a  when tire  22   a  revolves by θ degrees clockwise from the state of arrangement  2   h . Arrangement  3   h  is referred to as arrangement at “+90 degrees” below.  FIG.  5    thus illustrates twelve patterns of exemplary arrangement of tire detector  30  at 0 degree (360 degrees), +30 degrees, +60 degrees, +90 degrees, +120 degrees, +150 degrees, +180 degrees, +210 degrees, +240 degrees, +270 degrees, +300 degrees, and +330 degrees.  FIG.  5    shows a detection value from acceleration sensor  39  while vehicle  10  remains stopped. 
     As described with reference to  FIG.  4   , acceleration sensor  39  of tire detector  30  is a uniaxial acceleration sensor that detects an acceleration only in one direction and has a tire diameter direction (revolution diameter direction) as the detection direction. Therefore, as shown in  FIG.  5   , an acceleration of gravity in the detection direction is highest in arrangement  12   h  (0 degree) or arrangement  6   h  (+180 degrees) of tire detector  30 . 
     In the example in  FIG.  5   , the detection value from acceleration sensor  39  when tire detector  30  is in arrangement  12   h  is +1 G. The detection value from acceleration sensor  39  when tire detector  30  is in arrangement  6   h  is −1 G. 
     When tire detector  30  is in arrangement  1   h  or arrangement  11   h , the detection value from acceleration sensor  39  is +√3/2 G. When tire detector  30  is in arrangement  2   h  or arrangement  10   h , the detection value from acceleration sensor  39  is +1/2 G. When tire detector  30  is in arrangement  3   h  or arrangement  9   h , the detection value from acceleration sensor  39  is 0 G. 
     When tire detector  30  is in arrangement  5   h  or arrangement  7   h , the detection value from acceleration sensor  39  is −√3/2 G. When tire detector  30  is in arrangement  4   h  or arrangement  8   h , the detection value from acceleration sensor  39  is −1/2 G. Depending on a direction of attachment of tire detector  30 , positive and negative signs of the acceleration of gravity as the detection value shown in  FIG.  5    may be reversed. 
     Tire detector  30  transmits the UHF signal including the detection value from acceleration sensor  39  to monitoring unit  45 . Monitoring unit  45  can estimate arrangement of tire detector  30  based on the detection value from acceleration sensor  39 . As shown in  FIG.  5   , the detection values from acceleration sensor  39  are in line symmetry with respect to the Z axis that passes through central point CP 1 . 
     Monitoring unit  45  can obtain at least two arrangements as arrangement candidates for tire detector  30  based on the detection value from acceleration sensor  39 . For example, when monitoring unit  45  finds the detection value from acceleration sensor  39  as +√3/2 G, tire detector  30  obtains arrangement  1   h  and arrangement  11   h  as arrangement candidates. Alternatively, when monitoring unit  45  finds the detection value from acceleration sensor  39  as −1/2 G, tire detector  30  obtains arrangement  4   h  and arrangement  8   h  as arrangement candidates. 
     When the detection value from acceleration sensor  39  is +1 G, monitoring unit  45  estimates that tire detector  30  is in arrangement  12   h . When the detection value from acceleration sensor  39  is −1 G, monitoring unit  45  estimates that tire detector  30  is in arrangement  6   h.    
     Tire detector  30  is attached as being fixed to wheel WH of tire Tr. In other words, arrangement of tire detector  30  represents at which angle of revolution tire Tr has stopped. 
     &lt;Diagram of Appearance of Axle Detector  15 &gt; 
       FIG.  6    is a perspective view of an appearance of axle detector  15  attached to axle Ax. Axle detector  15  is supported as being fixed to axle Ax.  FIG.  6    shows revolution axis direction D 1 , revolution circumferential direction D 2 , and revolution diameter direction D 3  when axle Ax revolves. As shown in  FIG.  3   , the revolution axis of axle Ax is coaxial with the revolution axis of wheel WH. 
     Similarly to acceleration sensor  39  of tire detector  30 , acceleration sensor  39  of axle detector  15  is a uniaxial acceleration sensor that has revolution diameter direction D 3  as the detection direction. The direction of detection by acceleration sensor  39  of axle detector  15  is not limited to revolution diameter direction D 3  either, and it should only be a direction orthogonal to revolution axis direction D 1 . Axle Ax has an end surface FP 2  exposed while axle Ax is attached to vehicle  10 . 
     &lt;Detection Value from Acceleration Sensor  39  in Axle Detector  16   b&gt;   
       FIG.  7    is a transition diagram of arrangement of axle detector  16   b  when axle R 2  revolves.  FIG.  7    shows a cross-section when axle R 2  is viewed on the side of the positive direction (the outer side of vehicle  10 ) in the Y-axis direction and transition of arrangement of axle detector  16   b.    
     Similarly to  FIG.  5   ,  FIG.  7    shows arrangements  1   h  to  12   h  as twelve patterns of exemplary arrangements of axle detector  16   b . Since description of arrangement of axle detector  16   b  and the detection value from acceleration sensor  39  is the same as in  FIG.  5   , the description will not be repeated below. 
     Specifically, monitoring unit  45  can estimate arrangement of axle detector  15  in addition to arrangement of tire detector  30  based on the detection value from acceleration sensor  39  of axle detector  15 .  FIG.  8    is a diagram showing relation between arrangement of acceleration sensor  39  and a detection value shown in  FIGS.  5  and  7   . An exemplary arrangement of tire detector  30  and axle detector  15  with respect to twelve patterns of angles of revolution of tire Tr or axle Ax is described with reference to  FIGS.  5  to  7   . When tire Tr or axle Ax stops at another angle of revolution as well, the detection value from acceleration sensor  39  changes in accordance with a phase in  FIG.  8   . 
     &lt;Determination of Tire Position&gt; 
     A specific method of determining a tire position in vehicle  10  will be described below with reference to  FIGS.  9  to  18   . The tire position determination system in the present embodiment determines to which axle Ax which tire Tr is attached based on relationship between an angle of revolution of tire Tr and an angle of revolution of axle Ax. In other words, the tire position determination system determines a combination between axle Ax and tire Tr. The tire position determination system thus automatically determines the tire position also after tires are rotated. 
     Monitoring unit  45  obtains relationship between the angle of revolution of tire Tr and the angle of revolution of axle Ax based on the detection values from acceleration sensors  39  of tire detector  30  and axle detector  15 . In order to describe a method of obtaining relationship between the angle of revolution of tire Tr and the angle of revolution of axle Ax, exemplary relation of arrangement between tire detector  30  and axle detector  15  will be described below with reference to  FIGS.  9  and  10   . 
     For simplification of the description, the auto location function directed only to double tires  21  and double tires  22  will be described below. The tire position determination system, however, performs the auto location function to determine the tire position for all of tires Tr and axles Ax provided in vehicle  10 . 
       FIG.  9    is a diagram showing arrangement of double tires  22  on the rear first-row right side and axle R 2  when viewed on the side of the positive direction of the Y axis.  FIG.  9    shows wheels WH of tires  22   a  and  22   b , tire detectors  32   a  and  32   b , axle R 2 , and axle detector  16   b  while vehicle  10  remains stopped. 
       FIG.  9    shows relation of arrangement between tire detectors  32   a  and  32   b  and axle detector  16   b  in the present embodiment. When axle detector  16   b  is in arrangement  12   h , tire detector  32   a  is in arrangement  1   h  and tire detector  32   b  is in arrangement  9   h . Relation of arrangement between tire detectors  32   a  and  32   b  and axle detector  16   b  shown in  FIG.  9    is merely by way of example and tire detectors  32   a  and  32   b  and axle detector  16   b  may be arranged in another relation of arrangement. 
