PATENT DOCUMENT

Publication Number: US-11103749-B2
Application Number: US-201715692726-A
Country: US
Kind Code: B2

Title: Systems and methods of swimming analysis

Abstract:
Systems and methods of analyzing a user&#39;s motion during a swimming session are described. One or more motions sensors can collect motion data of the user. A processor circuit can make motion analysis based on the motion data. The processor circuit can determine if the user&#39;s arm swing is a genuine swim stroke. The processor circuit can also determine whether the user is swimming or turning. The processor circuit can also classify the user&#39;s swim stroke style. The processor circuit can also determine the user&#39;s swim stroke phase. The processor circuit can also determine the user&#39;s stroke orbit consistency.

Claims:
What is claimed is: 
     
       1. A method for improving an accuracy of a wearable device while classifying a user&#39;s swim stroke style, the method comprising:
 receiving, by a processor circuit of a wearable device, motion data from one or more motion sensors of the wearable device, wherein the one or more motion sensors comprises at least one of an accelerometer or a gyroscope; 
 determining, by the processor circuit, rotational data of the wearable device, wherein the rotational data is expressed in a frame of reference, 
 extracting, by the processor circuit, one or more features from the rotational data; 
 determining, by the processor circuit, the user&#39;s swim stroke style based on the one or more features; and 
 in response to determining the user&#39;s swim stroke style, determining, by the processor circuit, a level of orbit consistency for a plurality of swim strokes performed by the user based on the rotational data, wherein the level of orbit consistency measures a variation in direction of the plurality of swim strokes performed by the user; and 
 outputting, by the processor circuit, the determined swim stroke style and the level of orbit consistency for the plurality of swim strokes. 
 
     
     
       2. The method of  claim 1 , wherein the frame of reference is a body-fixed frame of reference with respect to the wearable device. 
     
     
       3. The method of  claim 1 , wherein the frame of reference is an inertial frame of reference. 
     
     
       4. The method of  claim 1 , wherein the one or more features comprise at least one of:
 a mean crown orientation of the wearable device, 
 a correlation of the user&#39;s arm rotation and the user&#39;s wrist rotation, or 
 a contribution of rotation about a crown of the wearable device to a total angular velocity. 
 
     
     
       5. The method of  claim 4 , wherein the determining comprises performing a first-tier analysis on at least one of the features. 
     
     
       6. The method of  claim 5 , wherein the first-tier analysis indicates an upwards mean crown orientation during a fastest part of a stroke for a backstroke or a downwards mean crown orientation during a fastest part of a stroke for a breaststroke. 
     
     
       7. The method of  claim 5 , wherein the first-tier analysis indicates a positive correlation of arm and wrist rotations for a backstroke or a negative correlation of arm and wrist rotations for a breaststroke. 
     
     
       8. The method of  claim 1 , wherein the one or more features comprise at least one of:
 a relative arm rotation about a band of the wearable device during a pull phase, 
 a moment arm of the user, 
 a ratio of acceleration along a z axis to rotation about a y axis, wherein the z axis and the y axis are both either in an inertial frame of reference or a fixed body frame of reference with respect to the wearable device, 
 a mean gravity crown weighted by acceleration, 
 a correlation between an orientation of top of the band of the wearable device and rotation around the band of the wearable device, 
 a root mean square (RMS) of a crown rotation, 
 a minimum rotation around a crown of the wearable device, 
 a maximum rotation around the band of the wearable device, or 
 a maximum rotation about an x axis divided by a maximum rotation about a y axis, wherein the x axis and the y axis are both either in an inertial frame of reference or a fixed body frame of reference with respect to the wearable device. 
 
     
     
       9. The method of  claim 8 , wherein the determining comprises performing a second-tier analysis on at least one of the features. 
     
     
       10. The method of  claim 9 , wherein an outcome of the second-tier analysis indicates a butterfly stroke or a freestyle stroke. 
     
     
       11. A wearable device configured to classify a user&#39;s swim stroke style, the device comprising:
 one or more motion sensors comprising at least one of an accelerometer or a gyroscope, the one or more motion sensors being configured to output motion data; and 
 a processor circuit in communication with the one or more motion sensors, the processor circuit being configured to:
 receive the motion data from the one or more motion sensors; 
 determine rotational data of the wearable device, wherein the rotational data is expressed in a frame of reference; 
 extract one or more features from the rotational data; 
 determine the user&#39;s swim stroke style based on the one or more features; 
 in response to determining the user&#39;s swim stroke style, determine a level of orbit consistency for a plurality of swim strokes performed by the user based on the rotational data, wherein the level of orbit consistency measures a variation in direction of the plurality of swim strokes performed by the user; and 
 output the determined swim stroke style and the level of orbit consistency for the plurality of strokes. 
 
 
     
     
       12. The wearable device of  claim 11 , wherein the frame of reference is a body-fixed frame of reference with respect to the wearable device. 
     
     
       13. The wearable device of  claim 11 , wherein the frame of reference is an inertial frame of reference. 
     
     
       14. The wearable device of  claim 11 , wherein the one or more features comprise at least one of:
 a mean crown orientation of the wearable device, 
 a correlation of the user&#39;s arm rotation and the user&#39;s wrist rotation, or 
 a contribution of rotation about a crown of the wearable device to a total angular velocity. 
 
     
     
       15. The wearable device of  claim 14 , wherein the determining comprises performing a first-tier analysis on at least one of the features. 
     
     
       16. The wearable device of  claim 15 , wherein the first-tier analysis indicates an upwards mean crown orientation during a fastest part of a stroke for a backstroke or a downwards mean crown orientation during a fastest part of a stroke for a breaststroke. 
     
     
       17. The wearable device of  claim 15 , wherein the first-tier analysis indicates a positive correlation of arm and wrist rotations for a backstroke or a negative correlation of arm and wrist rotations for a breaststroke. 
     
     
       18. The wearable device of  claim 11 , wherein the one or more features comprise at least one of:
 a relative arm rotation about a band of the wearable device during a pull phase, 
 a moment arm of the user, 
 a ratio of acceleration of the wearable device along a z axis to rotation of the wearable device about a y axis, wherein the z axis and the y axis are both either in an inertial frame of reference or a fixed body frame of reference with respect to the wearable device, 
 a mean gravity crown weighted by acceleration, 
 a correlation between an orientation of top of the band of the wearable device and rotation around the band of the wearable device, 
 a root mean square (RMS) of a crown rotation, 
 a minimum rotation around a crown of the wearable device, 
 a maximum rotation around the band of the wearable device, or 
 a maximum rotation of the wearable device about an x axis divided by a maximum rotation of the wearable device about the y axis, wherein the z axis and the y axis are both either in an inertial frame of reference or a fixed body frame of reference with respect to the wearable device. 
 
     
     
       19. The wearable device of  claim 18 , wherein the determining comprises performing a second-tier analysis on at least one of the features. 
     
     
       20. The wearable device of  claim 19 , wherein an outcome of the second-tier analysis indicates a butterfly stroke or a freestyle stroke.

Description:
PRIORITY CLAIM 
     This application claims priority to and the benefit of U.S. Provisional Patent Application No. 62/381,836, titled “Systems and Methods of Arm Swing Motion Determination”, which was filed on Aug. 31, 2016 and is incorporated by reference herein in its entirety. 
     This application claims priority to and the benefit of U.S. Provisional Patent Application No. 62/381,856, titled “Systems and Methods for Determining Orbit Consistency,” which was filed on Aug. 31, 2016 and is incorporated by reference herein in its entirety. 
     This application claims priority to and the benefit of U.S. Provisional Patent Application No. 62/381,644, titled “Systems and Methods for Motion Determination using Likelihood Ratios,” which is filed on Aug. 31, 2016 and is incorporated by reference herein in its entirety. 
     This application claims priority to and the benefit of U.S. Provisional Patent Application No. 62/381,972, titled “Systems and Methods of Classifying Swim Strokes,” which was filed on Aug. 31, 2016 and is incorporated by reference herein in its entirety. 
     This application claims priority to and the benefit of U.S. Provisional Patent Application No. 62/382,006, titled “Systems and Methods of Determining Swim Stroke Phase,” which was filed on Aug. 31, 2016 and is incorporated by reference herein in its entirety. 
    
