Patent Publication Number: US-2020292571-A1

Title: Method for estimating attachment posture of inertial sensor

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims the priority benefit of Japanese Patent Application No. 2019-043718, filed on Mar. 11, 2019. The entirety of the above-mentioned patent application is hereby incorporated by reference herein and made a part of this specification. 
     BACKGROUND 
     Technical Field 
     The disclosure relates to a method for estimating an attachment posture of an inertial sensor including an angular speed sensor with respect to a target person. 
     Description of Related Art 
     In the related art, technologies for observing exercise conditions of a target person by attaching an inertial sensor including an acceleration sensor and an angular speed sensor to a measurement target portion, such as the waist or a leg, of the target person and measuring an acceleration and an angular speed at the measurement target portion using the inertial sensor during exercise of the target person as can be seen in Patent Documents 1 and 2 are known (see Patent Documents 1 (Japanese Patent No. 6319446) and 2 (Japanese Patent Laid-Open No. 2016-112108), for example). 
     Incidentally, it is necessary to identify a relative posture relationship between a measurement target portion and an inertial sensor attached thereto (an attachment posture of the inertial sensor with respect to the measurement target portion) in advance in order to observe which direction of the measurement target portion an acceleration has occurred in and which direction of the measurement target portion an angular speed has occurred in, on the basis of an acceleration and an angular speed detected by the inertial sensor attached to the measurement target portion. 
     Meanwhile, it is typically difficult to precisely attach the inertial sensor to the measurement target portion of the target person who is a human in a predetermined posture. In addition, it is desirable that a degree of freedom in attachment posture of the inertial sensor with respect to the measurement target portion be high in terms of easiness in attachment of the inertial sensor to the measurement target portion and the like. 
     Thus, there is a requirement for a method for appropriately estimating (identifying) a relative posture relationship between the measurement target portion and the inertial sensor attached thereto. Here, a method using geomagnetism is typically conceivable as the method. However, since geomagnetism is likely to be affected by an environment, it is difficult to highly reliably and stably estimate the relative posture relationship between the measurement target portion and the inertial sensor according to a method using geomagnetism. 
     Note that although Patent Documents 1 and 2 disclose technologies of performing calibration related to the posture of the inertial sensor, the technologies are not technologies for estimating the relative posture relationship between the measurement target portion and the inertial sensor. 
     SUMMARY 
     According to an embodiment of the disclosure, there is provided a method for estimating an attachment posture of an inertial sensor that is a method for estimating a relative posture relationship between a measurement target portion of a target person and the inertial sensor that is attached to the measurement target portion and includes an angular speed sensor capable of detecting angular speeds in the respective coordinate axis direction in a sensor coordinate system, which is a three-dimensional coordinate system set in advance for the inertial sensor, the method including: a first process of allowing the target person to carry out exercise such that a posture at the measurement target portion is caused to change in a direction around an axis in a first direction, which is a predetermined direction set in advance with respect to the measurement target portion, while keeping the first direction constant; a second process of detecting, using the angular speed sensor, a set of the respective angular speeds in the three coordinate axes in the sensor coordinate system at one or more sampling times in the first process; and a third process of identifying first posture data indicating which direction the first direction of the measurement target portion corresponds to when seen in the sensor coordinate system, on the basis of one or more sets of angular speeds detected in the second process (first aspect). 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a configuration diagram of an entire system to which embodiments (a first embodiment and a second embodiment) of the disclosure are applied. 
         FIG. 2  is a perspective view illustrating an inertial sensor and a sensor coordinate system included in the system in  FIG. 1 . 
         FIG. 3  is a flowchart illustrating processing for estimating a direction of a coordinate axis Zb of a body-side coordinate system CSb at a measurement target portion of a target person according to the first embodiment. 
         FIG. 4  is a diagram illustrating an operation executed by the target person for processing for estimating a direction of a coordinate axis Yb in the body-side coordinate system CSb at the measurement target portion of the target person according to the first embodiment. 
         FIG. 5  is a flowchart illustrating processing for estimating the direction of the coordinate axis Yb in the body-side coordinate system CSb at the measurement target portion of the target person according to the first embodiment. 
         FIG. 6  is a graph illustrating, as an example, a change in angular speed with time that is detected in processing in STEP  11  in the flowchart in  FIG. 5 . 
         FIG. 7  is a diagram illustrating, as an example, an eigenvector calculated in processing in STEP  12  in the flowchart in  FIG. 5 . 
         FIG. 8  is a diagram illustrating a seated state of a target person executed for processing for estimating a direction of a coordinate axis Zb or Xb in a body-side coordinate system CSb at a measurement target portion of a target person according to the second embodiment. 
         FIG. 9  is a diagram illustrating an operation executed by the target person for processing for estimating a direction of a coordinate axis Yb in the body-side coordinate system CSb at a measurement target portion on a leg of the target person according to the second embodiment. 
         FIG. 10  is a diagram illustrating an operation executed by the target person for processing for estimating the direction of the coordinate axis Yb in the body-side coordinate system CSb at a measurement target portion on an upper body of the target person according to the second embodiment. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     The disclosure is to provide a method by which it is possible to appropriately estimate a relative posture relationship between a measurement target portion of a target person and an inertial sensor attached thereto. 
     According to the disclosure, since the target person carries out exercise as described above in the first process, an angular speed vector (an angular speed vector at each sampling time) defined by a set of angular speeds (a set of angular speeds in the directions of the three coordinate axes in the sensor coordinate system) detected in the second process is a vector in a direction that conforms to or substantially conforms to the first direction of the measurement target portion. Therefore, it is possible to identify the first posture data indicating which direction the first direction of the measurement target portion corresponds to when seen in the sensor coordinate system in the third process on the basis of the one or more sets of angular speeds detected in the second process. 
     Therefore, according to the first aspect, it is possible to appropriately identify (estimate) the relative posture relationship regarding which direction the first direction of the measurement target portion of the target person corresponds to with respect to the inertial sensor. 
     In the first aspect, the measurement target portion is preferably a lower leg or a thigh of a leg of the target person, and in a case in which the first direction is a left-right direction of the target person, the exercise that the target person is preferably allowed to carry out in the first process is an exercise that includes at least bending and stretching the leg such that a posture of the thigh or the lower leg of the leg is caused to change in a pitch direction (second aspect). 
     In this manner, it is possible to easily and stably allow the target person to carry out the exercise such that the posture of the thigh or the lower leg is caused to change in the direction around the axis in the first direction while keeping the first direction at the lower leg or the thigh of the leg of the target person constant in the first process. It is thus possible to highly reliably identify the first posture data related to the thigh or the lower leg of the leg of the target person in the third process. 
     Also, in the first aspect, the measurement target portion is preferably an upper body of the target person, the first direction is preferably a left-right direction of the target person, and the exercise that the target person is allowed to carry out in the first process is preferably exercise that includes at least inclining the upper body of the target person in a pitch direction (third aspect). 
     In this manner, it is possible to easily and stably allow the target person to carry out the exercise such that the posture of the upper body is caused to change in the direction around the axis in the first direction while keeping the first direction of the upper body of the target person constant in the first process. It is thus possible to highly reliably identify the first posture data related to the upper body of the target person in the third process. 