     Tire detectors  32   a  and  32   b  are fixed to wheels WH of respective tires  22   a  and  22   b . In other words, arrangement of tire detector  30  represents at which angle of revolution tire Tr has stopped. Axle detector  16   b  is fixed to axle R 2  In other words, arrangement of axle detector  15  represents at which angle of revolution axle Ax has stopped. By obtaining relation of arrangement between tire detectors  32   a  and  32   b  and axle detector  16   b , monitoring unit  45  can obtain correspondence between the angles of revolution of tires  22   a  and  22   b  and the angle of revolution of axle R 2 . 
       FIG.  10    is a diagram showing arrangement of double tires  21  on the rear first-row left side and axle R 1  when viewed on the side of the negative direction of the Y axis.  FIG.  10    shows wheels WH of tires  21   a  and  21   b , tire detectors  31   a  and  31   b , axle R 1 , and axle detector  16   a  while vehicle  10  remains stopped. 
     Tire detectors  31   a  and  31   b  and axle detector  16   a  are arranged in relation of arrangement as shown in  FIG.  10   . When axle detector  16   a  is in arrangement  12   h , tire detector  31   a  is in arrangement  10   h  and tire detector  31   b  is in arrangement  12   h . Relation of arrangement between tire detectors  31   a  and  31   b  and axle detector  16   a  shown in  FIG.  10    is merely by way of example and tire detectors  31   a  and  31   b  and axle detector  16   a  may be arranged in another relation of arrangement. 
     By obtaining relation of arrangement between tire detectors  31   a  and  31   b  and axle detector  16   a , monitoring unit  45  can obtain correspondence between the angles of revolution of tires  21   a  and  21   b  and the angle of revolution of axle R 1 . 
     &lt;Obtaining Angle of Revolution&gt; 
     Monitoring unit  45  obtains arrangement of tire detector  30  based on the detection value from acceleration sensor  39  of tire detector  30 , and obtains arrangement of axle detector  15  based on the detection value from acceleration sensor  39  of axle detector  15 . Monitoring unit  45  obtains correspondence between the angle of revolution of tire Tr and the angle of revolution of axle Ax based on relation between obtained arrangement of tire detector  30  and obtained arrangement of axle detector  15 . 
     Tire detector  30  and axle detector  15  are intermittently activated at timings different from each other and transmit the UHF signals. Since tire Tr is revolving while vehicle  10  is traveling, the detection value from acceleration sensor  39  changes over time. Therefore, while vehicle  10  is traveling, monitoring unit  45  is unable to obtain relation of arrangement between tire detector  30  and axle detector  15  even based on the received UHF signal. 
     In order to obtain relation of arrangement between tire detector  30  and axle detector  15 , monitoring unit  45  uses detection values from acceleration sensors  39  of tire detector  30  and axle detector  15  obtained during a period in which vehicle  10  remains stopped. Relation of arrangement between tire detector  30  and axle detector  15  at timing of stop of any vehicle  10  will be described below with reference to  FIGS.  11  and  12   . 
     Monitoring unit  45  determines whether or not vehicle  10  remains stopped based on a traveling speed received from a not-shown apparatus that detects a traveling speed of vehicle  10 . 
       FIG.  11    is a diagram showing arrangement of double tires  22  on the rear first-row right side and axle R 2  when viewed on the side of the positive direction of the Y axis during a first stop period. The first stop period refers to any period during which vehicle  10  stops. A point of start of the first stop period is a time point of stop of vehicle  10 , and a point of end of the first stop period is a time point when vehicle  10  pulls away. The angles of revolution of tire Tr and axle Ax at the time when the vehicle stops are different each time the vehicle stops, because tire Tr and axle Ax revolve with travel of vehicle  10 . In the first stop period, double tires  22  and axle R 2  remain stopped as having revolved clockwise by 30 degrees from the state shown in  FIG.  9   . 
       FIG.  12    is a diagram showing arrangement of double tires  21  on the rear first-row left side and axle R 1  when viewed on the side of the negative direction of the Y axis during the first stop period. In the first stop period, double tires  21  and axle R 1  remain stopped as having revolved clockwise by 120 degrees from the state shown in  FIG.  10   . 
     During the first stop period, tire detectors  31   a ,  31   b ,  32   a , and  32   b  and axle detectors  16   a  and  16   b  intermittently transmit the UHF signals at timings different from one another. Monitoring unit  45  has information indicated by the UHF signals received at different timings stored in storage  46 .  FIG.  13    shows a table in storage  46  where UHF signals received from tire detector  30  and axle detector  15  during the first stop period are collectively stored. 
     In a No column, an identifier for identifying data for each UHF signal is shown. In an ID column, an ID specific to each of tire detector  30  and axle detector  15  is shown. In a gravity (G) column, a detection value from acceleration sensor  39  is shown. In a stop ID column, a stop period at the time of reception of the UHF signal is shown. In an estimated angle column, an angle of revolution of tire Tr or axle Ax estimated by monitoring unit  45  is shown. 
     Monitoring unit  45  obtains information representing the ID column and the gravity (G) included in the UHF signal at the time of reception of the UHF signal and has the information stored in the table in  FIG.  13   . Monitoring unit  34  generates a new identifier in the No column based on new reception of the UHF signal and has the identifier stored together with data obtained from the UHF signal. Monitoring unit  45  generates a new stop ID each time vehicle  10  stops, and has the corresponding stop ID stored based on time of reception of the UHF signal. 
     Monitoring unit  45  estimates arrangement of axle detector  15  or tire detector  30  based on information shown in the gravity (G) column. For example, for a No column “101”, a value in the ID column is “13”. In another table stored in storage  46 , axle detector  16   a  is brought in correspondence in advance with the ID “13”. Monitoring unit  45  can determine that the data shown in the No column “101” is data based on the UHF signal transmitted from axle detector  16   a.    
     For the No column “101”, a value in the gravity (G) column is “−1/2”. As described with reference to  FIG.  7   , arrangement of axle detector  16   a  where the acceleration of gravity can be −1/2 is arrangement  4   h  (+120 degrees) or arrangement  8   h  (+240 degrees). Monitoring unit  45  can estimate that arrangement of axle detector  16   a  at the time of reception of the UHF signal indicating the No column “101” is arrangement  4   h  (+120 degrees) or arrangement  8   h  (+240 degrees). 
     Monitoring unit  45  estimates arrangement of axle detector  16   a  from the value of the acceleration of gravity, converts the estimated arrangement into angle information, and has the angle information stored in the estimated angle column. In the estimated angle column, data indicating that axle detector  16   a  is arranged at 120 degrees or 240 degrees is stored. In the estimated angle column, the angle of revolution of axle Ax is shown. 
     Monitoring unit  45  thus estimates the angle of revolution of axle Ax based on the UHF signal received from each axle detector  15  during the first stop period. Monitoring unit  45  estimates the angle of revolution of tire Tr based on the UHF signal received from each tire detector  30  during the first stop period.  FIG.  13    shows a table where the estimated angles of tire detectors  31   a ,  31   b ,  32   a , and  32   b  and axle detectors  16   a  and  16   b  are stored. 
     &lt;Obtaining Correspondence Between Angles of Revolution During First Stop Period&gt; 
       FIG.  14    shows a table of correspondence between angles of revolution during the first stop period.  FIG.  14    shows correspondence between the angle of revolution of each axle detector  15  and the angle of revolution of each tire detector  30  during the first stop period. The first stop period may correspond to the “first period” in the present disclosure. 
     For example, in the table in  FIG.  14   , information “0 degree or 120 degrees” is stored as correspondence between the angle of revolution of axle R 1  to which axle detector  16   a  having the ID number “13” is attached and the angle of revolution. 
     Monitoring unit  45  obtains correspondence between the angle of revolution of axle R 1  and the angle of revolution of tire  21   b  based on the estimated angle estimated in  FIG.  13   . Specifically, monitoring unit  45  obtains a difference in angle in each combination of the estimated angles. 