    
     CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application relates to co-pending U.S. patent application Ser. No. 15/691,245, titled “Systems and Methods for Determining Swimming Metrics,” which is file on Aug. 30, 2017 and is incorporated by reference herein in its entirety. 
     This application relates to co-pending U.S. patent application Ser. No. 15/692,237, titled “Systems and Methods of Swimming calorimetry,” which is filed on Aug. 31, 2017 and is incorporated by reference herein in its entirety. 
     FIELD 
     The present disclosure relates generally to swimming analysis. 
     BACKGROUND 
     When a user is doing activities that includes an arm swing motion, there is often a need to measure a user&#39;s arm extension. As an example, when a user is swimming laps, the user&#39;s arm extension can help distinguish between a small incidental arm swing motion and a true swim stroke. In addition, determining arm extension can be used to classify different types of swimming strokes. Accordingly, it is desirable to provide methods and systems of determining arm swing motion. 
     Further, when a user is doing activities that includes multiple types of motions, there is often a need to classify the types of motions. As an example, when a user is swimming laps, the user can switch between two types of motions: swimming and turning. As another example, when a user is running, the user can switch between running and walking. Knowing which type of motions a user is doing is useful in many applications including estimating energy expenditure of the user. Accordingly, it is desirable to provide methods and systems of determining a user&#39;s types of motions. 
     Generally, there are four common swim stroke styles: butterfly, freestyle, breaststroke and backstroke. When a user is swimming, the user can perform any of the different swim stroke styles and change styles throughout the course of his or her swimming session. Knowing which type of swim style a user is doing is useful in many applications including estimating energy expenditure of a user, stroke counting, lap counting and distance calibration. Accordingly, it is desirable to provide methods and systems for classifying swim stroke style. 
     However, classifying different swim stroke styles is difficult without breaking the swim stroke styles down into common individual phases (e.g., glide, pull, transition and recovery). Knowing a swim stroke phase that a user is executing is not only helpful in identifying swim stroke style, but is also useful in turn detection, lap counting, stroke counting, swimming versus not swimming detection, and coaching/measuring “stroke goodness” by comparing a user&#39;s stroke to an ideal set of phase parameters. Accordingly, it is desirable to provide methods and systems of determining swim stroke phase. 
     When a user is swimming, there is often a need to determine the consistency of the user&#39;s arm movements, or orbits. An example of a movement to track is a user&#39;s swimming stroke. For example, in an ideal situation, an individual swimming freestyle should exhibit nearly exact replicas of the stroke. But in practice, the ability of an individual to repeat a stroke exactly can be affected by many factors. Therefore, a measure of consistency of a user&#39;s stroke orbits can imply the user&#39;s skill, efficiency, fatigue, and/or health (e.g., inability to repeat movements may be a sign of disease or injury). Accordingly, it is desirable to provide methods and systems of determining consistency of a user&#39;s stroke orbits while swimming. 
     SUMMARY 
     The present disclosure relates to a method for improving an accuracy of a wearable device while determining a user&#39;s arm motion. In some embodiments, the method comprising: receiving, by a processor circuit of a wearable device, motion data from one or more motion sensors of the wearable device, wherein the one or more motion sensors comprises at least one of an accelerometer or a gyroscope; determining, by the processor circuit using the motion data, rotational data expressed in a first frame of reference based on the motion data; determining, by the processor circuit, a moment arm length based on the rotational data; comparing, by the processor circuit, the moment arm length with a threshold length; determining, by the processor circuit, the user&#39;s arm swing is a genuine swim stroke based upon comparing the moment arm length with the threshold length; calculating, by the processor circuit, at least one of a swimming metric or an energy expenditure of the user in response to determining the user&#39;s arm swing is a swim stroke, wherein the swimming metric comprises at least one of turns, breaths, laps, swim strokes, or swim stroke styles; and outputting, by the processor circuit, the at least one of the swimming metric or the energy expenditure of the user. In some embodiments, the first frame of reference can be a body-fixed frame of reference with respect to the user device. In some embodiments, the method can include solving a least-squares equation. 
     The present disclosure also relates to a method for improving an accuracy of a wearable device while determining a user is swimming. In some embodiments, the method can include: receiving, by a processor circuit of a wearable device, a set of training data of the user; receiving, by the processor circuit, motion data from one or more motion sensors of the wearable device, wherein the one or more motion sensors comprises at least one of an accelerometer or a gyroscope; determining, by the processor circuit, a yaw angle of the user based on the motion data; retrieving, by the processor circuit, a value of likelihood ratio corresponding to the yaw angle; and comparing, by the processor circuit, the value of likelihood ratio with a threshold value; determining, by the processor circuit, the user is swimming based upon comparing the value of likelihood ratio with the threshold value; calculating, by the processor circuit, at least one of a swimming metric or an energy expenditure of the user in response to determining the user is swimming, wherein the swimming metric comprises at least one of turns, breaths, laps, swim strokes, or swim stroke styles; and outputting, by the processor circuit, the at least one of the swimming metric or the energy expenditure of the user. 
     The present disclosure also relates to a method for improving an accuracy of a wearable device while classifying a user&#39;s swim stroke style. In some embodiments, the method can include: receiving, by a processor circuit of a wearable device, motion data from one or more motion sensors of the wearable device, wherein the one or more motion sensors comprises at least one of an accelerometer or a gyroscope; calculating, by the processor circuit, a fundamental period based on the received motion data; determining, by the processor circuit, rotational data of the wearable device, wherein the rotational data is expressed in a frame of reference; extracting, by the processor circuit, one or more features from the rotational data; determining, by the processor circuit, the user&#39;s swim stroke style based on the one or more features; and outputting, by the processor circuit, the determined swim stroke style. In some embodiments, the frame of reference can be a body-fixed frame of reference with respect to the wearable device. In some embodiments, the frame of reference can be an inertial frame of reference. 
     In some embodiments, the one or more features comprise at least one of: a mean crown orientation of the wearable device, a correlation of user&#39;s arm and wrist rotation, or a contribution of rotation about a crown of the wearable device to a total angular velocity. In some embodiments, the one or more features comprise at least one of: a relative arm rotation about a band of the wearable device during a pull phase, a moment arm of the user, a ratio of acceleration z to rotation y, a mean gravity crown weighted by acceleration, a correlation between an orientation of top of a band of the wearable device and rotation around a band of the wearable device, a root mean square (RMS) of a crown rotation, a minimum rotation around a crown of the wearable device, a maximum rotation around a band of the wearable device, or a maximum rotation x over y. 
     The present disclosure also relates to a method for improving an accuracy of a wearable device while determining phases of a user&#39;s swim stroke. In some embodiments, the method can include: receiving, by a processor circuit of a wearable device, motion data from one or more motion sensors of the wearable device, wherein the one or more motion sensors comprises at least one of an accelerometer or a gyroscope; determining, by the processor circuit using the motion data, a first set of rotational data of the wearable device, wherein the first set of rotational data is expressed in a first frame of reference; converting, by the processor circuit, the first set of rotational data of the wearable device into a second set of rotational expressed in a second frame of reference; determining, by the processor circuit, a glide phase of a user&#39;s swim stroke based the second set of rotational data; determining, by the processor circuit, a transition phase of the user&#39;s swim stroke based on the second set of rotational data; determining, by the processor circuit, a pull phase and a recovery phase of the user&#39;s swim stroke based on the determined glide phase and transition phase; calculating, by the processor circuit, one or more swimming metric of the user based on the determined glide, transition, pull and recovery phases of the user&#39;s swim stroke, wherein the one or more swimming metrics comprise at least one of turns, breaths, laps, swim strokes, or swim stroke styles; and outputting the calculated one or more swimming metrics of the user. In some embodiments, the first frame of reference can be a body-fixed frame of reference with respect to the wearable device. In some embodiments, the second frame of reference can be an inertial frame of reference. 
     The present disclosure also relates to a method for improving an accuracy of a wearable device while determining a user&#39;s stroke orbit consistency. In some embodiments, the method can include: receiving, by a processor circuit of a wearable device, motion data from one or more motion sensors of the wearable device, wherein the one or more motion sensors comprises at least one of an accelerometer or a gyroscope; determining, by the processor circuit using the motion data, rotational data of the user device, wherein the rotational data is expressed in a frame of reference; determining, by the processor circuit, a first direction along which the rotational data have the least variance in a first past period; determining, by the processor circuit, a second direction along which the rotational data have the least variance in a second past period; determining, by the processor circuit, a difference between the first direction and the second direction; determining, by the processor circuit, a stroke orbit consistency of the user based on the difference between the first direction and the second direction; and outputting, by the processor circuit, the determined stroke orbit consistency. In some embodiments, the frame of reference can be a body-fixed frame of reference with respect to the user device. In some embodiments, the frame of reference can be an inertial frame of reference. 