     Also, in the first to third aspects, in a case in which the inertial sensor is an inertial sensor that further includes an acceleration sensor capable of detecting accelerations in the respective coordinate axis directions in the sensor coordinate system, the method preferably further includes: a fourth process of allowing the target person to keep the measurement target portion still such that a second direction that is set in advance with respect to the measurement target portion as a direction that is different from the first direction is maintained in a vertical direction; a fifth process of detecting a set of the respective accelerations in directions of three coordinate axes in the sensor coordinate system using the acceleration sensor at one or more sampling times in the fourth process; and a sixth process of identifying second posture data indicating which direction the second direction of the measurement target portion corresponds to when seen in the sensor coordinate system, on the basis of one or more sets of accelerations detected in the fifth process (fourth aspect). 
     In this manner, the acceleration detected in the fifth process conforms to or substantially conforms to a gravity acceleration in the vertical direction, and the vertical direction is a direction in which the second direction of the measurement target portion is kept constant in the fourth process. Therefore, it is possible to identify the second posture data indicating which direction the second direction of the measurement target portion corresponds to when seen in the sensor coordinate system on the basis of the one or more sets of angular speeds detected in the fifth process in the sixth process. 
     Therefore, according to the fourth aspect, it is possible to appropriate identify (estimate) a relative posture relationship regarding which direction the second direction of the measurement target portion of the target person corresponds to with respect to the inertial sensor. 
     According to the fourth aspect, in a case in which the measurement target portion is a lower leg or a thigh of a leg or an upper body of the target person, the second direction is preferably a direction that is able to be directed in the vertical direction in a state in which the target person is standing up in an upright posture or in a state in which a body of the target person is kept still in contact with an object with a specific shape (fifth aspect). 
     In this manner, it is possible to easily realize the state of the target person in the fourth process. 
     In the fourth or fifth aspect, the method preferably further includes: a seventh process of identifying third posture data indicating which direction a third direction that perpendicularly intersects the first direction and the second direction corresponds to when seen in the sensor coordinate system on the basis of the first posture data identified in the third process and the second posture data identified in the sixth process, and in the seventh process, a vector obtained through a cross product operation of a vector in the first direction indicated by the first posture data and a vector in the second direction indicated by the second posture data is preferably identified as the third posture data (sixth aspect). 
     In this manner, it is possible to easily identify the third posture data indicating which direction the third direction that perpendicularly intersects the first direction and the second direction of the measurement target portion corresponds to when seen in the sensor coordinate system through the cross product operation of the vector in the first direction indicated by the first posture data that has already been identified and the vector in the second direction indicated by the second posture data that has already been identified. 
     In addition, a spatial posture relationship between the measurement target portion and the inertial sensor is identified by identifying the first posture data, the second posture data, and the third posture data that represent the three directions, namely the first direction, the second direction, and the third direction of the measurement target portion, and for example, it is possible to transform an arbitrary vector when seen in the sensor coordinate system into a vector when seen in a three-dimensional coordinate system set for a measurement target portion. 
     First Embodiment 
     A first embodiment of the disclosure will be described below with reference to  FIGS. 1 to 7 . Referring to  FIG. 1 , inertial sensors  10 ( i ) (i=1, 2, . . . ) are attached to a plurality of measurement target portions of a target person P (illustration of arms is omitted) in the embodiment. For example, an upper portion of an upper body and a waist portion (a lower portion of the upper body) and thighs and lower legs of the respective legs of the target person P may be defined as measurement target portions, and the respective inertial sensors  10 ( 1 ),  10 ( 2 ),  10 ( 3 ), and  10 ( 4 ) may be attached to the respective measurement target portions via appropriate attachment members such as belts, which are not illustrated, such that the inertial sensors moves integrally with the measurement target portions. 
     Note that the respective inertial sensors  10 ( 1 ),  10 ( 2 ),  10 ( 3 ), and  10 ( 4 ) may be provided in a tool attached to the target person P, such as a walking assist device, for example. In the following description, the inertial sensors  10 ( 1 ),  10 ( 2 ),  10 ( 3 ), and  10 ( 4 ) will simply be referred to as inertial sensors  10  when it is not necessary to distinguish each of the inertial sensors. 
     Each inertial sensor  10  includes an angular speed sensor  11  and an acceleration sensor  12  in a case body  10   a  as illustrated in  FIG. 2 . The angular speed sensor  11  is a sensor with a known configuration capable of detecting angular speeds generated in the inertial sensor  10  in directions of the respective coordinate axes Xs, Ys, and Zs (directions around the respective coordinate axes Xs, Ys, and Zs) in the sensor coordinate system CSs that is a three-dimensional coordinate system (three-axis orthogonal coordinate system) set (defined) in advance for each inertial sensor  10 . Also, the acceleration sensor  12  is a sensor with a known configuration capable of detecting parallel acceleration generated in the inertial sensor  10  in the directions of the respective coordinate axes Xs, Ys, and Zs (hereinafter, also referred to as an Xs axis, a Ys axis, and a Zs axis, respectively) in the sensor coordinate system CSs. 
     Note that orientations of the respective coordinate axes Xs, Ys, and Zs in the sensor coordinate system CSs illustrated in  FIG. 2  are illustrative orientations, and the orientations of the respective coordinate axes Xs, Ys, and Zs in the sensor coordinate system CSs in each inertial sensor  10  can arbitrarily be set in terms of design. For example, the Zs-axis direction and the Xs-axis direction or the Ys-axis direction in the illustrated example may be exchanged. 
     In addition, a wireless communication machine, which is not illustrated, is mounted in each inertial sensor  10 , and the inertial sensor  10  can perform wireless communication with an external measurement processing device  20 . The measurement processing device  20  can be configured of, for example, a personal computer, a smartphone, a tablet terminal, or a dedicated measurement gauge. In addition, the measurement processing device  20  can successively acquire detection data obtained by the angular speed sensor  11  and the acceleration sensor  12  from each inertial sensor  10  through communication with each inertial sensor  10 . 
     Note that the communication between each inertial sensor  10  and the measurement processing device  20  may be performed via a relay machine attached to the target person P, for example. In this case, the communication between each inertial sensor  10  and the relay machine may be wired communication. Further, the measurement processing device  20  may be able to be attached to the target person P, or the measurement processing device  20  may be a device provided in a device to be attached to the target person P, such as a walking assist device. In these cases, the communication between each inertial sensor  10  and the measurement processing device  20  may be wired communication. 
     A body-side coordinate system CSb(i) (i=1, 2, . . . ) that is a three-dimensional coordinate system (three-axis orthogonal coordinate system) is set (defined) in advance as illustrated as an example in  FIG. 1 , for example, for each measurement target portion of the target person P. 
     Specifically, a body-side coordinate system CSb( 1 ) in which a front-back direction of an upper portion of the upper body, a left-right direction of the upper portion of the upper body, and a body core axis direction of the upper portion of the upper body are defined as the directions of the three respective coordinate axes Xb, Yb, and Zb may be set for the upper portion of the upper body of the target person P to which the inertial sensor  10 ( 1 ) is attached. 
     Also, a body-side coordinate system CSb( 2 ) in which a front-back direction of a waist portion, a left-right direction of the waist portion, and a body core axis direction of the waist portion, for example, are defined as the respective directions of the three coordinate axes Xb, Yb, and Zb is set for the waist portion (a lower portion of the upper body) to which the inertial sensor  10 ( 2 ) is attached. 
     In addition, a body-side coordinate system CSb( 3 ) in which a front-back direction of a thigh, a left-right direction of the thigh, and a longitudinal direction of the thigh are defined as the respective directions of the three coordinate axes Xb, Yb, and Zb is set for the thigh of each leg to which the inertial sensor  10 ( 3 ) is attached. 
     Also, a body-side coordinate system CSb( 4 ) in which a front-back direction of a lower leg, a left-right direction of the lower leg, and a longitudinal direction of the lower leg are defined as the respective directions of the three coordinate axes Xb, Yb, and Zb, for example, is set for the lower leg of each leg to which the inertial sensor  10 ( 4 ) is attached. 