     As shown in  FIG.  13   , arrangement of axle detector  16   a  having the ID number “13” is estimated as arrangement  4   h  (+120 degrees) or arrangement  8   h  (+240 degrees). Arrangement of tire detector  31   b  having the ID number “03” is also similarly estimated as arrangement  4   h  (+120 degrees) or arrangement  8   h  (+240 degrees). 
     When axle detector  16   a  is in arrangement  4   h  (+120 degrees) and tire detector  31   b  is in arrangement  4   h  (+120 degrees), the difference in angle is 0 degree. When axle detector  16   a  is in arrangement  4   h  (+120 degrees) and tire detector  31   b  is in arrangement  8   h  (+240 degrees), the difference in angle is 120 degrees. 
     When axle detector  16   a  is in arrangement  8   h  (+240 degrees) and tire detector  31   b  is in arrangement  4   h  (+120 degrees), the difference in angle is 120 degrees. When axle detector  16   a  is in arrangement  8   h  (+240 degrees) and tire detector  31   b  is in arrangement  8   h  (+240 degrees), the difference in angle is 0 degree. In other words, the difference in angle in each combination of the estimated angles of the detectors having the ID number “13” and the ID number “03” is 0 degree or 120 degrees. 
     In the table in  FIG.  14   , information “60 degrees or 180 degrees” is stored as correspondence between the angle of revolution of axle R 1  to which axle detector  16   a  having the ID number “13” is attached and the angle of revolution of tire  32   a  to which tire detector  22   a  having the ID number “05” is attached. 
     As shown in  FIG.  13   , arrangement of axle detector  16   a  having the ID number “13” is estimated as arrangement  4   h  (+120 degrees) or arrangement  8   h  (+240 degrees). Arrangement of tire detector  32   a  having the ID number “05” is estimated as arrangement  2   h  (+60 degrees) or arrangement  10   h  (+300 degrees). 
     When axle detector  16   a  is in arrangement  4   h  (+120 degrees) and tire detector  32   a  is in arrangement  2   h  (+60 degrees), the difference in angle is 60 degrees. When axle detector  16   a  is in arrangement  4   h  (+120 degrees) and tire detector  32   a  is in arrangement  10   h  (+300 degrees), the difference in angle is 180 degrees. 
     When axle detector  16   a  is in arrangement  8   h  (+240 degrees) and tire detector  32   a  is in arrangement  2   h  (+60 degrees), the difference in angle is 180 degrees. When axle detector  16   a  is in arrangement  8   h  (+240 degrees) and tire detector  32   a  is in arrangement  10   h  (+300 degrees), the difference in angle is 60 degrees. In other words, the difference in angle in each combination of the estimated angles of the detectors having the ID number “13” and the ID number “05” is 60 degrees or 180 degrees. 
     Monitoring unit  45  thus obtains the difference in angle between the estimated angles in the combination of the ID numbers and has the difference in angle stored in the table in  FIG.  14   . Monitoring unit  45  thus obtains correspondence between the angle of revolution of each axle Ax and the angle of revolution of each tire Tr during the first stop period. Each piece of data shown in  FIG.  14    may correspond to the “first correspondence” in the present disclosure. 
     &lt;Obtaining Correspondence Between Angles of Revolution During Second Stop Period&gt; 
     After monitoring unit  45  obtains correspondence during the first stop period shown in  FIG.  14   , it obtains again correspondence between the angle of revolution of each axle Ax and the angle of revolution of each tire Tr during the second stop period following the first stop period. The second stop period may correspond to the “second period” in the present disclosure. 
       FIG.  15    is a diagram showing arrangement of double tires  22  on the rear first-row right side and axle R 2  when viewed on the side of the positive direction of the Y axis during the second stop period. The second stop period refers to a period, with stop again of vehicle  10  being defined as a point of start thereof after the first stop period ends as a result of pulling away of vehicle  10 . A time point when vehicle  10  pulls away again is defined as a point of end of the second stop period. During the second stop period, double tires  22  and axle R 2  remain stopped as having revolved clockwise by 150 degrees from the state shown in  FIG.  9   . 
       FIG.  16    is a diagram showing arrangement of double tires  21  on the rear first-row left side and axle R 1  when viewed on the side of the negative direction of the Y axis during the second stop period. During the second stop period, double tires  21  and axle R 1  remain stopped as having revolved clockwise by 270 degrees from the state shown in  FIG.  10   . 
       FIG.  17    shows a table in storage  46  where UHF signals received from tire detector  30  and axle detector  15  during the second stop period are collectively stored. Monitoring unit  45  has data shown in the table in  FIG.  17    stored with a method similar to the method described with reference to  FIG.  13   . 
       FIG.  18    shows a table of correspondence between angles of revolution during the second stop period. Monitoring unit  45  obtains correspondence between the angles of revolution during the second stop period based on the table shown in  FIG.  17   . Monitoring unit  45  has data shown in the table in  FIG.  18    stored with a method similar to the method described with reference to  FIG.  14   . Each piece of data shown in  FIG.  18    may correspond to the “second correspondence” in the present disclosure. 
     &lt;Comparison of Correspondence&gt; 
     Monitoring unit  45  compares the correspondence during the first stop period shown in  FIG.  14    with the correspondence during the second stop period shown in  FIG.  18   , and determines to which axle Ax which tire Tr is attached based on a result of comparison. In other words, monitoring unit  45  determines a combination between axle Ax and tire Tr. 
     Monitoring unit  45  refers to the table in  FIG.  14    and the table in  FIG.  18    stored in storage  46 . Monitoring unit  45  compares the difference in angle at the time of first stop and the difference in angle at the time of second stop for the ID number “13” and the ID number “03”. 
     The difference in angle at the time of first stop is “0 degree or 120 degrees.” 
     The difference in angle at the time of second stop is “0 degree or 180 degrees.” The difference in angle at the time of first stop and the difference in angle at the time of second stop include “0 degree” in common. Both of the difference in angle at the time of first stop and the difference in angle at the time of second stop being “0 degree” means that relationship exhibited by the ID number “13” and the ID number “03” has not changed. More specifically, in other words, correspondence between the angle of revolution of axle R 1  to which axle detector  16   a  having the ID number “13” is attached and the angle of revolution of tire  21   b  to which tire detector  31   b  having the ID number “03” is attached has not changed between the time of first stop and the time of second stop. 
     As described above, tire Tr attached to axle Ax revolves in synchronization with revolution of axle Ax to which the tire is attached. Therefore, the difference between the angle of revolution of axle Ax and the angle of revolution of tire Tr attached to axle Ax is the same between the time of first stop and the time of second stop. 
     When both of the difference in angle at the time of first stop and the difference in angle at the time of second stop are “0 degree,” monitoring unit  45  can determine that the difference between the angle of revolution of axle R 1  and the angle of revolution of tire  21   b  is the same between the time of first stop and the time of second stop. Monitoring unit  45  thus determines that attachment of tire  21   b  to axle R 1  is likely. 
     An example in which the difference in angle at the time of first stop and the difference in angle at the time of second stop are compared with each other for the ID number “13” and the ID number “05” will now be described. 
     The difference in angle at the time of first stop is “60 degrees or 180 degrees.” The difference in angle at the time of second stop is “90 degrees.” The difference in angle at the time of first stop and the difference in angle at the time of second stop do not include a difference in angle in common, which means that relationship exhibited by the ID number “13” and the ID number “05” has changed between the time of first stop and the time of second stop. 
     More specifically, correspondence between the angle of revolution of axle R 1  to which axle detector  16   a  having the ID number “13” is attached and the angle of revolution of tire  22   a  to which tire detector  32   a  having the ID number “05” is attached has changed between the time of first stop and the time of second stop. Since the difference in angle of axle Ax and the difference in angle of tire Tr attached to axle Ax cannot change between the time of first stop and the time of second stop, monitoring unit  45  can determine that tire  22   a  is not attached to axle R 1 . 