     In some embodiments, the method can include determining an axis of rotation. In some embodiments, the first past period can be substantially 10 seconds. In some embodiments, the second past period can be substantially 3 minutes. 
     The present disclosure also relates to a method for improving an accuracy of a wearable device while determining a user&#39;s stroke orbit consistency. In some embodiments, the method can include: receiving, by a processor circuit of a wearable device, motion data from one or more motion sensors of the wearable device, wherein the one or more motion sensors comprises at least one of an accelerometer or a gyroscope; determining, by the processor circuit using the motion data, rotational data expressed in a frame of reference; determining, by the processor circuit, a histogram of the user&#39;s stroke orbit using the rotational data; determining, by the processor, a level of entropy based on the histogram; determining, by the processor circuit, a level of orbit consistency of the user based on the determined level of entropy; and outputting, by the processor circuit, the determined level of orbit consistency of the user. In some embodiments, the frame of reference can be a body-fixed frame of reference with respect to the user device. In some embodiments, the frame of reference can be an inertial frame of reference. 
     Other features and advantages will become apparent from the following detailed description and drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Various objects, features, and advantages of the present disclosure can be more fully appreciated with reference to the following detailed description of the present disclosure when considered in connection with the following drawings, in which like reference numerals identify like elements. 
         FIG. 1  illustrates a wearable device (or a “user device”) according to some embodiments of the present disclosure. 
         FIG. 2  illustrates a block diagram of a wearable device according to some embodiments of the present disclosure. 
         FIG. 3  illustrates a companion device according to some embodiments of the present disclosure. 
         FIGS. 4A-4D  illustrate examples of a body-fixed frame of reference according to some embodiments of the present disclosure. 
         FIG. 5  illustrates a set of rotational data of a wearable device in a body-fixed frame of reference according to some embodiments of the present disclosure. 
         FIG. 6  illustrates an example of an inertial frame of reference according to some embodiments of the present disclosure. 
         FIGS. 7A-7D  illustrate examples of an inertial frame of reference according to some embodiments of the present disclosure. 
         FIG. 8  illustrates a set of rotational data of a wearable device in an inertial frame of reference according to some embodiments of the present disclosure. 
         FIG. 9  illustrates a method of determining a direction of gravity according to some embodiments of the present disclosure. 
         FIG. 10  illustrates a method of determining a direction of gravity according to some embodiments of the present disclosure. 
         FIG. 11  illustrates a method of determining a user&#39;s moment arm according to some embodiments of the present disclosure. 
         FIG. 12  illustrates an example of a moment arm length according to some embodiments of the present disclosure. 
         FIG. 13  illustrates motion data of a wearable device in a body-fixed frame of reference according to some embodiments of the present disclosure. 
         FIGS. 14A-14B  illustrates exemplary moment arm calculations according to some embodiments of the present disclosure. 
         FIG. 15  illustrates a method of classifying a user&#39;s types of motions while swimming according to some embodiments of the present disclosure. 
         FIGS. 16A and 16B  illustrate an example of classifying a user&#39;s types of motions according to some embodiments of the present disclosure. 
         FIG. 17  illustrates a method of receiving motion information from one or more sensors of a wearable device according to some embodiments of the present disclosure. 
         FIG. 18  illustrates yaw angles of a user while swimming according to some embodiments of the present disclosure. 
         FIG. 19  illustrates a method of classifying a user&#39;s swim stroke styles while swimming according to some embodiments of the present disclosure. 
         FIG. 20  illustrates an example of classifying a user&#39;s swim stroke style according to some embodiments of the present disclosure. 
         FIG. 21  illustrates an example of classifying a user&#39;s swim stroke style according to some embodiments of the present disclosure. 
         FIG. 22  illustrates an example of classifying a user&#39;s swim stroke style according to some embodiments of the present disclosure. 
         FIG. 23  illustrates an example of classifying a user&#39;s swim stroke style according to some embodiments of the present disclosure. 
         FIG. 24  illustrates an example of classifying a user&#39;s swim stroke style according to some embodiments of the present disclosure. 
         FIG. 25  illustrates an example of classifying a user&#39;s swim stroke style according to some embodiments of the present disclosure. 
         FIG. 26  illustrates an example of classifying a user&#39;s swim stroke style according to some embodiments of the present disclosure. 
         FIG. 27  illustrates an example of classifying a user&#39;s swim stroke style according to some embodiments of the present disclosure. 
         FIG. 28  illustrates an example of classifying a user&#39;s swim stroke style according to some embodiments of the present disclosure. 
         FIGS. 29A-29B  illustrate swim stroke phases of different swim stroke styles according to some embodiments of the present disclosure. 
         FIG. 30  illustrates a method of determining a user&#39;s swim stroke phase according to some embodiments of the present disclosure. 
         FIGS. 31A-31D  illustrate graphs that identify different swim stroke phases according to some embodiments of the present disclosure. 
         FIGS. 32A and 32B  illustrate an example of classifying a user&#39;s types of motions according to some embodiments of the present disclosure. 
         FIG. 33  illustrates a process of determining a user&#39;s stroke orbit consistency during a swimming session according to some embodiments of the present disclosure illustrates wrist angle of a wearable device according to some embodiments of the present disclosure. 
         FIG. 34  illustrates an orbit of a user&#39;s stroke according to some embodiments of the present disclosure. 
         FIG. 35  illustrates orbits of a user&#39;s strokes according to some embodiments of the present disclosure. 
         FIG. 36  illustrates running differences between the direction of axis of rotation of users&#39; short term stroke orbits and the direction of axis of rotation of the users&#39; long term/average stroke orbits at different sampling points according to some embodiments of the present disclosure. 
         FIG. 37  illustrates a process of determining a user&#39;s stroke orbit consistency during a swimming session according to some embodiments of the present disclosure. 
         FIG. 38  illustrates a heat map of a user&#39;s stroke orbits according to some embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     In the following description, numerous specific details are set forth regarding the systems, methods and media of the present disclosure and the environment in which such systems, methods and media may operate, etc., in order to provide a thorough understanding of the present disclosure. It will be apparent to one skilled in the art, however, that the present disclosure may be practiced without such specific details, and that certain features, which are well known in the art, are not described in detail in order to avoid complication of the present disclosure. In addition, it will be understood that the examples provided below are exemplary, and that it is contemplated that there are other systems, methods, and media that are within the scope of the present disclosure. 
     The present disclosure describes a wearable device that may be configured to determine a user&#39;s arm extension during the user&#39;s activities. The wearable device can include one or more motion sensors to collect data about the wearable device&#39;s position and orientation in space and to track changes to the wearable device&#39;s position and orientation over time. Because a user can wear the wearable device, the motion information can provide information about the user&#39;s movements. For example, when a user is swimming, the user&#39;s arms are typically swinging along a particular path and at a particular frequency. If the user wears the wearable device on the user&#39;s wrist, the wearable device may be able to infer that the user is swimming in a certain style by sensing the way the user&#39;s arm moves in a certain path. When the user is swimming, there is a fairly periodic motion of the user&#39;s arm/wrist that can be tracked by the wearable device. 
       FIG. 1  shows an example of a wearable device (or a “user device”)  100  according to some embodiments of the present disclosure. In some embodiments, wearable device  100  may be any suitable wearable device, such as a watch and/or a fitness band configured to be worn around an individual&#39;s wrist. 
       FIG. 2  depicts a block diagram of exemplary components that may be found within wearable device  100  according to some embodiments of the present disclosure. In some embodiments, wearable device  100  can include a main processor  210  (or “application processor”), a motion co-processor  215 , a memory  220 , one or more motion sensors  240 , a display  270 , an interface  280 , and a heart rate sensor  290 . Wearable device  100  may include additional modules, fewer modules, or any other suitable combination of modules that perform any suitable operation or combination of operations. 
     In some embodiments, main processor  210  can include one or more cores and can accommodate one or more threads to run various applications and modules. Software can run on main processor  210  capable of executing computer instructions or computer code. Main processor  210  can also be implemented in hardware using an application specific integrated circuit (ASIC), programmable logic array (PLA), field programmable gate array (FPGA), or any other integrated circuit. 