     Therefore, the body-side coordinate systems CSb(I) (i=1, 2, . . . ) at each measurement target portion is set such that the three coordinate axes Xb, Yb, and Zb (hereinafter, also referred to as an Xb axis, a Yb axis, and a Zb axis) in each body-side coordinate system CSb(i) conforms to or substantially conforms to the front-back direction, the left-right direction, and the vertical direction (gravity direction) of the target person P, respectively, in a posture state of each measurement target portion in a state in which the target person P is standing up in an upright posture on a horizontal floor surface (the state illustrated in  FIG. 1 ) in the embodiment. 
     Therefore, the body-side coordinate systems CSb( 1 ), CSb( 2 ), CSb( 3 ), and CSb( 4 ) will simply be referred to as body-side coordinate systems CSb when it is not necessary to distinguish each of the body-side coordinate systems in the following description. Note that orientations of the respective coordinate axes Xb, Yb, and Zb in each body-side coordinate system CSb can arbitrarily be set in terms of design. For example, the Zb-axis direction and the Xb-axis direction or the Yb-axis direction in each body-side coordinate system CSb may be replaced from those in the aforementioned example. 
     In the system that includes the inertial sensors  10 ( i ) (i=1, 2, . . . ) and the measurement processing device  20  as described above, the measurement processing device  20  can observe exercise conditions of the upper body of the respective legs of the target person P using detection data such as angular speeds and accelerations obtained by the respective inertial sensors  10 . For example, it is possible to observe a direction and a degree of acceleration of each measurement target portion that has occurred, how the direction and the degree of the acceleration change with time, a direction in which the posture of each measurement target portion changes and a degree of angular speed with which the posture of each measurement target portion changes, how the direction and the degree of the angular speed change with time, or the like during exercise, such as walking, of the target person P. 
     Further, it is also possible to successively estimate a posture of each measurement target portion when seen in a global coordinate system (a world coordinate system set in an exercise environment of the target person P) through an arithmetic operation of a strapdown scheme from the detection data such as the angular speed and the acceleration obtained by each inertial sensor  10 , for example. 
     In this case, since the detection data obtained from each inertial sensor  10  is detection data of the angular speed or the acceleration when seen in the sensor coordinate system CSs of each inertial sensor  10 , it is necessary to identify a relative posture relationship between the body-side coordinate system CSb at each measurement target portion and the sensor coordinate system CSs of the inertial sensor  10  attached to the measurement target portion (in other words, a relative posture relationship between each measurement target portion and the inertial sensor  10  attached thereto) for observing the exercise conditions of the target person P as described above. 
     On the other hand, when each inertial sensor  10  is attached to the measurement target portion of the target person P, it is typically difficult to precisely attach the inertial sensor  10  to the measurement target portion such that the relative posture relationship between the body-side coordinate system CSb of the measurement target portion and the sensor coordinate system CSs of the inertial sensor  10  (the relative posture relationship between each measurement target portion and the inertial sensor  10 ) conforms to a desired posture relationship. 
     Thus, processing of identifying (estimating) the relative posture relationship between the body-side coordinate system CSb of each measurement target portion and the sensor coordinate system CSs of the inertial sensor  10  attached to the measurement target portion in advance is executed before the observation of the exercise conditions of the target person P in the embodiment. 
     Specifically, processing of estimating which orientation the orientation of each of the coordinate axes Xb, Yb, and Zb in the body-side coordinate system CSb at each measurement target portion corresponds to when seen in the sensor coordinate system CSs of the inertial sensor  10  attached to the measurement target portion (hereinafter, referred to as coordinate axis direction estimation processing) is performed. 
     In this case, the coordinate axis direction estimation processing for the coordinate axis Zb among the three coordinate axes Xb, Yb, and Zb in each body-side coordinate system CSb is performed as follows. In other words, the target person P stands up and is kept still in the upright posture as illustrated in  FIG. 1  in the coordinate axis direction estimation processing. Note that at this time, the standing state of the target person P may be assisted by an arbitrary tool or a helper such that a minimum force in the transverse direction acts on the target person P. 
     In the state in which the target person P is standing up and kept still in the upright posture in this manner, the measurement processing device  20  executes the processing illustrated in  FIG. 3  for each measurement target portion. Specifically, in STEP  1 , the measurement processing device  20  detects a set of accelerations in the respective coordinate axis direction in the sensor coordinate system CSs of the inertial sensor  10  (in other words, a set of elements in the directions of the respective coordinate axes Xs, Ys, and Zs of acceleration vectors that have been generated in the inertial sensor  10 ) at a predetermined sampling cycle using the acceleration sensor  12  of the inertial sensor  10  at each measurement target portion during a predetermined period of time. 
     In this manner, the measurement processing device  20  acquires detection data of the acceleration vectors (acceleration vectors when seen in the sensor coordinate system CSs of the inertial sensor  10 ) of the inertial sensor  10  at a plurality of sampling times for each measurement target portion in the state in which the target person P is standing up and kept still in the upright posture. 
     Next, in STEP  2 , the measurement processing device  20  executes processing of averaging a plurality of pieces of detection data of the acceleration vectors when seen in the sensor coordinate system CSs of the inertial sensor  10  for each measurement target portion. In other words, the measurement processing device  20  calculates an average acceleration vector ↑As_ave that is a set of acceleration average values in the directions of the respective coordinate axes Xs, Ys, an Zs by calculating an average value of the detection values of accelerations in the directions of the respective coordinate axes Xs, Ys, and Zs in the sensor coordinate system CSs of the inertial sensor  10  at each measurement target portion. Note that the reference signs to which “↑” is applied represent vectors in the specification. 
     Here, the acceleration vector detected in STEP  1  is an acceleration vector detected by the acceleration sensor  12  of each inertial sensor  10  in a state in which the target person P is standing up and kept still in the upright posture, and the acceleration vector conforms to or substantially conforms to a gravity acceleration vector in the vertical direction. In addition, the direction (Zb-axis direction) of the coordinate axis Zb among the respective coordinate axes Xb, Yb, and Zb in the body-side coordinate system CSb at each measurement target portion conforms to or substantially conforms to the vertical direction in the state in which the target person is standing up and kept still in the upright posture in the embodiment. 
     Therefore, it is possible to regard the direction of the average acceleration vector ↑As_ave calculated in STEP  2  for each measurement target portion as representing the Zb-axis direction of the body-side coordinate system CSb at each measurement target portion when seen in the sensor coordinate system CSs of the inertial sensor  10  at the measurement target portion. 
     Thus, the measurement processing device  20  then identifies (estimates) an element of a column corresponding to the Zb axis of a transformation matrix R (CSb→CSs) for performing coordinate transformation of the vector amount from the body-side coordinate system CSb to the sensor coordinate system CSs of the inertial sensor  10  at each measurement target portion on the assumption that the direction of the average acceleration vector ↑As_ave calculated in STEP  2  is the Zb-axis direction of the body-side coordinate system CSb at the measurement target portion in STEP  3 . 
     The aforementioned transformation matrix R (CSb→CSs) is a three-dimensional matrix that transforms coordinates from an arbitrary vector (αxb, αyb, αzb) T  seen in the body-side coordinate system CSb to a vector (αxs, αys, αzs) T  seen in the sensor coordinate system CSs as represented by Equation (1) below. Note that each of αxb, αyb, and αzb represents a value in each of the directions of the coordinate axes Xb, Yb, and Zb in the body-side coordinate system CSb, each of αxs, αys, and αzs represents a value in each of the directions of the coordinate axes Xs, Ys, and Zs in the sensor coordinate system CSs, and the suffix “T” means transposition. Note that each of vectors (e11, e21, e31) T , (e12, e22, e32) T , and (e13, e23, e33) T  of the respective columns in the transformation matrix R (CSb→CSs) is a unit vector. Also, a transposed matrix R (CSb→CSs) T  of the transformation matrix R (CSb→CSs) is a transformation matrix R (CSs→CSb)(=an inverse matrix of R(CSb→CSs)) in order to transform coordinates from the sensor coordinate system CSs to the body-side coordinate system CSb. 
     