     When the difference in angle at the time of first stop and the difference in angle at the time of second stop include a difference in angle in common, monitoring unit  45  thus determines that attachment of tire Tr brought in correspondence with the ID number to axle Ax is likely. When the difference in angle at the time of first stop and the difference in angle at the time of second stop do not include a difference in angle in common, monitoring unit  45  can determine that tire Tr brought in correspondence with the ID number is not attached to axle Ax. 
     In the examples in  FIGS.  14  and  18   , each of the combination of the ID numbers “13” and “03”, the combination of the ID numbers “13” and “04”, the combination of the ID numbers “14” and “05”, and the combination of the ID numbers “14” and “06” includes a difference in angle in common. Monitoring unit  45  can determine that attachment of tire  21   a  and tire  21   b  to axle R 1  is likely and attachment of tire  22   a  and tire  22   b  to axle R 2  is likely. 
     On the other hand, each of the combination of the ID numbers “14” and “03”, the combination of the ID numbers “14” and “04”, the combination of the ID numbers “13” and “05”, and the combination of the ID numbers “13” and “06” does not include a difference in angle in common. Monitoring unit  45  can determine that tire  22   a  and tire  22   b  are not attached to axle R 1  and tires  21   a  and tire  21   b  are not attached to axle R 2 . 
     Monitoring unit  45  thus determines which tire Tr revolves in synchronization with which axle Ax, based on a result of comparison between the difference between the angles of revolution at the time of first stop and the difference between the angles of revolution at the time of second stop. In other words, monitoring unit  45  determines to which axle Ax which tire Tr is not attached. 
     Even when tire Tr is not attached to axle Ax, depending on the angles of revolution at the time of first stop and the angles of revolution at the time of second stop, a difference in angle in common may be included. Monitoring unit  45 , however, can determine a combination indicating to which axle Ax which tire Tr is attached, by performing processing for comparison between a plurality of stop periods. 
     &lt;Processing Procedure in Determination as to Tire Position&gt; 
       FIG.  19    is a flowchart showing tire position determination processing performed by monitoring unit  45 . Monitoring unit  45  determines whether or not vehicle  10  has stopped (step S 101 ). Specifically, monitoring unit  45  determines whether or not tire Tr and axle Ax remain stopped. 
     When vehicle  10  has not stopped (NO in step S 101 ), monitoring unit  45  has the processing remain in step S 101 . When vehicle  10  has stopped (YES in step S 101 ), monitoring unit  45  determines whether or not it has received the UHF signal from tire detector  30  or axle detector  15  (step S 102 ). Tire detector  30  and axle detector  15  transmit the UHF signals intermittently at different timings. 
     When monitoring unit  45  has received the UHF signal (YES in step S 102 ), it has information included in the UHF signal stored in storage  46  together with the stop ID (step S 103 ). 
     When the monitoring unit has not received the UHF signal (NO in step S 102 ), it determines whether or not vehicle  10  has pulled away (step S 104 ). When vehicle  10  has not pulled away (NO in step S 104 ), monitoring unit  45  has the process return to step S 102  When vehicle  10  has pulled away (YES in step S 104 ), monitoring unit  45  updates the stop ID (step S 105 ). Specifically, monitoring unit  45  generates a stop ID to be given when the vehicle stops next time. 
     Monitoring unit  45  determines whether or not there are a plurality of stop IDs for which information in the UHF signal from each of tire detector  30  and axle detector  15  is available (step S 106 ) Specifically, since tire detector  30  and axle detector  15  transmit the UHF signals intermittently at different timings, it is not necessarily the case that the UHF signals are received from all of tire detectors  30  and axle detectors  15  during the stop period. Therefore, monitoring unit  45  determines whether or not there are at least two stop periods during which it receives the UHF signals from all of tire detectors  30  and axle detectors  15 . 
     When there are not a plurality of stop IDs for which information in the UHF signal from each of tire detector  30  and axle detector  15  is available (NO in step S 106 ), monitoring unit  45  repeats processing from step S 101  to step S 106 . When there are a plurality of stop IDs for which information in the UHF signal from each of tire detector  30  and axle detector  15  is available (YES in step S 106 ), monitoring unit  45  compares the difference in angle of revolution between the different stop IDs. 
     Monitoring unit  45  determines to which axle Ax which tire Tr is not attached. At this time, monitoring unit  45  determines to which axle Ax which tire Tr is likely to be attached. By repeating the processing procedure shown in  FIG.  19    a plurality of times, monitoring unit  45  can improve accuracy of a result of determination. 
     As described above, monitoring unit  45  in the present embodiment estimates the angle of revolution of tire Tr based on the detection value from tire detector  30  and estimates the angle of revolution of axle Ax based on the detection value from axle detector  15 . The “angle of revolution of tire Tr” estimated during the first stop period may correspond to the “first value” in the present disclosure. The “angle of revolution of axle Ax” estimated during the first stop period may correspond to the “second value” in the present disclosure. 
     The “angle of revolution of tire Tr” estimated during the second stop period may correspond to the “third value” in the present disclosure. The “angle of revolution of axle Ax” estimated during the second stop period may correspond to the “fourth value” in the present disclosure. Monitoring unit  45  may determine the tire position only based on the detection value from tire detector  30  and the detection value from axle detector  15 , without estimating the angle of revolution of tire Tr and the angle of revolution of axle Ax based on the detection value from tire detector  30  and the detection value from axle detector  15 . In other words, monitoring unit  45  may perform processing for comparing the detection values from acceleration sensors  39  to determine the tire position only based on the detection values from acceleration sensors  39  without conversion of the detection values from acceleration sensors  39  into the “estimated angles” shown in  FIGS.  13  and  17   . 
     First Modification of First Embodiment 
     In the tire position determination system described above, as shown in  FIGS.  9  and  10   , axle detector  15  and tire detector  30  are attached to any positions by a user, and there is no regularity in arrangement of axle detector  15  and tire detector  30 . Axle detector  15  and tire detector  30 , however, may be attached in specific arrangement in advance. 
     For example, tire detectors  31   a  and  31   b  attached to respective tires  21   a  and  21   b  and axle detector  16   a  attached to axle R 1  can be attached in advance such that a difference in angle between them is set to 0 degree. Similarly, tire detectors  32   a  and  32   b  attached to respective tires  22   a  and  22   b  and axle detector  16   b  attached to axle R 2  can be attached in advance such that a difference in angle between them is set to 0 degree. 
     When arrangement of axle detector  15  and tire detector  30  is thus determined in advance, monitoring unit  45  obtains information on arrangement of axle detector  15  and tire detector  30  through input unit  53 . For example, input unit  53  accepts information on arrangement of axle detector  15  and tire detector  30 . Monitoring unit  45  can thus perform comparison processing based on the correspondence obtained from information on arrangement of axle detector  15  and tire detector  30  and correspondence between the angles of revolution estimated during the stop period. 
       FIG.  20    shows a table in storage  46  where UHF signals received during the first stop period are stored when axle detector  15  and tire detector  30  are attached in advance in specific arrangement.  FIG.  21    shows a table in storage  46  where UHF signals received during the second stop period are stored when axle detector  15  and tire detector  30  are attached in advance in specific arrangement. 
     As described above, when tire detector  30  and axle detector  15  are attached such that the difference in angle therebetween is set to 0 degree, as shown in  FIG.  20   , arrangement of tire detector  30  and axle detector  15  estimated based on the UHF signals received during the first stop period may be arrangement  12   h  (0 degree). Since axle R 1  and axle R 2  do not revolve in synchronization as shown in  FIG.  21   , during the second stop period, estimated arrangement of tire detector  30  and axle detector  15  is different. 
     Specifically, the detection values from the acceleration sensors of axle detector  16   a  corresponding to the ID number “13”, tire detector  31   b  corresponding to the ID number “03”, and tire detector  31  corresponding to the ID number “04” are +1. The detection values from the acceleration sensors of axle detector  16   b  corresponding to the ID number “14”, tire detector  32   a  corresponding to the ID number “05”, and tire detector  32   b  corresponding to the ID number “06” are +1/2. 