     In some embodiments, wearable device  100  also includes motion co-processor  215  which may draw less power than the main processor  210 . Whereas the main processor  210  may be configured for general purpose computations and communications, the motion co-processor  215  may be configured to perform a relatively limited set of tasks, such as receiving and processing data from motion sensor  240 , heart rate sensor  290 , and other modules within the wearable device  100 . In many embodiments, the main processor  210  may be powered down at certain times to conserve power, while the motion co-processor  215  remains powered on. Thus, the motion co-processor  215  is sometimes referred to as an “always-on” processor (AOP). Motion co-processor  215  may control when the main processor  210  is powered on or off. 
     Memory  220  can be a non-transitory computer readable medium, flash memory, a magnetic disk drive, an optical drive, a programmable read-only memory (PROM), a read-only memory (ROM), or any other memory or combination of memories. Memory  220  can include one or more modules  230 . 
     Main processor  210  or motion co-processor  215  can be configured to run module  230  stored in memory  220  that is configured to cause main processor  210  or motion co-processor  215  to perform various steps that are discussed throughout the present disclosure, such as, for example, the methods described in connection with  FIG. 4 ,  FIG. 11 , and  FIG. 12 . 
     In some embodiments, wearable device  100  can include one or more motion sensors  240 . For example, motion sensors  240  can include a gyroscope  250  and an accelerometer  260 . In some embodiments, accelerometer  260  may be a three-axis accelerometer that measures linear acceleration in up to three-dimensions (for example, x-axis, y-axis, and z-axis). In some embodiments, gyroscope  250  may be a three-axis gyroscope that measures rotational data, such as rotational movement and/or angular velocity, in up to three-dimension (for example, yaw, pitch, and roll). In some embodiments, accelerometer  260  may be a microelectromechanical system (MEMS) accelerometer, and gyroscope  250  may be an MEMS gyroscope. Main processor  210  or motion co-processor  215  of wearable device  100  may receive motion information from one or more motion sensors  240  to track acceleration, rotation, position, or orientation information of wearable device  100  in six degrees of freedom through three-dimensional space. 
     In some embodiments, wearable device  100  may include other types of sensors in addition to accelerometer  260  and gyroscope  250 . For example, wearable device  100  may include an altimeter or barometer, or other types of location sensors, such as a GPS sensor. Wearable device  100  may also include display  270 . Display  270  may be a screen, such as a crystalline (e.g., sapphire) or glass touchscreen, configured to provide output to the user as well as receive input from the user via touch. For example, display  270  may be configured to display a current heart rate or daily average energy expenditure. Display  270  may receive input from the user to select, for example, which information should be displayed, or whether the user is beginning a physical activity (e.g., starting a session) or ending a physical activity (e.g., ending a session), such as a swimming session, a running session, a weight lifting session, a walking session or a cycling session. In some embodiments, wearable device  100  may present output to the user in other ways, such as by producing sound with a speaker (not shown), and wearable device  100  may receive input from the user in other ways, such as by receiving voice commands via a microphone (not shown). 
     In some embodiments, wearable device  100  may communicate with external devices via interface  280 , including a configuration to present output to a user or receive input from a user. Interface  280  may be a wireless interface. The wireless interface may be a standard Bluetooth (IEEE 802.15) interface, such as Bluetooth v4.0, also known as “Bluetooth low energy.” In other embodiments, the interface may operate according to a cellphone network protocol such as Long Term Evolution (LTE) or a Wi-Fi (IEEE 802.11) protocol. In other embodiments, interface  280  may include wired interfaces, such as a headphone jack or bus connector (e.g., Lightning, Thunderbolt, USB, etc.). 
     Wearable device  100  can measure an individual&#39;s current heart rate from heart rate sensor  290 . Heart rate sensor  290  may also be configured to determine a confidence level indicating a relative likelihood of an accuracy of a given heart rate measurement. In other embodiments, a traditional heart rate monitor may be used and may communicate with wearable device  100  through a near field communication method (e.g., Bluetooth). 
     Wearable device  100  may be configured to communicate with a companion device  300  ( FIG. 3 ), such as a smartphone, as described in more detail herein. In some embodiments, wearable device  100  may be configured to communicate with other external devices, such as a notebook or desktop computer, tablet, headphones, Bluetooth headset, etc. 
     The modules described above are examples, and embodiments of wearable device  100  may include other modules not shown. For example, some embodiments of wearable device  100  may include a rechargeable battery (e.g., a lithium-ion battery), a microphone or a microphone array, one or more cameras, one or more speakers, a watchband, water-resistant casing or coating, etc. In some embodiments, all modules within wearable device  100  can be electrically and/or mechanically coupled together. In some embodiments, main processor  210  can coordinate the communication among each module. 
       FIG. 3  shows an example of a companion device  300  according to some embodiments of the present disclosure. Wearable device  100  may be configured to communicate with companion device  300  via a wired or wireless communication channel (e.g., Bluetooth, Wi-Fi, etc.). In some embodiments, companion device  300  may be a smartphone, tablet computer, or similar portable computing device. Companion device  300  may be carried by the user, stored in the user&#39;s pocket, strapped to the user&#39;s arm with an armband or similar device, placed in a mounting device, or otherwise positioned within communicable range of wearable device  100 . In some embodiments, companion device  300  may include a variety of sensors, such as location and motion sensors (not shown). When companion device  300  is available for communication with wearable device  100 , wearable device  100  may receive additional data from companion device  300  to improve or supplement its calibration or calorimetry processes. For example, in some embodiments, wearable device  100  may not include a GPS sensor as opposed to an alternative embodiment in which wearable device  100  may include a GPS sensor. In the case where wearable device  100  may not include a GPS sensor, a GPS sensor of companion device  300  may collect GPS location information, and wearable device  100  may receive the GPS location information via interface  280  ( FIG. 2 ) from companion device  300 . 
     In another example, wearable device  100  may not include an altimeter or barometer, as opposed to an alternative embodiment in which wearable device  100  may include an altimeter or barometer. In the case where wearable device  100  may not include an altimeter or barometer, an altimeter or barometer of companion device  300  may collect altitude or relative altitude information, and wearable device  100  may receive the altitude or relative altitude information via interface  280  ( FIG. 2 ) from the companion device  300 . 
     In another example, wearable device  100  may receive motion information from companion device  300 . Wearable device  100  may compare the motion information from companion device  300  with motion information from one or more motion sensors  240  of wearable device  100 . Motion information such as data from accelerometer  260  and/or gyroscope  250  may be filtered (e.g. by a high-pass, low-pass, band-pass, or band-stop filter) in order to improve the quality of motion information. For example, a low-pass filter may be used to remove some ambient noise. 
     Wearable device  100  may use sensed and collected motion information to predict a user&#39;s activity. Examples of activities may include, but are not limited to, walking, running, cycling, swimming, weight lifting etc. Wearable device  100  may also be able to predict or otherwise detect when a user is sedentary (e.g., sleeping, sitting, standing still, driving or otherwise controlling a vehicle, etc.) Wearable device  100  may use a variety of motion information, including, in some embodiments, motion information from a companion device. Wearable device  100  may use a variety of heuristics, algorithms, or other techniques to predict the user&#39;s activity. Wearable device  100  may also estimate a confidence level (e.g., percentage likelihood, degree of accuracy, etc.) associated with a particular prediction (e.g., 90% likelihood that the user is swimming) or predictions (e.g., 60% likelihood that the user is swimming and 40% likelihood that the user is performing a non-swimming activity). 
     There are multiple frames of reference that are useful to consider when characterizing a device&#39;s motion, for example, a body-fixed reference frame and an inertial reference frame. Switching between these reference frames can be accomplished by performing a rotation, or a series of rotations. Because most of the data that is being collected by the motion sensors is in the body-fixed reference frame, in order to use the data to count swimming strokes, the data is first transformed from the body-fixed reference frame to the inertial frame. 
       FIG. 4A  illustrates an example of a body-fixed frame of reference  400  according to some embodiments of the present disclosure. In  FIG. 4A , the rotational axes of body-fixed frame of reference  400  are with respect to wearable device  100 . For example, the z-axis is perpendicular to the display surface  160  of wearable device  100 . The x-axis and the y-axis can be chosen relatively arbitrarily as long as the three axes are perpendicular to each other. In  FIG. 4A , the x-axis is parallel with the direction pointed by crown  120  of wearable device  100 , and the y-axis is parallel with the direction of band  140  of wearable device  100  (assuming the direction pointed by crown  120  of wearable device  100  is perpendicular to the direction of band  140  of wearable device  100 ). 