       
         
           
             
               
                 
                   
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     In this case, the column corresponding to the Zb axis of the transformation matrix R (CSb→CSs) is the right side of Equation (1) in the transformation matrix R(CSb→CSs) and is a column applied to the third element αzb (the element in the Zb-axis direction) of the vector (αxb, αyb, αzb) T , that is, the third column. Also, in a case in which the direction of the average acceleration vector ↑As_ave calculated in STEP  2  for each measurement target portion is regarded as the Zb-axis direction of the body-side coordinate system CSb at each measurement target portion, the average acceleration vector ↑AS_ave is a vector that is proportional to (e13, e23, e33) T  that is a vector calculated by assigning (0, 0, 1) T  to (αxb, αyb, αzb) T  in the right side of Equation (1). 
     Thus, in STEP  3 , the measurement processing device  20  calculates the vector (e13, e23, e33) T  of the third column in the transformation matrix R(CSb→CSs) for each measurement target portion using Equation (2a) or (2b) below. In other words, the measurement processing device  20  calculates the vector (e13, e23, e33) T  of the third column in the transformation matrix R(CSb→CSs) by transforming the average acceleration vector ↑As_ave into a unit vector. 
     Note that which of Equations (2a) and (2b) is to be used to calculate the vector (e13, e23, e33) T  of the third column depends on to which direction of each coordinate axis the positive direction of each coordinate axis in each of the sensor coordinate system CSs and the body-side coordinate system CSb is to be set. 
     
       
         
           
             
               
                 
                   
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     In this manner, the element of the column corresponding to the Zb axis of the transformation matrix R(CSb→CSs) is estimated (identified) for each measurement target portion. In the embodiment, the coordinate axis direction estimation processing for the coordinate axis Zb of each body-side coordinate system CSb is performed as described above. 
     Note that in the embodiment, the Zb-axis direction of the body-side coordinate system CSb at each measurement target portion corresponds to the second direction in the disclosure, and the vector (e13, e23, e33) T  of the third column of the transformation matrix R(CSb→CSs) corresponds to the second posture data in the disclosure. 
     Next, the coordinate axis direction estimation processing for the coordinate axis Yb, for example, among the three coordinate axes Xb, Yb, and Zb in each body-side coordinate system CSb is performed as follows. In other words, in the coordinate axis direction estimation processing, the target person P performs a leaning motion in which the upper body is inclined forward in the pitch direction (the direction around the axis in the left-right direction) from the state in which the target person P is standing up in the upright posture (the state at the time t 0 ) and both legs are bent in the pitch direction (more specifically, both legs are bent such that the postures of thighs and lower legs of the respective legs are caused to change in the pitch direction) as illustrated in  FIG. 4 , for example, then the target person P executes a returning motion of returning to the state in which the target person P is standing up in the upright posture (the state at the time t 2 ) by causing the postures of the upper body and the thighs and the lower legs of the respective legs to change in the directions opposite to the directions of the leaning motion from the state in which the target person P leans through the leaning motion (the state at the time t 1 ). Note that in this case, a helper, an appropriate tool, or the like may assist the aforementioned leaning motion and the returning motion of the target person P. Also, these motions of the target person P are preferably performed relatively quickly (such that the motions are not excessively slowly performed). 
     In this manner, the measurement processing device  20  executes the processing illustrated in the flowchart in  FIG. 5  for each measurement target portion in parallel to the exercise of the target person P. Specifically, in STEP  11 , the measurement processing device  20  successively detects a set of angular speeds in the directions of the respective coordinate axes in the sensor coordinate system CSs of the inertial sensor  10  (in other words, a set of elements in the directions of the respective coordinate axes Xs, Ys, and Zs of the angular speed vectors that have occurred in the inertial sensor  10 ) using the angular speed sensor  11  in the inertial sensor  10  at each measurement target portion during the exercise of the target person P, in a predetermined sampling cycle. 
     In this manner, the measurement processing device  20  acquires detection data of the angular speed vectors (the angular speed vectors when seen in the sensor coordinate system CSs of the inertial sensor  10 ) of the inertial sensor  10  at a plurality of sampling times for each measurement target portion during exercise of the leaning motion and the returning motion of the target person P. In this case, the detection values of the elements in the directions of the respective coordinate axes Xs, Ys, and Zs of the angular speed vectors change with time in a waveform pattern illustrated as an example in the graph in  FIG. 6 , for example. 
     Next, in STEP  12 , the measurement processing device  20  calculates an eigenvector ↑E of the first main element through known main element analysis processing from a plurality of pieces of detection data (detection data obtained during exercise of either the leaning motion or the returning motion) of the angular speed vectors when seen in the sensor coordinate system CSs of the inertial sensor  10  for each measurement target portion. The eigenvector ↑E of the first main element is a vector in a main (or representative) direction of the angular speed vectors of the plurality of pieces of detection data. In a case in which measurement points indicating the plurality of pieces of detection data of the angular speed vectors in the sensor coordinate system CSs are obtained as illustrated as an example in  FIG. 7 , the vector ↑E as represented by the thick line arrow in the drawing is calculated as the eigenvector ↑E of the first main element through the main element analysis processing. 
     Here, since the angular speed vectors detected in STEP  11  are angular speed vectors detected by the angular speed sensor  11  in each inertial sensor  10  under exercise conditions that the target person P sequentially performs the leaning motion and the returning motion, the directions of the angular speed vectors are maintained in substantially a constant direction in a state in which the directions conforms to or substantially conforms to the left-right direction of the target person P during the exercise of each of the leaning motion and the returning motion. Note that the orientations of the angular speed vectors are opposite orientations between the leaning motion and the returning motion. 
     Also, since the inclining motion of the upper body and the bending and stretching of the respective legs of the target person P are performed in the pitch direction (the direction around the axis in the left-right direction) under the exercise conditions that the target person P is performing the leaning motion and the returning motion, the direction of the coordinate axis Yb (Yb-axis direction) among the respective coordinate axes Xb, Yb, and Zb in the body-side coordinate system CSb at each measurement target portion is kept substantially constant in a state in which the direction conforms to or substantially conforms to the left-right direction of the target person P. 
     Therefore, it is possible to regard the direction of the eigenvector ↑E calculated in STEP  12  for each measurement target portion as representing the Yb-axis direction of the body-side coordinate system CSb at the measurement target portion when seen in the sensor coordinate system CSs of the inertial sensor  10  at each measurement target portion. 
     Thus, the measurement processing device  20  determines an element of a column corresponding to the Yb axis of the transformation matrix R (CSb→CSs) on the assumption that the direction of the eigenvector ↑E calculated in STEP  12  for each measurement target portion is the Yb-axis direction of the body-side coordinate system CSb at the measurement target portion, in next STEP  13 . 
     In this case, the column corresponding to the Yb axis of the transformation matrix R (CSb→CSs) is a column applied to the second element αyb (the element in the Yb-axis direction) of the vector (αxb, αyb, αzb) T  in the right side of Equation (1) in the transformation matrix R (CSb→CSs), that is, a second column. In addition, in a case in which the direction of the eigenvector ↑E calculated in STEP  12  for each measurement target portion is regarded as the Yb-axis direction of the body-side coordinate system CSb at the measurement target portion, the eigenvector ↑E is a vector that is proportional to (e21, e22, e23) T  that is a vector calculated by assigning (0, 1, 0) T  to (αxb, αyb, αzb) T  in the right side of Equation (1) described above. 
     Thus, in STEP  13 , the measurement processing device  20  calculates the vector (e12, e22, e32) T  of the second column in the transformation matrix R (CSb→CSs) for each measurement target portion by Equation (3a) or (3b) below. In other words, the measurement processing device  20  calculates the vector (e12, e22, e32) T  of the second column in the transformation matrix R (CSb→CSs) by transforming the eigenvector ↑E for each measurement target portion into a unit vector. 
     Note that which of Equations (3a) and (3b) is used to calculate the vector (e12, e22, e32) T  of the second column depends on to which orientation of the direction of each coordinate axis the positive direction of each coordinate axis in each of the sensor coordinate system CSs and the body-side coordinate system CSb is set. 
     