     Even when axle detector  15  and tire detector  30  are thus attached in advance in specific arrangement, monitoring unit  45  can determine the combination of axle Ax and tire Tr attached to that axle Ax, because relationship between the angle of revolution of axle Ax and the angle of revolution of tire Tr attached to axle Ax does not change. 
     Second Modification of First Embodiment 
     In the embodiment described above, as shown in  FIG.  6   , axle detector  15  is attached to a side surface of axle Ax. Axle detector  15 , however, may be attached onto an end surface FP 2  of axle Ax. 
       FIG.  22    is a perspective view of an appearance of axle detector  15  attached to axle Ax in a second modification. As shown in  FIG.  3   , end surface FP 2  of axle Ax adopted in a large-sized vehicle such as a truck or a bus is attached to pass through wheel WH of tire Tr. In other words, end surface FP 2  is exposed to the outside of vehicle  10  while axle Ax is attached to vehicle  10 . 
     When tire Tr is coupled to a vehicle body with the use of an axle shaft, it may be difficult to arrange axle detector  15  on the side surface of axle Ax synchronous in revolution with tire Tr. Then, as shown in  FIG.  22   , by attachment of axle detector  15  to end surface FP 2  exposed while axle Ax is attached to vehicle  10 , attachment of axle detector  15  can be facilitated. 
     Third Modification of First Embodiment 
     An example in which monitoring unit  45  in the embodiment described above determines the tire position based on the detection values from axle detector  15  and tire detector  30  during a period for which the vehicle remains stopped is described. Monitoring unit  45 , however, may determine the tire position by time synchronization, based on detection values from axle detector  15  and tire detector  30  during traveling. 
     In the tire position determination system in a third modification, a timer for time synchronization is provided in each tire detector  30  and each axle detector  15 . Tire detectors  30  and axle detectors  15  each include a timer in time synchronization. Tire detector  30  and axle detector  15  each transmit the UHF signal based on count of specific time by the timer. Monitoring unit  45  can thus obtain the detection value from each tire detector  30  and the detection value from each axle detector  15  at the same timing. 
     Alternatively, the tire position determination system may include an initiator that transmits a command signal to each tire detector  30  and each axle detector  15 . The initiator collectively transmits the command signals to tire detectors  30 . Each tire detector  30  transmits the UHF signal to monitoring unit  45  by being triggered by reception of the command signal defined as the prescribed activation condition. Monitoring unit  45  can thus obtain the detection value from each tire detector  30  and the detection value from each axle detector  15  at the same timing. 
     Second Embodiment 
     The tire position determination system that determines the position of tire Tr to which tire detector  30  is attached by obtaining the combination of axle detector  15  attached to axle Ax and tire detector  30  attached to tire Tr is described in the first embodiment above. An example in which a nut loosening detector instead of axle detector  15  is employed in the tire position determination system in a second embodiment will be described. Description of features overlapping with those in the first embodiment will not be repeated in the second embodiment. 
     In the example in the second embodiment, a single nut loosening detector is provided for a single axle Ax. In other words, since vehicle  10  in the second embodiment includes six axles Ax, vehicle  10  is similarly provided with six nut loosening detectors. All nut loosening detectors provided in vehicle  10  in the second embodiment will collectively be referred to as a “nut loosening detector  70 ” below. 
     Nut loosening detector  70  is in such a configuration that pressure sensor  38  is removed from the configuration of tire detector  30  shown in  FIG.  2   . In other words, nut loosening detector  70  is similar in configuration to axle detector  15  described in the first embodiment. 
       FIG.  23    is a diagram showing a nut loosening detector  71  attached to nut NW. Nut loosening detector  71  corresponds to axle R 2 .  FIG.  23    shows one of nuts NW used for tire  22   a  on the vehicle inner side and tire  22   b  on the vehicle outer side shown in  FIG.  3   . For simplification of illustration,  FIG.  23    does not show inner nut NIN described with reference to  FIG.  3   . 
     As shown in  FIG.  23   , wheels WH of tires  22   b  and  22   a  are fastened to hub H 2  by means of nut NW and bolt BT. Specifically, nut NW is screwed to bolt BT inserted in a wheel hole  221  so that wheels WH of tires  22   b  and  22   a  are fastened to hub H 2 . 
     A nut cap  241  is attached to the vehicle outer side of nut NW. As shown in  FIG.  23   , nut cap  241  includes a ceiling portion  241   a  and a side surface portion  241   b . Side surface portion  241   b  is provided to circumferentially surround nut NW. Ceiling portion  241   a  is provided to face a tip end  251  of bolt BT. A washer  243  is provided between nut NW and wheel WH. 
     In an example in the second embodiment, nut loosening detector  71  is attached to an inner surface  241   c  of ceiling portion  241   a  of nut cap  241 . In other words, nut loosening detector  71  is arranged in a space S in nut cap  241  where bolt BT is accommodated. Nut loosening detector  71  may be attached to nut NW itself rather than nut cap  241 . 
     Nut loosening detector  71  obtains relative positional relation between nut NW and the vehicle body, for example, based on an acceleration in a uniaxial direction detected by an acceleration sensor, and determines whether or not nut NW has loosened. So long as nut loosening detector  70  includes the acceleration sensor, any technique may be adopted as the technique to detect loosening of the nut. For example, nut loosening detector  70  may detect loosening of nut NW with the use of a magnetic sensor. In the second embodiment, nut NW represents an exemplary “first revolving body” in the present disclosure. Nut loosening detector  70  represents an exemplary “revolving body detector” in the present disclosure. 
     The tire position determination system in the second embodiment obtains a combination of nut loosening detector  70  and tire detector  30  with the technique described in the first embodiment. Specifically, each of nut loosening detector  70  and tire detector  30  includes an acceleration sensor and transmits a detection value from the acceleration sensor to monitoring unit  45 . While nut NW is not loose, nut NW revolves in synchronization with tire Tr. 
     The “revolving body that revolves in synchronization with tire Tr” in the present disclosure refers to an object that revolves at an angular velocity (rad/s) equal to an angular velocity around the revolution axis of tire Tr. “Revolving in synchronization with tire Tr” means that a member attached to tire Tr revolves together with tire Tr. Thus, the member rotates or revolves around a revolution axis the same as the revolution axis of tire Tr. Axle Ax is fixed at a position superimposed on a revolution axis Ar 1  of tire Tr shown in  FIG.  3   . Therefore, when tire Tr revolves, axle Ax rotates around revolution axis Ar 1  of tire Tr as being integrated with tire Tr. 
     On the other hand, nut NW is fixed to wheel WH at a position distant from revolution axis Ar 1  of tire Tr. Therefore, when tire Tr revolves, nut NW revolves around revolution axis Ar 1  of tire Tr as being integrated with tire Tr. Therefore, axle Ax and nut NW revolve in synchronization with tire Tr. 
     Thus, monitoring unit  45  can obtain a corresponding combination from the detection value from the acceleration sensor received from nut loosening detector  70  and the detection value from tire detector  30  also in the second embodiment. 
     Furthermore, in the second embodiment, each nut loosening detector  70  transmits information including a specific identifier to monitoring unit  45  in addition to the detection value from the acceleration sensor. Monitoring unit  45  can thus identify from which nut loosening detector  70  it receives the detection value from the acceleration sensor received from nut loosening detector  70 . 
     In the example in the second embodiment, at which tire position each nut loosening detector  70  should be arranged is determined in advance. More specifically, for example, tire position information indicating “rear first-row right side” is provided on a surface of nut loosening detector  71 . The tire position information may be provided in advance by a manufacturer of nut loosening detector  71 , or a user himself/herself may determine the tire position where the nut loosening detector is to be arranged for each nut loosening detector  70 . The tire position is thus linked with each nut loosening detector  70 . 