       FIGS. 4B-4D  illustrate examples to express one or more orientations in body-fixed frame of reference  400  according to some embodiments of the present disclosure. In  FIG. 4B , an orientation/direction  410  has an angle (ϕ)  402  with respect to the positive x-axis, an angle (θ)  404  with respect to the positive y-axis, and an angle (ψ)  406  with respect to the positive z-axis. The direction  410  can be expressed in body-fixed frame of reference  400  as [cos(ϕ), cos(θ), cos(ψ)], which is a non-limiting example/format of the first set of three dimensional rotational data. For example, direction  420  in  FIG. 4B  is parallel with and pointing toward the positive x-axis, so the angle (ϕ) between direction  420  and the positive x-axis is 0-degree; the angle (θ) between direction  420  and the positive y-axis is 90-degrees; and the angle (ψ) between direction  420  and the positive z-axis is 90-degrees. Therefore, direction  420  can be expressed as [cos(0), cos(90), cos(90)], which is [1, 0, 0]. As another example, direction  430  in  FIG. 4B  is parallel with and pointing toward the positive z-axis, so the angle (ϕ) between direction  430  and the positive x-axis is 90-degrees; the angle (θ) between direction  430  and the positive y-axis is 90-degrees; and the angle (ψ) between direction  430  and the positive z-axis is 0-degree. Therefore, direction  430  can be expressed as [cos(90), cos(90), cos(0)], which is [0, 0, 1]. As yet another example, direction  440  represents direction of gravity in  FIG. 4B  and is parallel with and pointing toward the negative y-axis, so the angle (ϕ) between direction  440  and the positive x-axis is 90-degrees; the angle (θ) between direction  440  and the positive y-axis is 180-degrees; and the angle (ψ) between direction  440  and the positive z-axis is 90-degrees. Therefore, direction  440  can be expressed as [cos(90), cos(180), cos(90)], which is [0, −1, 0]. 
     In  FIG. 4C , wearable device  100  is held vertically. As discussed earlier, the x-axis is parallel with the direction pointed by crown  120 , the y-axis is parallel with band  140 , and the z-axis is perpendicular to display surface  160 . Direction  450  in  FIG. 4C  represents the direction pointed by crown  120 , so the angle (ϕ) between direction  450  and the positive x-axis is 0-degrees; the angle (θ) between direction  450  and the positive y-axis is 90-degrees; and the angle (ψ) between direction  450  and the positive z-axis is 90-degrees. Therefore, direction  450  can be expressed as [cos(0), cos(90), cos(90)], which is [1, 0, 0], As another example, direction  440  represents direction of gravity in  FIG. 4C  and is parallel with and pointing toward the negative y-axis, so the angle (ϕ) between direction  440  and the positive x-axis is 90-degree; the angle (θ) between direction  440  and the positive y-axis is 180-degrees; and the angle (ψ) between direction  440  and the positive z-axis is 90-degrees. Therefore, direction  440  in  FIG. 4C  can be expressed as [cos(90), cos(180), cos(90)], which is [0, −1, 0], 
     In  FIG. 4D , wearable device  100  is rotated 45-degrees clockwise compared with  FIG. 4C . As discussed earlier, the x-axis is parallel with the direction pointed by crown  120 , the y-axis is parallel with band  140 , and the z-axis is perpendicular to display surface  160 . Direction  450  in  FIG. 4D  represents the direction pointed by crown  120 , so the angle (ϕ) between direction  450  and the positive x-axis is 0-degrees; the angle (θ) between direction  450  and the positive y-axis is 90-degrees; and the angle (ψ) between direction  450  and the positive z-axis is 90-degrees. Therefore, direction  450  can be expressed as [cos(0), cos(90), cos(90)], which is [1, 0, 0], As another example, direction  440  represents the direction of gravity in  FIG. 4D . The angle (ϕ) between direction  440  and the positive x-axis is 45-degrees; the angle (θ) between direction  440  and the positive y-axis is 135-degrees; and the angle (ψ) between direction  440  and the positive z-axis is 90-degrees. Therefore, direction  440  in  FIG. 5D  can be expressed as [cos(45), cos(135), cos(0)], which is [0.707, −0.707, 0]. 
     It is noted that the expression of direction  450  is the same in  FIG. 4C  and  FIG. 4D  even though wearable device  100  has rotated. This is because the body-fixed frame of reference  400  is always fixed with respect to wearable device  100 . As a result, when the position of wearable device  100  changes, the three axes in the body-fixed frame of reference  400 , as well as direction  450 , change too, while the relative position between direction  450  and the three axes remain the same. On the other hand, although the direction of gravity  440  does not change in an “absolute” sense, it does change its position relative to the wearable device  100 , when the wearable device  100  changes position. Therefore, the expression of gravity direction  440  does not stay fixed in the body-fixed frame of reference  400  when wearable device  100  changes position. 
       FIG. 5  illustrates a first set of rotational data of wearable device  100  according to some embodiments of the present disclosure. Specifically,  FIG. 5  illustrates estimation of the gravity in the body-fixed frame of reference  400 . The x-axis shows cos(ϕ) where ϕ is the angle between gravity and the positive x-axis in the body-fixed frame of reference  400 . The y-axis shows cos(θ), where θ is the angle between gravity and the positive y-axis in the body-fixed frame of reference  400 . The z-axis shows cos(ψ), where ψ is the angle between gravity and the positive z-axis in the body-fixed frame of reference  400 . For example, if at a moment wearable device  100  is facing up toward the sky, and display surface is parallel with the ground, then the gravity direction can be expressed as [0, 0, −1]. As another example, if crown is pointed towards the ground, then the gravity direction can be expressed as [1, 0, 0]. Gravity estimation in body-fixed frame of reference can help indicate when wearable device  100  is making a pitch and/or roll movement. For example, as discussed above, when a user&#39;s wrist was in a position such that crown is pointed towards the ground, the gravity direction is [1, 0, 0]. If the user then is rolling his or her wrist up for 90-degree, then display surface of wearable device  100  is facing up toward the sky, and display surface is parallel with the ground, then the gravity direction is expressed as [0, 0, −1]. If the user then is pitching his or her wrist up for 90-degree, then crown of wearable device  100  is facing up toward the sky, and the gravity direction is expressed as [−1, 0, 0]. These examples illustrate that gravity direction in the body-fixed frame of reference  400  can change in response to pitch and/or roll movement. In some embodiments, the gravity estimation in body-fixed frame of reference  400  can be used together with accelerometer  260  to estimate gravity. However, the gravity direction in the body-fixed frame of reference  400  does not change in response to yaw movement. For example, if wearable device  100  is facing up toward the sky, and display surface is parallel with the ground, then the gravity direction is expressed as [0, 0, −1]; then if the user making yaw movement along the horizon plane, the gravity direction remains as [0, 0, −1]. Also, as discussed above, because wearable device  100  is rotating the same as the body-fixed frame of reference  400 , the directions of wearable device  100  and components thereof are fixed. For example, no matter whether crown is pointing up, straight, or down, the crown direction is always expressed in body-fixed frame of reference  400  as [1, 0, 0]. Therefore, in some embodiments, it is more suitable to express the positions of wearable device  100  in a frame of reference that is not body-fixed in order to more readily indicate the movements of wearable device  100  with respect to external references. 
       FIG. 6  illustrates an inertial frame of reference  600  according to some embodiments of the present disclosure. In  FIG. 6 , the z-axis (or the yaw axis) is based on the direction of gravity. The x-axis (or the roll axis) and the y-axis (or the pitch axis) can be chosen relatively arbitrarily as long as the three axes are perpendicular to each other. 
       FIGS. 7A-7D  illustrate an example of an inertial frame of reference  700  according to some embodiments of the present disclosure.  FIG. 7A  depicts inertial frame of reference  700  in a context where a user is swimming. In  FIG. 7A , the user wears wearable device  100 . But the z-axis (or the yaw axis) in the inertial frame of reference is based on the direction of gravity rather than the wearable device itself. Additionally, assuming the user is swimming laps, the x-axis (or the roll axis) is substantially parallel to the direction of the laps, and the y-axis (or the pitch axis) is perpendicular to the other two axes. In some embodiments, the x-axis (or the roll axis) and the y-axis (or the pitch axis) can be chosen relatively arbitrarily as long as the three axes are perpendicular to each other. In  FIG. 7A , the z-axis is also referred to as yaw axis because any yaw movement rotates around the z-axis. Similarly, the x-axis is also referred to as roll axis because any roll movement rotates around the x-axis. And the y-axis is also referred to as pitch axis because any pitch movement rotates around the y-axis. By knowing the difference between the three-axis in the fixed-body frame of reference  400  and the three-axis in the inertial frame of reference  700 , the rotational data expressed in the fixed-body frame of reference  400  can be converted into the rotational data expressed in the inertial frame of reference  700  using techniques appreciated by people skilled in the art such as the one discussed in Sabatini. 
       FIG. 7B  illustrates that wearable device  100  can make rotational movement with respect to inertial frame of reference  700 . In  FIG. 7B , an orientation/direction  710  has an angle (ϕ)  702  with respect to the positive x-axis, an angle (θ)  704  with respect to the positive y-axis, and an angle (ψ)  706  with respect to the positive z-axis. The direction  710  can be expressed in body-fixed frame of reference  700  as [cos(ϕ), cos(θ), cos(ψ)], which is a non-limiting example/format of the second set of rotational data. 