       
         
           
             
               
                 
                   
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     In this manner, the element of the column corresponding to the Yb-axis element in the transformation matrix R(CSb→CSs) is estimated (identified) for each measurement target portion. Note that the eigenvector ↑E calculated in STEP  12  may be a unit vector, and in this case, the eigenvector ↑E may be identified directly as the vector (e12, e22, e32) T  of the second column. In the embodiment, the coordinate axis direction estimation processing for the coordinate axis Yb in each body-side coordinate system CSb is performed as described above. 
     Note that in the embodiment, the Yb-axis direction in the body-side coordinate system CSb at each measurement target portion corresponds to the first direction according to the disclosure, and the vector (e12, e22, e32) T  of the second column in the transformation matrix R (CSb→CSs) corresponds to the first posture data according to the disclosure. 
     Next, coordinate axis direction estimation processing for the remaining coordinate axis Xb among the three coordinate axes Xb, Yb, and Zb in each body-side coordinate system CSb is performed as follows. In other words, the measurement processing device  20  obtains a vector (e11, e21, e31) T  of the first column corresponding to an Xb-axis element in the transformation matrix R(CSb→CSs) as a unit vector that perpendicularly intersects the vector (e12, e22, e32) T  of the second column and the vector (e13, e23, e33) T  of the third column obtained as described above in the coordinate axis direction estimation processing. Specifically, the vector (e11, e21, e31) T  of the first column is calculated through a cross product operation (an arithmetic operation of a vector product) of the vector (e12, e22, e32) T  of the second column and the vector (e13, e23, e33) T  of the third column in this case. 
     Note that in the embodiment, the Xb-axis direction of the body-side coordinate system CSb at each measurement target portion corresponds to the third direction according to the disclosure, and the vector (e11, e21, e31) T  of the first column in the transformation matrix R(CSb→CSs) corresponds to the third posture data according to the disclosure. 
     In the embodiment, the element of each column in the transformation matrix R(CSb→CSs) is obtained for each measurement target portion as described above. In this manner, the relative posture relationship between the sensor coordinate system CSs and the body-side coordinate system CSb (in other words, the relative posture relationship between the inertial sensor  10  and the measurement target portion) is identified by the transformation matrix R(CSb→CSs) for each measurement target portion. 
     In this case, the coordinate axis direction estimation processing related to the coordinate axis Zb in the body-side coordinate system CSb at each measurement target portion is performed using the detection data of the accelerations in the state in which the target person P is standing up in the upright posture. In addition, it is possible to relatively stably maintain the Zb-axis direction that is a direction of one of the coordinate axes in the body-side coordinate system CSb at each measurement target portion in a state in which the Zb-axis direction conforms to or substantially conforms to the vertical direction in the state in which the target person P is standing up in the upright posture. Therefore, it is possible to identify the column vector (the vector of the third column) in the transformation matrix R(CSb→CSs) representing the Zb-axis direction of the body-side coordinate system CSb when seen in the sensor coordinate system CSs for each measurement target portion with high reliability. 
     In addition, the coordinate axis direction estimation processing related to the coordinate axis Yb in the body-side coordinate system CSb when seen in the sensor coordinate system CSs at each measurement target portion is performed using the detection data of the angular speeds in the state in which the target person P is carrying out the leaning motion or the returning motion. Also, in a case in which the target person P sequentially carries out the leaning motion and the returning motion, it is possible to relatively stably maintain the Yb-axis direction that is the direction of one of the coordinate axes in the body-side coordinate system CSb at each measurement target portion and the direction of the angular speed vector of the inertial sensor  10  at the measurement target portion in a state in which the Yb-axis direction and the direction of the angular speed vector conform to or substantially conform to the left-right direction of the target person P. Therefore, it is possible to identify the column vector (the vector of the second column) in the transformation matrix R(CSb→CSs) representing the Yb-axis direction in the body-side coordinate system CSb when seen in the sensor coordinate system CSs with high reliability for each measurement target portion. 
     In addition, the coordinate axis direction estimation processing related to the coordinate axis Yb can be performed for all the measurement target portions by performing the leaning motion and the subsequent returning motion once in the embodiment. 
     Further, it is also possible to identify the column vector (the vector of the first column) in the transformation matrix R(CSb→CSs) representing the Xb-axis direction in the body-side coordinate system CSb when seen in the sensor coordinate system CSs with high reliability since the column vector (the vector of the first column) in the transformation matrix R(CSb→CSs) representing the Xb-axis direction in the body-side coordinate system CSb when seen in the sensor coordinate system CSs is obtained through the cross product operation from the other two column vectors (the vectors of the second column and the third column) identified as described above for each measurement target portion. 
     Second Embodiment 
     Next, the second embodiment of the disclosure will be described with reference to  FIGS. 8 to 10 . Note that since the embodiment is different from the first embodiment only in a part of the coordinate axis direction estimation processing, description of matters that are the same as those in the first embodiment will be omitted. 
     In the first embodiment, the target person P stands up in the upright posture in order to estimate the Zb-axis direction in the body-side coordinate system CSb at each measurement target portion, and the target person P carries out the leaning motion and the returning motion in order to estimate the Yb-axis direction. Meanwhile, the embodiment is an embodiment in which directions of two coordinate axes in the body-side coordinate system CSb at each measurement target portion can be estimated in a state in which the target person P is seated in an object placed such that the target person P can be seated therein with the longitudinal direction of thighs of the respective legs being substantially horizontally aligned, for example, a chair Chr. Note that in the embodiment, the chair Chr is an example of an “object with a specific shape” according to the disclosure, and the state in which the target person P is seated in the chair Chr corresponds to the state in which the body of the target person P is in contact with the “object with a specific shape”. 
     In the embodiment, coordinate axis direction estimation processing for the coordinate axis Zb in the body-side coordinate system CSb at each measurement target portion (an upper portion of the upper body, a waist portion, lower legs of the respective legs) other than the thighs of the respective legs among the measurement target portions of the target person P and the coordinate axis direction estimation processing for the coordinate axis Xb in the body-side coordinate system CSb (CSb( 3 )) at the thighs of the respective legs are performed as follows. 
     In the coordinate axis direction estimation processing, the target person P is kept still in a state in which the target person P is seated in the chair Chr such that the upper body and the lower legs of the respective legs are in an upright state in the vertical direction and the thighs of the respective legs extend in the horizontal direction on a seat surface of the chair Chr as illustrated in  FIG. 8 , for example. Note that at this time, the standing state of the upper body of the target person P may be assisted by an appropriate tool or a helper in order to minimize a force in the transverse direction acting on the upper body of the target person P. 
     The measurement processing device  20  executes the processing (the processing of detecting the accelerations using the acceleration sensor  12  in each inertial sensor  10 ) in STEP  1  and further executes the aforementioned processing in STEP  2  similarly to the first embodiment in the state in which the target person P is seated in the chair Chr in this manner, thereby calculating the average acceleration vector ↑As_ave for each measurement target portion. 
     Here, the Zb-axis direction in the body-side coordinate system CSb conforms to or substantially conforms to the vertical direction (gravity direction) for each measurement target portion other than the thighs of the respective legs of the target person P in the state in which the target person P is seated in the chair Chr as described above. Thus, the measurement processing device  20  identifies the element of the column (third column) corresponding to the Zb axis in the transformation matrix R(CSb→CSs) by executing the aforementioned processing in STEP  3  similarly to the first embodiment after the execution of the processing in STEP  2  for each measurement target portion other than the thighs of the respective legs of the target person P. In other words, the measurement processing device  20  calculates the vector (e13, e23, e33) T  of the third column in the transformation matrix R (CSb→CSs) through the arithmetic operation processing of Equation (2a) or (2b) described above for each measurement target portion other than the thighs of the respective legs of the target person P. 
     Meanwhile, the Xb-axis direction in the body-side coordinate system CSb (CSb( 3 )) conforms to or substantially conforms to the vertical direction (gravity direction) for the thighs of the respective legs of the target person P in the state in which the target person P is seated in the chair Chr as described above. Thus, for the thighs of the respective legs of the target person P, the measurement processing device  20  identifies (estimates) an element of a column corresponding to the Xb axis in the transformation matrix R(CSb→CSs) on the assumption that the direction of the average acceleration vector ↑As_ave calculated in STEP  2  is the Xb-axis direction in the body-side coordinate system CSb (CSb( 3 )) at the thighs. 
     In this case, since the column corresponding to the Xb axis in the transformation matrix R(CSb→CSs) is the first column, the measurement processing device  20  calculates the vector (e11, e21, e31) T  of the first column in the transformation matrix R(CSb→CSs) by transforming the average acceleration vector ↑As_ave calculated for the thighs into a unit vector as represented by Equations (4a) or (4b) below. 
     Note that which of Equations (4a) and (4b) is to be used to calculate the vector (e11, e21, e31) T  of the first column depends on to which orientation of the directions of the respective coordinate axes the positive direction of each coordinate axis in each of the sensor coordinate system CSs and the body-side coordinate system CSb is set. 
     