     Monitoring unit  45  determines the combination of nut loosening detector  70  and tire detector  30  with the technique described in the first embodiment, and thereafter can link the tire position information linked with nut loosening detector  70  with tire detector  30 . Monitoring unit  45  can thus inform a user of the tire position of tire detector  30 . 
     An advantage of linking the tire position with nut loosening detector  70  will be described. Tire detector  30  is attached in the inside of tire Tr. Therefore, when tires are rotated, axle Ax to which the nut loosening detector is attached together with tire Tr changes. As shown in  FIG.  23   , on the other hand, nut cap  241  to which nut loosening detector  70  is attached and nut NW to which nut loosening detector  70  may be attached can readily be removed from bolt BT. Therefore, the user can remove nut loosening detector  70  before tires are rotated. After tires are rotated, the user can attach nut loosening detector  70  again to the same axle Ax. Nut loosening detector  70  can thus be attached at the tire position shown on the surface of nut loosening detector  70  before and after tires are rotated. 
     Thus, the tire position determination system in the second embodiment can link the tire position with nut loosening detector  70  that is readily removed, instead of axle detector  15 , and with that tire position being defined as the reference, the tire position determination system can determine the tire position of tire detector  30 . 
     The timing of transmission of the detection value detected by the acceleration sensor from nut loosening detector  70  and tire detector  30  is not limited to arbitrary timing while vehicle  10  remains stopped. Nut loosening detector  70  and tire detector  30  may be configured such that all of nut loosening detectors  70  and tire detectors  30  transmit the detection values at the same timing, for example, based on reception of a specific signal from another device. The specific signal received from another device may be, for example, a trigger signal received from monitoring unit  45  or a synchronous signal received from a communication satellite. 
     In one aspect, the tire position determination system in the second embodiment may include axle detector  15  in addition to nut loosening detector  70  and tire detector  30 . In this case, monitoring unit  45  can determine the tire position of tire detector  30  and the tire position of nut loosening detector  70  with the tire position of axle detector  15  being defined as the reference. In other words, monitoring unit  45  detects a combination of three features which are axle detector  15 , tire detector  30 , and nut loosening detector  70  attached to a revolving body that revolves in synchronization. Monitoring unit  45  can thus determine to which nut NW of tire Tr corresponding to which axle Ax each nut loosening detector  70  is attached. 
     In another aspect, in the second embodiment, nut loosening detector  70  and axle detector  15  may be included without tire detector  30  being included. In this case, monitoring unit  45  can determine the tire position of nut loosening detector  70  with the tire position of axle detector  15  being defined as the reference. 
     Thus, what is combined in the present embodiment is not limited to two components such as tire detector  30  and nut loosening detector  70 , and three components such as axle detector  15 , tire detector  30 , and nut loosening detector  70  can be combined into one. Axle detector  15 , tire detector  30 , and nut loosening detector  70  will collectively be referred to as a “detector” below. One unit of a plurality of detectors attached to a revolving body that revolves in synchronization will collectively be referred to as a “group”. In the example in the second embodiment, the total number of groups is the same as the number of axles Ax. In other words, the total number of groups is set to six. An example in which a plurality of detectors are included in one group will be described below. 
     First Modification of Second Embodiment 
     In the second embodiment described above, the example in which a single nut loosening detector  70  is provided for a single axle Ax is described. As shown in  FIG.  3   , a plurality of nuts NW are attached to one wheel WH. In a first modification of the second embodiment, a construction in which a plurality of nut loosening detectors  70  are attached to a single axle Ax will be described. 
       FIG.  24    is a diagram for illustrating attachment of a plurality of nut loosening detectors  70  to single axle Ax.  FIG.  24    shows the diagram of tire  22   b  when viewed on the side of the positive direction of the Y axis. As shown in  FIG.  24   , in the first modification of the second embodiment, a nut loosening detector  71   a  and a nut loosening detector  71   b  are attached to axle R 2  corresponding to tire  22   b . In the first modification of the second embodiment, two nut loosening detectors  70  are similarly attached also to another axle Ax. In the first modification of the second embodiment, nut loosening detector  71   b  represents an exemplary “second revolving body detector” in the present disclosure. 
     Monitoring unit  45  can detect inclusion of nut loosening detector  71   a , nut loosening detector  71   b , and tire detector  32   b  in the same group with the technique described in the first embodiment. Furthermore, by receiving the detection value detected by the acceleration sensor from tire detector  32   a , monitoring unit  45  can also detect inclusion of tire detector  32   a  in that group in addition to tire detector  32   b . When axle detector  16   b  is attached to axle R 2 , monitoring unit  45  can also detect inclusion of axle detector  16   b  in that group, based on the detection value from the acceleration sensor of axle detector  16   b.    
     In other words, monitoring unit  45  can detect attachment of all of five detectors which are nut loosening detectors  71   a  and  71   b , tire detectors  32   a  and  32   b , and axle detector  16   b  to the revolving body that revolves in synchronization. The tire position determination system in the first modification of the second embodiment can determine in which group each detector is included even when a plurality of detectors are included in one group in such a manner that a plurality of nut loosening detectors  70  are attached to a single axle Ax. 
     The number of nut loosening detectors  70  attached to a single wheel as shown in  FIG.  24    is not limited to two. For example, nut loosening detectors  71   a  to  71   h  may be attached to eight respective nuts NW shown in  FIG.  24   . In this case, eleven detectors may be included in one group. When nuts NW more than the nuts shown in  FIG.  24    are attached, the number of detectors included in one group may be larger than eleven. 
     Second Modification of Second Embodiment 
     According to the description in the first modification of the second embodiment described above, there may be groups as many as axles Ax and a plurality of detectors may be included in one group. In a second modification of the second embodiment, a method of determining whether or not a detector is appropriately included in each group will be described. Specifically, monitoring unit  45  in the second modification of the second embodiment detects a wrong position of attachment of nut loosening detector  70 . 
     In an example in  FIG.  24   , two nut loosening detectors  71   a  and  71   b  are attached to a single wheel. Two nut loosening detectors  70  are similarly attached also to another axle Ax. In other words, in the second modification of the second embodiment, it is determined in advance that two nut loosening detectors  70  for one axle detector  15  are included in the same group. 
     When the number of nut loosening detectors  70  to be attached to a single axle detector  15  is thus determined in advance, in the second modification of the second embodiment, occurrence of an error of a portion of attachment of nut loosening detector  70  is detected based on whether or not nut loosening detector(s)  70  in number different from the predetermined number is (are) included in one group. 
     For example, an example in which monitoring unit  45  determines that only nut loosening detector  71   a  among nut loosening detectors  70  is included in a group including axle detector  16   b  of axle R 2  is assumed. In this case, monitoring unit  45  can detect only a single nut loosening detector  70  in spite of the fact that two nut loosening detectors  70  should be attached to axle detector  16   b , and hence it detects attachment of nut loosening detector  71   b  to wheel WH of another tire Tr or detachment of the nut loosening detector. 
     More specifically, when three nut loosening detectors  70  are included in another group, monitoring unit  45  informs a user of the fact that the position of attachment of nut loosening detector  70  is wrong, and when the total number of nut loosening detectors  70  in all groups is smaller than twelve, the monitoring unit informs the user of the possibility of detachment of at least one of nut loosening detectors  70 . Thus, in the second modification of the second embodiment, by determining the number of nut loosening detectors  70  to be included in one group in advance, a wrong position of attachment of nut loosening detector  70  and loss of nut loosening detector  70  due to detachment from wheel WH can be detected. In other words, monitoring unit  45  determines whether or not the number of revolving bodies that revolve in synchronization with tire Tr matches with the predetermined number. 
     Third Embodiment 
     In the first embodiment, the tire position determination system that determines a position of tire Tr to which tire detector  30  is attached by obtaining a combination of axle detector  15  attached to axle Ax and tire detector  30  attached to tire Tr is described. In a third embodiment, a revolving body position determination system that detects a combination of revolving bodies with the use of a nut loosening detector instead of tire detector  30  will be described. In the third embodiment, description of the construction overlapping with that in the first and second embodiments will not be repeated. 