       FIGS. 7C and 7D  illustrate how same orientations in  FIGS. 4C and 4D  can be expressed differently in inertial frame of reference  700 . In  FIG. 7C , wearable device  100  is held vertically, which is the same as  FIG. 4C . As discussed earlier, the z-axis is based on the gravity in inertial frame of reference  700 . In  FIG. 7C , the positive z-axis is chosen as the direct opposite position of gravity, the x-axis is perpendicular to the z-axis and pointing right horizontally, and the y-axis is perpendicular to both x-axis and y-axis and pointing “out” of  FIG. 7C . Direction  450  in  FIG. 7C  represents the direction pointed by crown  120 , so the angle (ϕ) between direction  450  and the positive x-axis is 0-degree; the angle (θ) between direction  450  and the positive y-axis is 90-degree; and the angle (ψ) between direction  450  and the positive z-axis is 90-degree. Therefore, direction  450  can be expressed as [cos(0), cos(90), cos(90)], which is [1, 0, 0]. As another example, direction  440  represents direction of gravity in  FIG. 7C  and is parallel with and pointing toward the negative z-axis, so the angle (ϕ) between direction  440  and the positive x-axis is 90-degree; the angle (θ) between direction  440  and the positive y-axis is 90-degree; and the angle (ψ) between direction  440  and the positive z-axis is 180-degree. Therefore, direction  440  in  FIG. 7C  can be expressed as [cos(90), cos(90), cos(180)], which is [0, 0, −1]. 
     In  FIG. 7D , wearable device  100  is rotated 45-degree clockwise compared with  FIG. 7C . Because the three axes are based on gravity, they can remain the same as  FIG. 7C . Direction  450  in  FIG. 7D  represents the direction pointed by crown  120 , and the angle (ϕ) between direction  450  and the positive x-axis is 45-degree; the angle (θ) between direction  450  and the positive y-axis is 90-degree; and the angle (ψ) between direction  450  and the positive z-axis is 135-degree. Therefore, direction  450  can be expressed as [cos(45), cos(90), cos(135)], which is [0.707, 0, −0.707]. As another example, direction  440  represents direction of gravity in  FIG. 7D . The angle (ϕ) between direction  440  and the positive x-axis is 90-degree; the angle (θ) between direction  440  and the positive y-axis is 90-degree; and the angle (ψ) between direction  440  and the positive z-axis is 180-degree. Therefore, direction  440  in  FIG. 7D  can be expressed as [cos(90), cos(90), cos(180)], which is [0, 0, −1]. 
     It is noted that the expression of gravity direction  440  is the same in  FIG. 7C  and  FIG. 7D  even though wearable device  100  has rotated. This is because the inertial frame of reference  700  is always fixed with respect to gravity. As a result, when position of wearable device  100  changes, the three axes in inertial frame of reference  700  do not move along. On the other hand, the direction  450  does move with respect to the three axes, so the expression of direction  450  can be changed in the inertial frame of reference  400  even though it is fixed in body-fixed frame of reference  400 . 
       FIG. 8  illustrates a first set of rotational data of wearable device  100  according to some embodiments of the present disclosure. Specifically,  FIG. 8  illustrates estimation of crown direction in the inertial frame of reference  700  while a user is swimming laps. The x-axis shows cos(ϕ), where ϕ is the angle between crown direction and the positive x-axis in the inertial frame of reference  700 . The y-axis shows cos(θ), where θ is the angle between crown direction and the positive y-axis in the inertial frame of reference  700 . The z-axis shows cos(ψ), where ψ is the angle between crown direction and the positive z-axis in the inertial frame of reference  700 . For example, if at a moment wearable device  100  is facing up toward the sky, display surface is parallel with the ground, and crown is toward the positive x-axis, then the crown direction can be expressed as [1, 0, 0]; if wearable device  100  is making a yaw movements, and crown is toward the negative x-axis, then the crown direction can be expressed as [−1, 0, 0]. As another example, if crown is pointed towards the ground, then the crown direction can be expressed as [0, 0, 1]. The rotational data in  FIG. 8  are largely divided into two clusters,  802  and  804 , because every time the user makes a turn, the angle ϕ between crown direction and the positive x-axis in the inertial frame of reference  700  changes substantially around 180-degree. Therefore, rotational data expressed in  FIG. 8  can indicate wearable device  100  undergoes a steady-state change in heading when the data are switching from cluster  802  to cluster  804 , or vice versa. 
       FIG. 9  shows a method  900  for determining a direction of gravity according to some embodiments of the present disclosure. Knowing the direction of gravity is important to determine a frame of reference for motion information, such as rotational data, of wearable device  100 . In some embodiments, method  900  can be modified by, for example, having steps combined, divided, rearranged, changed, added, and/or removed. Gravity determination method  900  may begin at step  910 . 
     At step  910 , motion information may be received from the one or more motion sensors  240  on a wearable device (e.g., wearable device  100 ) of a user. In some embodiments, motion information may include three-dimensional rotational information from one or more sensors  240  such as gyroscope  250  and three-dimensional acceleration information from one or more sensors  240  such as accelerometer  260 . 
     At step  920 , the angular velocity of wearable device  100  may be determined with respect to a frame of reference such as a body-fixed frame of reference or an inertial frame of reference. 
     At step  930 , the gravity determination method  900  may determine whether the angular velocity of wearable device  100  determined at step  920  is below a threshold. For example, the threshold may be approximately 0.05 radians per second, 0.2 radians per second, or 0.5 radians per second, etc. If the angular velocity exceeds the threshold (e.g., when the user is doing exercise), the gravity determination method  900  may return to step  910 . In some embodiments, the gravity determination method  900  may pause or wait for a period of time (e.g., 1 second, 5 seconds, 1 minute, etc.) before proceeding at step  910 . 
     If the angular velocity is below the threshold (e.g., when the user is relatively still), the gravity determination method  900  may proceed to step  940 . In some embodiments, at step  930  wearable device  100  also determines if the magnitude of forces acting on wearable device  100  are approximately equal to the normal force of gravity (1G) before proceeding to step  940 . If the magnitude is not approximately the normal magnitude, the gravity determination method  900  may also return to block  910 . Estimating direction of gravity when the angular velocity is below the threshold (e.g., when the user is relatively still) is important because in that way wearable device  100  will not be interfered or confused by acceleration due to other movements. Hypothetically, if wearable device  100  is having a 1 g acceleration along x-axis, then wearable device  100  may have mistaken the direction of gravity. 
     At step  940 , the direction of gravity relative to wearable device  100  may be estimated. For example, in some embodiments, when wearable device  100  is held relatively still, accelerometer  260  within wearable device  100  may provide data about the direction of forces acting on wearable device  100 , which may be attributable primarily to gravity. In some embodiments, gravity determination method  900  may also determine whether the user wearing wearable device  100  is accelerating (e.g., speeding up or slowing down) or traveling at an approximately constant velocity so as to further improve the estimate of the direction of gravity. 
     In some embodiments, gravity determination method  900  may end after outputting the estimated direction of gravity. In other embodiments, the gravity determination method  900  may return to step  910  to refine or otherwise repeat the method of estimating the direction of gravity relative to the wearable device. 
       FIG. 10  shows a method  1000  for determining a direction of gravity according to some embodiments of the present disclosure. In some embodiments, the method  1000  can be modified by, for example, having steps combined, divided, rearranged, changed, added, and/or removed. Gravity determination method  1000  can be used when the user has companion device  300  and may begin at step  1010 . 
     At step  1010 , gravity determination method  1000  may periodically or continuously check for the presence of a companion device (e.g., companion device  300 ). For example, in some embodiments, wearable device  100  may determine whether a connection (e.g., Bluetooth, IEEE 802.11 Wi-Fi, or other wireless or wired communication channel) has been established or may be established with companion device  300 . If the companion device  300  is present, gravity determination method  1000  may proceed to step  1020 . 
     At step  1020 , the direction of gravity relative to companion device  300  may be estimated. In some embodiments, in contrast to the gravity determination method  1000 , it may not be necessary to check whether the angular velocity of companion device  300  is below a threshold because most or all of rotation of the angular velocity of companion device  300  may be orthogonal to the direction of gravity. 
     At step  1030 , the direction of gravity relative to companion device  300  may be outputted. In some embodiments, the direction of gravity relative to companion device  300  may be combined or otherwise compared with the direction of gravity relative to wearable device  100 . In some embodiments, companion device  300  may further determine a rotation rate around the direction of gravity relative to the companion device and output the rotation rate instead of or in addition to the direction of gravity relative to companion device  300 . 
     In some embodiments, gravity determination method  1000  may end after outputting the estimated direction of gravity. In other embodiments, gravity determination method  1000  may return to step  1010  to refine or otherwise repeat the method of estimating the direction of gravity relative to the wearable device. 
     Determining Arm Swing Motion 
       FIG. 11  shows a flow chart illustrating a process  1100  of determining whether a user&#39;s arm swing motion is a genuine swim stroke or an incidental motion according to some embodiments of the present disclosure. In some embodiments, the method includes the steps of receiving motion information from one or more motion sensors  240  (step  1110 ). In some embodiments, the process  1100  can be modified by, for example, having steps combined, divided, rearranged, changed, added, and/or removed. 
     At step  1110 , wearable device  100  receives three dimensional motion information from a motion sensor  240 . At step  1120 , the wearable device  100  determines a first set of three dimensional rotational data of the wearable device  100 . Rotational data can include angular velocity and angular acceleration. 
     Angular velocity can be expressed by Eq. 1 below:
 