       
         
           
             
               
                 
                   
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     In the embodiment, the coordinate axis direction estimation processing for the coordinate axis Zb in the body-side coordinate system CSb at each measurement target portion (the upper portion of the upper body, the waist portion, and the lower legs of the respective legs) other than the thighs of the respective legs of the target person P and the coordinate axis direction estimation processing for the coordinate axis Xb in the body-side coordinate system CSb at each of the thighs of the legs are performed as described above. 
     Note that in the embodiment, the Zb-axis direction in the body-side coordinate system CSb at each measurement target portion other than the thighs of the respective legs of the target person P corresponds to the second direction according to the disclosure, and the vector (e13, e23, e33) T  of the third column in the transformation matrix R(CSb→CSs) corresponds to the second posture data according to the disclosure. Also, the Xb-axis direction in the body-side coordinate system CSb at each of the thighs corresponds to the second direction according to the disclosure, and the vector (e11, e21, e31) T  of the first column in the transformation matrix R(CSb→CSs) corresponds to the second posture data according to the disclosure, for the thighs of the respective legs. 
     Next, coordinate axis direction estimation processing for the coordinate axis Yb in the body-side coordinate system CSb at each measurement target portion (thighs and lower legs) of the respective legs of the target person P is performed as follows, for example. In other words, the target person P carries out a leg lifting motion in which both legs are lifted while rotating the legs in the pitch direction at hip joints from a state in which the target person P is seated in the chair Chr similarly to the state in  FIG. 8  (the state at the time t 10 ) as illustrated in  FIG. 9  and then carries out a leg returning motion in which both the legs are lowered and returned to the original state (the state at the time t 12 ) from the state in which both the legs are lifted through the leg lifting motion (the state at the time t 11 ) through a motion opposite to the leg lifting motion (a motion in the pitch direction) in the coordinate axis direction estimation processing. 
     Note that the leg lifting motion and the leg returning motion of the target person P may be assisted by a helper, an appropriate tool, or the like. Also, the lower legs of the respective legs and the upper body of the target person P may be inclined with respect to the vertical direction in the state at the time of starting the leg lifting motion (the state at the time t 10 ) and the state at the time of ending the leg returning motion (the state at the time t 12 ). In addition, the thighs of the respective legs of the target person P may be inclined with respect to the horizontal direction. Also, the leg lifting motion and the leg returning motion of the target person P are preferably relatively quickly carried out (such that the leg lifting motion and the leg returning motion are not excessively slowly carried out). 
     As described above, the measurement processing device  20  executes the aforementioned processing (STEP  11  to  13 ) illustrated in the flowchart in  FIG. 5  similarly to the first embodiment for each of the thighs and the lower legs of the respective legs in parallel to the exercise of the respective legs carried out by the target person P. In this case, the angular speed vector that occurs in the inertial sensor  10  at each of the thighs and the lower legs of the respective legs is kept constant in a state in which the angular speed vector conforms to or substantially conforms to the left-right direction of the target person P in the state in which the target person P is carrying out the leg lifting motion or the leg returning motion. Therefore, it is possible to appropriately identify (estimate) the element of the column corresponding to the Yb axis in the transformation matrix R(CSb→CSs) by executing the processing illustrated in the flowchart in  FIG. 5 . 
     Next, coordinate axis direction estimation processing for the coordinate axis Yb in the body-side coordinate system CSb at measurement target portions (the upper portion of the upper body and the waist portion) of the upper body of the target person P is performed as follows, for example. In other words, the target person P carries out an upper body forward inclination motion in which the upper body is inclined forward in the pitch direction from a state in which the target person P is seated in the chair Chr (the state at the time t 20 ) similarly to  FIG. 8  as illustrated in  FIG. 10 , for example, and then carries out an upper body returning motion in which the upper body is inclined backward in the pitch direction to return the upper body to the original state (the state at the time t 22 ) from the state in which the upper body is inclined forward through the upper body forward inclination motion (the state at the time t 21 ) in the coordinate axis direction estimation processing. Note that in this case, the upper body forward inclination motion and the upper body returning motion of the target person P may be assisted by a helper, an appropriate tool, or the like. Also, the body core axis direction of the upper body may be inclined with respect to the vertical direction in the state at the time of starting the upper body forward inclination motion (the state at the time t 20 ) and the state at the time of ending the upper body returning motion (the state at the time t 22 ). In addition, these motions of the target person P are preferably relatively quickly carried out (such that the motions are not excessively slowly carried out). 
     The measurement processing device  20  executes the aforementioned processing illustrated in the flowchart in  FIG. 5  similarly to the first embodiment for each of the upper portion of the upper body and the waist portion in parallel to the exercise of the upper body carried out by the target person P. In this case, the angular speed vector that occurs in the inertial sensor  10  at each of the upper portion of the upper body and the waist portion is kept substantially constant in a state in which the angular speed vector conforms to or substantially conforms to the left-right direction of the target person P in the state in which the target person P is carrying out the upper body forward inclination motion or the upper body returning motion. Therefore, it is possible to appropriately identify (estimate) the element of the column corresponding to the Yb axis in the transformation matrix R(CSb→CSs) by executing the processing illustrated in the flowchart in  FIG. 5 . 
     Note that the target person P may carry out the leg lifting motion and the upper body forward inclination motion in parallel and may also carry out the leg returning motion and the upper body returning motion in parallel. In this case, it is possible to carry out the processing illustrated in the flowchart in  FIG. 5  in parallel for each of the measurement target portions at the thighs and the lower legs of the respective legs and the upper portion of the upper body and the waist portion. 
     Also, in the embodiment, the Yb-axis direction in the body-side coordinate system CSb at each measurement target portion of the target person P corresponds to the first direction according to the disclosure, and the vector (e12, e22, e32) T  of the second column in the transformation matrix R(CSb→CSs) corresponds to the first posture data according to the disclosure. 
     Next, coordinate axis direction estimation processing for the coordinate axis Xb in the body-side coordinate system CSb at each measurement target portion (the upper portion of the upper body, the waist portion, and the lower legs of the respective legs) other than the thighs of the respective legs of the target person P and coordinate axis direction estimation processing for the coordinate axis Zb in the body-side coordinate system CSb (CSb( 3 )) at the thighs of the respective legs are performed as follows. 