     The revolving body position determination system in the third embodiment does not include tire detector  30  but includes only nut loosening detector  70  and axle detector  15 . In an example in the third embodiment, as in the second embodiment, a single nut loosening detector is provided for a single axle Ax. In other words, since vehicle  10  in the third embodiment includes six axles Ax, vehicle  10  is similarly provided with six nut loosening detectors. 
     As described above, monitoring unit  45  in the first embodiment specifies a position of tire detector  30  with a position of axle detector  15  being defined as the reference. Monitoring unit  45  in the second embodiment specifies a position of tire detector  30  with a position of nut loosening detector  70  being defined as the reference. In the example in the third embodiment, monitoring unit  45  specifies a position of nut loosening detector  70  with a position of axle detector  15  being defined as the reference. 
     In the third embodiment, tire position information is not provided on the surface of nut loosening detector  70  as in the second embodiment. In other words, monitoring unit  45  is unable to specify the tire position based on information received from nut loosening detector  70 . Monitoring unit  45  in the third embodiment specifies a position of nut loosening detector  70  based on the position of axle detector  15 , by combining axle detector  15  fixed to axle Ax with nut loosening detector  70 . Monitoring unit  45  in the third embodiment determines a position of attachment of axle detector  15  based on an identifier received from axle detector  15 . In other words, monitoring unit  45  determines whether or not axle detector  15  and nut loosening detector  70  revolve in synchronization with each other to bring the position of attachment determined based on the identifier received from axle detector  15  in correspondence with nut loosening detector  70 , and specifies the position of nut loosening detector  70 . Monitoring unit  45  in the third embodiment can thus detect at which position nut loosening detector  70  is attached. 
     For example, when nut loosening detector(s)  70  in number different from the predetermined number is (are) combined with one axle detector  15 , monitoring unit  45  in the third embodiment informs a user of the fact that the position of attachment of nut loosening detector  70  is wrong or the possibility of detachment of at least one of nut loosening detectors  70  as in the second modification of the second embodiment. In the third embodiment, nut loosening detector  70  can thus appropriately be managed. 
     In the third embodiment, axle detector  16   b  may correspond to the “third revolving body detector” in the present disclosure. In the third embodiment, referring to  FIGS.  1  and  23   , nut loosening detector  71  attached at a position corresponding to axle detector  16   b  may correspond to the “fourth revolving body detector” in the present disclosure. Nut loosening detector  70  other than nut loosening detector  71  in the third embodiment may correspond to the “fifth revolving body detector” in the present disclosure. 
     Fourth Embodiment 
     In the first to third embodiments, a construction in which at least a plurality of detectors are included in one group is described. For example, in the second embodiment, a construction in which tire detector  30  and nut loosening detector  70  are included in one group is described. In a fourth embodiment, an example in which it is only nut loosening detector  70  that is included as a detector in one group, with tire detector  30  having been removed from the construction in the second embodiment, will be described. In the fourth embodiment, description of the construction overlapping with that in the second embodiment will not be repeated. 
     Referring to  FIG.  1   , vehicle  10  in the fourth embodiment includes front axles F 1  and F 2  and front tires  11  and  12  and rear axles R 1  and R 2  and rear tires  21   b  and  22   b . In other words, vehicle  10  in the fourth embodiment is in such a construction that axles R 3  and R 4  and tires  23 ,  24 ,  21   a , and  22   a  are removed from vehicle  10  shown in  FIG.  1   . In summary, vehicle  10  in the fourth embodiment is a vehicle including four axles Ax and four tires Tr. 
     The revolving body position determination system in the fourth embodiment includes as detectors, only four nut loosening detectors  70 , without including tire detector  30  and axle detector  15 . Each of four nut loosening detectors  70  is determined in advance to be attached to tires  11 ,  12 ,  21   b , and  22   b , respectively. Monitoring unit  45  in the fourth embodiment obtains a detected value of an acceleration from each of four nut loosening detectors  70 . Monitoring unit  45  determines whether or not there is nut loosening detector  70  that can be combined among four nut loosening detectors  70 , with the technique described in the first embodiment. 
     When monitoring unit  45  detects combinable nut loosening detector  70  among four nut loosening detectors  70 , it informs a user of the fact that the position of attachment of nut loosening detector  70  is wrong. Detection of combinable nut loosening detector  70  means that a plurality of nut loosening detectors  70  are included in one group. Four nut loosening detectors  70  are in a state that they are not attached to respective tires  11 ,  12 ,  21   b , and  22   b , and in this case, vehicle  10  is in such a state that a plurality of nut loosening detectors  70  are attached to single tire Tr. 
     For example, a state that two nut loosening detectors  70  are attached to tire  11 , one nut loosening detector  70  is attached to tire  12 , one nut loosening detector  70  is attached to tire  21   b , and nut loosening detector  70  is not attached to tire  22   b  may be applicable as such a state. Therefore, monitoring unit  45  in the fourth embodiment informs a user of the fact that nut loosening detector  70  is attached at a wrong position of attachment which is not a predetermined position of attachment. When monitoring unit  45  in the fourth embodiment does not detect combinable nut loosening detector  70 , it may inform the user of the fact that there is no abnormality of the position of attachment of nut loosening detector  70 . 
     Thus, when each nut loosening detector  70  is not combined with another nut loosening detector  70 , the revolving body position determination system in the fourth embodiment can determine that nut loosening detector  70  is attached appropriately to a predetermined portion of attachment. Though a construction in which only one detector is included in a group is described in the fourth embodiment by referring to nut loosening detector  70 , one detector to be included in the group may be tire detector  30  or axle detector  15  rather than nut loosening detector  70 . 
     Modification in Common to First to Fourth Embodiments 
     An example in which revolution diameter direction D 3  orthogonal to revolution axis direction D 1  of tire Tr is defined as detection direction D 3  of tire detector  30  is described with reference to  FIG.  4   . Detection direction D 3  of tire detector  30 , however, is not limited to revolution diameter direction D 3  orthogonal to revolution axis direction D 1 , and any direction intersecting with revolution axis direction D 1  may be applicable as the detection direction. In other words, detection direction D 3  should only be a direction inclined with respect to revolution axis direction D 1 , and should only be a direction intersecting with an XY plane in  FIG.  3   . 
     In other words, the acceleration in the direction intersecting with revolution axis direction D 1  contains at least a component in revolution diameter direction D 3 . Therefore, by extracting the component in revolution diameter direction D 3  from the acceleration in the direction intersecting with revolution axis direction D 1 , tire detector  30  can detect the acceleration generated in the revolution diameter direction D 3 . Tire detector  30  can thus transmit a detected value of the acceleration generated in revolution diameter direction D 3  to monitoring unit  45 . 
     For nut loosening detector  70  and axle detector  15  as well, the direction of detection of the acceleration should only be a direction containing at least a component in a target direction of detection. All of nut loosening detector  70 , axle detector  15 , and tire detector  30  included in vehicle  10  do not have to detect the acceleration in the direction intersecting with revolution axis direction D 1 , but at least one detector of nut loosening detector  70 , axle detector  15 , and tire detector  30  may detect the acceleration in the direction intersecting with revolution axis direction D 1 . 
     It should be understood that the embodiments disclosed herein are illustrative and non-restrictive in every respect. The scope of the present disclosure is defined by the terms of the claims rather than the description above and is intended to include any modifications within the scope and meaning equivalent to the terms of the claims. 
     The illustrative embodiments and modifications thereof described above are specific examples of aspects below. 