ω=[rad/s]  Eq. 1.
 
     Angular acceleration can be represented by Eq. 2 below:
 
α=Δω/Δ t   Eq. 2.
 
     In some embodiments, the rotational data is received from gyroscope  250  and is expressed in a body-fixed frame of reference with respect to wearable device  100 . 
     The motion information can also include acceleration measurements of wearable device  100  in up to three-dimensions. The acceleration measurements can be a combination of the radial and tangential acceleration and can be expressed by Eq. 3 below:
 
α=ω×(ω× r )+(α× r )  Eq.3
 
     r=moment arm 
     In some embodiments, the acceleration measurements are received from accelerometer  260  and are expressed in a body-fixed frame of reference with respect to wearable device  100 . 
     At step  1130 , based on the rotational data received from the gyroscope and the acceleration measurements received from the accelerometer, the moment arm can be computed. In some embodiments, for example as shown in  FIG. 12 , the moment arm  1215 , computed by wearable device  100 , represents the extension of the arm from the shoulder joint  1210 . As shown in  FIG. 12 , the moment arm  1215  is the perpendicular distance between the shoulder joint  1210  and the shoulder joint&#39;s line of force  1220 . The line of force  1220  is tangential to the user&#39;s arm swing around the shoulder joint, and is constantly changing direction. 
     In one embodiment the moment arm is computed by taking the matrix representation of the cross product of a=ω×(ω×r)+(α×r) as shown in Eq. 3. The following is the computation of the cross product of acceleration (a) to find the moment arm, r:
 
 a=WWr  
         (where Wr represents the cross product of (ω×r))+Ur (where Ur represents the cross product of (α×r);
 
 a =( WW+U ) r  
 
We can solve for r by solving the Least-Squares equation for r, for example, by using the Moore Penrose pseudoinverse.
       