     That is, the measurement processing device  20  calculates the vector (e11, e21, e31) T  of the first column corresponding to the Xb axis through a cross product operation (an arithmetic operation of a vector product) between the vector (e12, e22, e32) T  of the second column corresponding to the Yb axis and the vector (e13, e23, e33) T  of the third column corresponding to the Zb axis in the body-side coordinate system CSb at each measurement target portion similarly to the first embodiment in the coordinate axis direction estimation processing for the coordinate axis Xb in the body-side coordinate system CSb at each measurement target portion (the upper portion of the upper body, the waist portion, and the lower legs of the respective legs) other than the thighs of the respective legs of the target person P. In this manner, the Xb-axis direction (the direction when seen in the sensor coordinate system CSs) in the body-side coordinate system CSb at each measurement target portion other than the thighs of the respective legs of the target person P is identified. 
     Meanwhile, the measurement processing device  20  obtains the vector (e13, e23, e33) T  of the third column corresponding to the Zb-axis element in the transformation matrix R(CSb→CSs) as a unit vector that perpendicularly intersects the vector (e11, e21, e31) T  of the first column obtained as described above for the thigh and the vector (e12, e22, e32) T  of the second column for the thigh of each leg of the target person P. Specifically, the vector (e13, e23, e33) T  of the third column is calculated by the cross product operation (the arithmetic operation of the vector product) of the vector (e11, e21, e31) T  of the first column and the vector (e12, e22, e32) T  of the second column. 
     Note that in the embodiment, the Xb-axis direction in the body-side coordinate system CSb at each measurement target portion other than the thighs of the respective legs of the target person P corresponds to the third direction according to the disclosure, and the vector (e11, e21, e31) T  of the first column in the transformation matrix R(CSb→CSs) corresponds to the third posture data according to the disclosure. Also, the Zb-axis direction in the body-side coordinate system CSb at each thigh corresponds to the third direction according to the disclosure, and the vector (e13, e23, e33) T  of the third column in the transformation matrix R(CSb→CSs) corresponds to the third posture data according to the disclosure for the thigh of each leg. 
     In the embodiment, the element of each column in the transformation matrix R(CSb→CSs) is obtained for each measurement target portion as described above. In this manner, the relative posture relationship between the sensor coordinate system CSs and the body-side coordinate system CSs (in other words, the relative posture relationship between the inertial sensor  10  and the measurement target portion) is identified (estimated) by the transformation matrix R(CSb→CSs) for each measurement target portion similarly to the first embodiment. 
     In this case, the coordinate axis direction estimation processing related to the coordinate axis Zb in the body-side coordinate system CSb at each measurement target portion other than the thighs of the respective legs of the target person P and the coordinate axis direction estimation processing related to the coordinate axis Xb in the body-side coordinate system CSb of the thigh of each leg are performed using the acceleration detection data in the state in which the target person P is seated in the chair Chr as illustrated in  FIG. 8 . In addition, in the state in which the target person P is seated in this manner, it is possible to relatively stably maintain the Zb-axis direction in the body-side coordinate system CSb at each measurement target portion other than the thighs of the respective legs and the Xb-axis direction in the body-side coordinate system CSb at the thigh of each leg in a state in which the Zb-axis direction and the Xb-axis direction conforms to or substantially conforms to the vertical direction (gravity direction). 
     Therefore, it is possible to highly reliably identify the column vector (the vector of the third column) in the transformation matrix R(CSb→CSs) representing the Zb-axis direction in the body-side coordinate system CSb when seen in the sensor coordinate system CSs for each measurement target portion other than the thighs of the respective legs. Also, it is possible to highly reliably identify the column vector (the vector of the first column) in the transformation matrix R(CSb→CSs) representing the Xb-axis direction in the body-side coordinate system CSb when seen in the sensor coordinate system CSs for the thighs of the respective legs. 
     Also, the coordinate axis direction estimation processing related to the coordinate axis Yb in the body-side coordinate system CSb when seen in the sensor coordinate system CSs at each measurement target portion is performed using angular speed detection data in a state in which the target person P is sequentially performing the leg lifting motion and the leg returning motion or in a state in which the target person P is sequentially performing the upper body forward inclination motion and the upper body returning motion. Also, in a case in which the target person P sequentially performs the leg lifting motion and the leg returning motion, it is possible to relatively stably maintain the Yb-axis direction in the body-side coordinate system CSs at each of the thighs and the lower legs of the respective legs and the direction of the angular speed vector of the inertial sensor  10  at each of the thighs and the lower legs in a state in which the Yb-axis direction and the direction of the angular speed vector conform to or substantially conform to the left-right direction of the target person P. 
     Also, in a case in which the target person P sequentially performs the upper body forward inclination motion and the upper body returning motion, it is possible to relatively stably maintain the Yb-axis direction in the body-side coordinate system CSb at each of the upper portion of the upper body and the waist portion and the direction of the angular speed vector of the inertial sensor  10  at each of the upper portion of the upper body and the waist portion in a state in which the Yb-axis direction and the direction of the angular speed vector conform to or substantially conform to the left-right direction of the target person P. 
     Therefore, it is possible to highly reliably identify the column vector (the vector of the second column) in the transformation matrix R(CSb→CSs) representing the Yb-axis direction in the body-side coordinate system CSb when seen in the sensor coordinate system CSs for each measurement target portion similarly to the first embodiment. 
     Further, the column vector (the vector of the first column) in the transformation matrix R(CSb→CSs) representing the Xb-axis direction in the body-side coordinate system CSb when seen in the sensor coordinate system CSs for each measurement target portion other than the thighs of the respective legs of the target person P is obtained through the cross product operation from other two column vectors (the vectors of the second column and the third column) identified as described above. Therefore, it is also possible to highly reliably identify the column vector (the vector of the first column) in the transformation matrix R(CSb→CSs) representing the Xb-axis direction in the body-side coordinate system CSb when seen in the sensor coordinate system CSs for each measurement target portion other than the thighs of the respective legs of the target person P. 
     Also, the column vector (the vector of the third column) in the transformation matrix R(CSb→CSs) representing the Zb-axis direction in the body-side coordinate system CSb when seen in the sensor coordinate system CSs for the thigh of each leg of the target person P is obtained through a cross product operation from other two column vectors (the vectors of the first column and the second column) identified as described above. Therefore, it is possible to highly reliably identify the column vector (the vector of the third column) in the transformation matrix R(CSb→CSs) representing the Zb-axis direction in the body-side coordinate system CSb when seen in the sensor coordinate system CSs for the thigh of each leg of the target person P. 