     (Clause 1) A tire position determination system according to one aspect of the present disclosure is a tire position determination system provided in a vehicle including a first revolving body that revolves in synchronization with any tire among a plurality of tires including a first tire. The tire position determination system includes a first tire detector, a revolving body detector, and a monitoring unit. The first tire detector is attached to the first tire and detects an acceleration applied in a direction intersecting with an axial direction of a revolution axis of the first tire. The revolving body detector is attached to the first revolving body and detects an acceleration applied in a direction intersecting with an axial direction of a revolution axis of the first revolving body. The monitoring unit is configured to receive information from the first tire detector and the revolving body detector. The monitoring unit obtains, during a first period, first correspondence representing relation between a first value based on a detection value from the first tire detector and a second value based on a detection value from the revolving body detector, obtains, during a second period, second correspondence representing relation between a third value based on a detection value from the first tire detector and a fourth value based on a detection value from the revolving body detector, and determines whether or not the first tire is revolving in synchronization with the first revolving body based on a result of comparison between the first correspondence and the second correspondence. 
     According to the aspect above, whether or not correspondence between an angle of revolution of the revolving body and an angle of revolution of the first tire in the first stop period has varied in the second stop period is determined. Whether or not the first tire revolves in synchronization with the first revolving body is thus determined and a tire attached to the revolving body can be determined. 
     (Clause 2) In the tire position determination system according to Clause 1, the first period and the second period are each a stop period of the vehicle, and the first period is a stop period different from the second period. 
     According to the aspect above, the detection value from each axle detector  15  and the detection value from each tire detector  30  can be synchronized with each other, without an initiator or a timer for time synchronization being provided. 
     (Clause 3) In the tire position determination system according to Clause 1 or 2, the first value and the third value each represent an angle of revolution of the first tire estimated from the detection value from the first tire detector, and the second value and the fourth value each represent an angle of revolution of the first revolving body estimated from the detection value from the revolving body detector. 
     According to the aspect above, the angle of revolution of the first tire and the angle of revolution of the first revolving body are estimated from detection values from acceleration sensors for each stop period, and correspondence can be obtained based on the estimated angle of revolution of the first tire and the estimated angle of revolution of the first revolving body. 
     (Clause 4) The tire position determination system according to Clause 1 or 2 further includes an input unit connected to the monitoring unit. The input unit accepts input of information on the first correspondence. 
     According to the aspect above, comparison processing can be performed based on detection values from acceleration sensors  39  in one stop period, and time required until a result of comparison is obtained can be shorter. 
     (Clause 5) In the tire position determination system according to Clauses 1 to 4, the first revolving body is an axle attached to the first tire. 
     According to the aspect above, the tire position of tire detector  30  can be determined with the tire position where axle Ax is attached being defined as the reference. 
     (Clause 6) In the tire position determination system according to Clause 5, the first revolving body includes a first end surface exposed while the first revolving body is attached to the vehicle, and the revolving body detector is attached onto the first end surface. 
     According to the aspect above, attachment of axle detector  15  can be facilitated. 
     (Clause 7) In the tire position determination system according to Clauses 1 to 4, the first revolving body is a fastening member that fastens a wheel of the first tire and another member to each other. 
     According to the aspect above, the tire position of tire detector  30  can be determined with the tire position where nut NW representing a fastening member is attached being defined as the reference. 
     (Clause 8) In the tire position determination system according to Clause 7, the monitoring unit determines a position of attachment of the revolving body detector based on an identifier received from the revolving body detector. 
     According to the aspect above, the tire position of tire detector  30  can be determined with information on the tire position linked with nut loosening detector  70  being defined as the reference. 
     (Clause 9) The tire position determination system according to Clause 7 or 8 further includes a second revolving body that revolves in synchronization with any tire among the plurality of tires and a second revolving body detector attached to the second revolving body, the second revolving body detector detecting an acceleration applied in a direction intersecting with an axial direction of a revolution axis of the second revolving body. 
     According to the aspect above, a plurality of nut loosening detectors  70  can be combined with tire detector  30 . 
     (Clause 10) In the tire position determination system according to Clause 9, the monitoring unit determines whether or not the number of revolving bodies that revolve in synchronization with the first tire matches with a predetermined number. 
     According to the aspect above, a wrong position of attachment of a detector and loss due to detachment thereof can be determined based on the number of detectors to be included in a group. 
     (Clause 11) In the tire position determination system according to Clauses 1 to 10, the first tire detector detects an acceleration in a direction orthogonal to a revolution axis direction of the first tire. 
     According to the aspect above, any direction of detection by the tire detector may be applicable so long as it contains a component in a desired direction of detection. 
     (Clause 12) In the tire position determination system according to Clauses 1 to 11, the revolving body detector detects an acceleration in a direction orthogonal to a revolution axis direction of the first revolving body. 
     According to the aspect above, any direction of detection by the revolving body detector may be applicable so long as it contains a component in a desired direction of detection. 
     (Clause 13) The tire position determination system according to Clauses 1 to 12 further includes a second tire detector attached to a second tire different from the first tire, the second tire detector detecting an acceleration applied in a direction intersecting with an axial direction of a revolution axis of the second tire. The monitoring unit obtains, during the first period, third correspondence representing relation between a value based on a value detected by the second tire detector and a value based on a value detected by the revolving body detector, obtains, during the second period, fourth correspondence representing relation between a value based on a value detected by the second tire detector and a value based on a value detected by the revolving body detector, and determines whether or not the second tire is revolving in synchronization with the first revolving body based on a result of comparison between the third correspondence and the fourth correspondence. 
     According to the aspect above, in vehicle  10  including a plurality of tires and a plurality of axles, a tire attached to each axle can be determined. 
     (Clause 14) In the tire position determination system according to Clause 13, the second tire detector detects the acceleration in a direction orthogonal to a revolution axis direction of the second tire. 
     According to the aspect above, any direction of detection by the second tire detector may be applicable so long as it contains a component in a desired direction of detection. 
     (Clause 15) A revolving body position determination system is provided in a vehicle including a third revolving body and a fourth revolving body that revolve in synchronization with any tire among a plurality of tires. The revolving body position determination system includes a third revolving body detector attached to the third revolving body, the third revolving body detector detecting an acceleration applied in a direction intersecting with an axial direction of a revolution axis of the third revolving body, a fourth revolving body detector attached to the fourth revolving body, the fourth revolving body detector detecting an acceleration applied in a direction intersecting with an axial direction of a revolution axis of the fourth revolving body, and a monitoring unit that receives information from the third revolving body detector and the fourth revolving body detector. The monitoring unit determines a position of attachment of the third revolving body detector based on an identifier received from the third revolving body detector, obtains, during a first period, first correspondence representing relation between a first value based on a detection value from the third revolving body detector and a second value based on a detection value from the fourth revolving body detector, obtains, during a second period, second correspondence representing relation between a third value based on a detection value from the third revolving body detector and a fourth value based on a detection value from the fourth revolving body detector, and determines whether or not the third revolving body and the fourth revolving body revolve in synchronization with each other based on a result of comparison between the first correspondence and the second correspondence. 
     According to the aspect above, the position of the fourth revolving body can be detected with a position of attachment of the third revolving body being defined as the reference. 
     (Clause 16) In the revolving body position determination system according to Clause 15, the monitoring unit determines whether or not the number of revolving bodies that revolve in synchronization with the third revolving body matches with a predetermined number. 
     According to the aspect above, a wrong position of attachment of a detector and loss due to detachment thereof can be determined based on the number of combined detectors, and the detector can appropriately be managed. 
     (Clause 17) The revolving body position determination system according to Clause 15 or 16 further includes a fifth revolving body that revolves in synchronization with any tire among the plurality of tires and a fifth revolving body detector attached to the fifth revolving body, the fifth revolving body detector detecting an acceleration applied in a direction intersecting with an axial direction of a revolution axis of the fifth revolving body. 
     According to the aspect above, a plurality of nut loosening detectors  70  can be combined with axle detector  15 . 
     Though embodiments of the present invention have been described, it should be understood that the embodiments disclosed herein are illustrative and non-restrictive in every respect. The scope of the present invention is defined by the terms of the claims and is intended to include any modifications within the scope and meaning equivalent to the terms of the claims.