     Further, it is possible to acquire the acceleration detection data and the angular speed detection data used in the coordinate axis direction estimation processing in the seated state of the target person P in the embodiment and thereby to easily apply the detection data to a target person P, for whom it is difficult to be in the upright posture state (for example, a child, a person with weak leg strength, or the like). 
     Note that the disclosure is not limited to the aforementioned first embodiment or the second embodiment and other embodiments can also be employed. Hereinafter, some of other embodiments will be described. 
     In the aforementioned respective embodiment, the inertial sensor  10  at each measurement target portion detects an angular speed when the target person P is carrying out the exercise of causing the postures of the measurement target portions at the upper body and the respective legs of the target person P to change in the pitch direction, and the direction of the coordinate axis Yb (the coordinate axis in the left-right direction) at each measurement target portion when seen in the sensor coordinate system CSs is identified on the basis of the detection data. 
     Instead, the inertial sensor  10  at each measurement target portion may detect the angular speed vector when the target person P is carrying out the exercise of causing the postures of the measurement target portions at the upper body and the respective legs of the target person P, for example, to change in a rolling direction (the direction around the axis in the front-back direction of the target person P), and the direction of the coordinate axis Xb (the coordinate axis in the front-back direction) at each measurement target portion when seen in the sensor coordinate system CSs may be identified on the basis of the detection data. 
     In this case, exercise of causing the upper body to be inclined leftward and rightward, exercise of swinging the respective legs on the left side or the right side around the hip joint, or the like can be employed, for example, as the exercise in the rolling direction. Also, in this case, the Yb-axis direction at each measurement target portion may be identified through the cross product operation between the vector of the third column (this can be identified similarly to the aforementioned respective embodiments) representing the Zb-axis direction in the transformation matrix R(CSb→CSs) and the vector of the first column representing the Xb-axis direction. 
     In addition, the motion of the target person P from which the angular speed vector is detected for identifying the Yb-axis direction (or the Xb-axis direction) at each measurement target portion may be performed individually for each measurement target portion. 
     In addition, the eigenvector ↑E as a center (or representative) vector of angular speed vectors through main element analysis processing from the angular speed vector detection data and the direction of the eigenvector ↑E is identified as the Yb-axis direction, for identifying the direction of the coordinate axis Yb (the coordinate axis in the left-right direction) at each measurement target portion in the respective embodiments. 
     However, a direction of one angular speed vector (or an angular speed vector obtained by performing filtering with low pass properties on the detection data of the angular speed vectors) detected at a sampling time at which the size (absolute value) of the detected angular speed vectors reaches a peak value (maximum value) may be identified as the Yb-axis direction during the execution of the motion of causing the posture of each measurement target portion to change in the pitch direction (for example, the leaning motion or the returning motion or the like). 
     Alternatively, mutual ratios of elements in the directions of the three coordinate axes Xs, Ys, and Zs of a plurality of angular speed vectors detected at a plurality of sampling times during execution of a motion of causing the posture of each measurement target portion to change in the pitch direction, for example, may be averaged (including weighted average), and a direction of a vector with the average ratio (a vector with a mutual ratio of the elements in directions of the three coordinate axes Xs, Ys, an Zs of the vector that conforms to the average ratio) may be identified as the Yb-axis direction. In this case, it is desirable to set weights of the aforementioned mutual ratios for angular speed vectors with larger sizes (absolute values) to be relatively higher in the aforementioned processing of averaging the mutual ratios. 
     Alternatively, three coordinate axis elements successively detected are respectively integrated during execution of motion of causing the posture of each measurement target portion to change in the pitch direction, and a direction of a vector with a ratio corresponding to a mutual ratio of these integrated values (a vector with a mutual ratio of elements in the three coordinate axes Xs, Ys, Zs direction of the vector that conforms to the mutual ratio of the integrated values) may be identified as the Yb-axis direction, for example. 
     The method of identifying the Yb-axis direction as described above is similarly applied to a case in which the angular speed vectors are detected during a motion in the rolling direction at each measurement target portion and the Xb-axis direction is identified from the angular speed vectors. 
     Also, the measurement target portions are not limited to the upper body or the respective legs of the target person P, and measurement target portions may be set at arms of the target person P, for example. In this case, it is possible to identify the coordinate axis direction of the upward-downward direction (longitudinal direction) of the arms from acceleration detection data in a state in which the target person P let his/her arms with the measurement target portions drop downward, for example. Also, it is possible to identify the coordinate axis direction in the left-right direction of the arms from angular speed vectors detected during execution of a motion of swinging the arms with the measurement target portion forward or backward in the pitch direction around shoulder joints, for example. In addition, it is possible to identify the coordinate axis direction in the front-back direction of the arms from angular speed vectors detected during execution of exercise of swinging the arms with the measurement target portions rightward or leftward in the rolling direction around the shoulder joints, for example. 
     In addition, the coordinate axis direction estimation processing for one coordinate axis in the body coordinate system Cb at a measurement target portion is executed with the coordinate axis directed in the vertical direction in the state in which the target person P is seated and kept still in the chair Chr in the aforementioned second embodiment. However, in order to enable the one coordinate axis in the body coordinate system Cb at the measurement target portion to be directed in the vertical direction and kept still, an appropriate portion of the body of the target person P may be caused to abut on another object (an object with a specific shape) other than the chair Chr, and the coordinate axis direction estimation processing for the one coordinate axis (the coordinate axis directed in the vertical direction) in the body coordinate system Cb at the measurement target portion may be executed in this state. 
     It will be apparent to those skilled in the art that various modifications and variations can be made to the disclosed embodiments without departing from the scope or spirit of the disclosure. In view of the foregoing, it is intended that the disclosure covers modifications and variations provided that they fall within the scope of the following claims and their equivalents.