     The moment arm can be normalized (N) by taking several samples of accelerometer and gyroscope measurements and finding the average, which can be represented by the equations below:
 
 a   N =( WW+U ) N   r  
 
 r   N =( WW+U ) N   \a   N  
 
     The computed length of the moment arm represents the user&#39;s arm extension, and can be used to determine whether the swimmer&#39;s arm swing motion was incidental or a genuine swimming stroke. For example, a user&#39;s incidental arm swing generally rotates around the user&#39;s elbow joint or wrist, whereas the user&#39;s genuine swim stroke generally rotates around the user&#39;s shoulder. Therefore, an incidental arm swing will have a shorter moment arm length than a genuine swim stroke. As a result, the larger the moment arm length, the more likely the user&#39;s arm swing motion is a genuine swim stroke. 
     At step  1140 , based on the computed moment arm, the wearable device can determine whether the swimmer&#39;s arm swing motion was a true swimming stroke and/or classify the arm swing motion as a specific type of swim stroke. Swim stroke types can include freestyle, butterfly, back stroke and breast stroke. In one embodiment, the wearable device stores training data that associates a moment arm length minimum threshold with a true swim stroke. The wearable device can compare the computed moment arm length with the stored threshold, and if the computed arm length is greater than the stored threshold, then the user&#39;s arm swing motion is determined to be a true stroke. The training data can be customized for a particular swimmer based on gender, age, or swimming level and/or other suitable characteristic. In some embodiments, the set of training data are observed from training sessions of the swimmer. 
     For example, a moment arm of less than 5 cm is very likely not a stroke, and a moment arm greater than 25 cm is very likely a stroke. However, between 5-25 cm, the arm swing is likely a stroke, but different levels of confidence will be associated with each length. 
       FIG. 13  illustrates a first set of rotational data, including acceleration data, of wearable device  100  for a suitable period of time according to some embodiments of the present disclosure, e.g., 60 seconds. Specifically,  FIG. 13  illustrates a first set of rotational data of wearable device  100  worn on a user&#39;s wrist during a swimming session, and the first set of rotational data is expressed in the body-fixed frame of reference as described in connection with  FIGS. 4A-4D . The x-axis represents WW+u and is measured in rad 2 /s 2 , and the y-axis represents acceleration normalized by gravity and is measured in m/s 2 . 
     The time period can be set by a user or the time period can be fixed. In some embodiments, the time period is proportional to a period that the user needs to complete several strokes. The wearable device  100  can dynamically set the time period based on average duration of user&#39;s strokes detected by wearable device  100 . For example, if it takes a user three seconds to finish a stroke, then the time period can be set to nine seconds. In some embodiments, wearable device  100  can do sub-stroke measurements (e.g., 250 ms) or multi-stroke measurements (e.g., 6-9 seconds). A sub-stroke measurement tends to provide a near real-time measurement, but can be a noisy estimate. While a multi-stroke measurement provides an “average” estimate of moment arm. 
     In the embodiment shown in  FIG. 13 , the rotational data, including acceleration data, is measured from two sessions of arm swings: one session of arm swings is rotating around the shoulder joint, as shown by the cluster of dots  1310  that appear at the top of the graph, and the other session of arm swing is rotating around elbow joint, as shown by the cluster of dots  1320  that appear at the bottom of the graph. The slope of the data that is measured from the arm swings around the shoulder joint is steeper than the slope of the data measured from the arm swings around the elbow joint. In this embodiment, the steepness of the slope corresponds to the length of the moment arm. In other words, the steeper the slope, the greater the length of the moment arm. Typically, for a swim stroke, the moment arm length will be greater from the shoulder joint (as represented in  FIG. 13  by the steeper slope of dot cluster  1310 ) than the elbow joint. If the rotation of the arm swing occurs solely around the shoulder, then the moment arm is calculated from the wrist to the shoulder. If the rotation of the arm swing occurs solely around the elbow, then the moment arm is calculated from wrist to elbow. If however, the arm swing motion is a combination of shoulder rotation and wrist rotation, then the combined motion can provide an approximation of the moment arm of that combined motion. 
     In one embodiment, the wearable device  100  stores training data that associates a moment arm length value that is characteristic of each of the different swim stroke types. The wearable device can compare the computed moment arm length with the characteristic moment arm length value to determine the type of swim stroke. The characteristic moment arm length value for each of the different swim stroke types can be customized for a particular swimmer based on gender, age, swimming level and/or other suitable characteristic. In some embodiments, the set of training data are observed from training sessions of the swimmer.  FIG. 14A  shows exemplary moment arm measurements characteristic of breaststroke and  FIG. 14B  shows exemplary moment arm measurements characteristic of freestyle. 
     In some embodiments, the wearable device  100  converts the first set of motion data from the motion sensors, including the rotational data from the gyroscope and the acceleration measurements from the accelerometer, into a second set of motion information. One drawback of the motion information expressed in the body-fixed frame of reference is, however, that the body-fixed frame of reference cannot readily indicate the movement and/or position of the user&#39;s arm/wrist, because the body-fixed frame of reference is with respect to wearable device  100 , and wearable device  100  is changing as well while swimming. 
     To address this issue, wearable device  100  converts the motion data in the body-fixed frame of reference into rotational data in an inertial frame of reference using techniques appreciated by people skilled in the art such as the one discussed in “Kalman-filter-based orientation determination using inertial/magnetic sensors: observability analysis and performance evaluation,” Angelo Maria Sabatini, published Sep. 27, 2011, Sensors 2011, 11, 9182-9206. 
     Motion Determination Using Likelihood Ratios 
     In many motion/fitness experiments that are conducted for trials, a proctor can tag the type of motion being performed by a user and record one or more characteristics associated with the type of motion. As the user changes the type of motion, the proctor can tag the change of the motion type as well. 
     For example, when a user is swimming laps back and forth, a proctor can tag when the user is actually swimming forward and when the user is turning. The proctor can also record one or more characteristics associated with the user&#39;s swimming or turning, such as speed and yaw angle. After a large number of experiments, there will be a significant amount of data detailing swimming behavior versus turning behavior. As discussed in more detail below, these training data can then be used together with the user&#39;s motion information sensed by a wearable device worn by the user to determine the user&#39;s types of motions in real time. 
       FIG. 15  shows a flow chart illustrating a process  1500  of determining whether a user is swimming or turning during a swimming session according to some embodiments of the present disclosure. In some embodiments, the process  1500  can be modified by, for example, having steps combined, divided, rearranged, changed, added, and/or removed. As described in more detail below, in some embodiments, the process  1500  can include five steps. At step  1510 , wearable device  100  receives a set of training data of the user. At step  1520 , based on the set of training data of the user, wearable device  100  determines a plurality of likelihood ratios for a plurality of yaw angles, LR (yaw). At step  1530 , wearable device  100  determines a yaw angle of the user based on motion information received from one or more sensors  240  of wearable device  100 . At step  1540 , wearable device  100  retrieves a value of LR (yaw) that is corresponding to the yaw angle. At step  1550 , wearable device  100  determines whether the user is swimming or turning by comparing the value of LR (yaw) with a threshold. 
     At step  1510 , wearable device  100  receives a set of training data of the user. In some embodiments, the set of training data are observed from training sessions of the user. As discussed above, during these training sessions, a proctor can monitor the user and specify whether the user is swimming or turning. The proctor can also record certain characteristics of the user while swimming. For example, the proctor can record the user&#39;s speed and/or yaw angle. In some embodiments, a proctor is not needed; instead, by analyzing the raw data from the accelerometer and/or gyroscope, it can be determined when the user was swimming and turning. As a result, in some embodiments, the learning data can be analyzed and tagged post session. 
     The yaw angle can indicate the angle between the user&#39;s instantaneous swimming direction and the user&#39;s steady-state swimming direction. For example,  FIG. 18  illustrates yaw angles of a user while swimming according to some embodiments of the present disclosure. In  FIG. 18 , the user is swimming a lap from the south end  1810  to the north end  1820  of a pool. The direction  1830  indicates the steady-state swimming direction of the user. The directions  1840 ,  1850 ,  1860 , and  1870  indicate four scenarios of instantaneous swimming directions of the user. If the user&#39;s instantaneous swimming direction is  1840 , then there is 0 degrees between direction  1840  and direction  1830 , and the yaw angle of the user can be indicated as 0 degrees. If the user&#39;s instantaneous swimming direction is  1850 , then there is 90 degrees clockwise from direction  1830  to direction  1850 , and the yaw angle of the user can be indicated as 90 degrees. If the user&#39;s instantaneous swimming direction is  1860 , then there is 180 degrees clockwise from direction  1830  to direction  1860 , and the yaw angle of the user can be indicated as 180 degrees. If the user&#39;s instantaneous swimming direction is  1870 , then there is 270 degrees clockwise from direction  1830  to direction  1870 , and the yaw angle of the user can be indicated as 270 degrees. Other suitable ways to indicate the yaw angle can also be used. For example, in some embodiments, when the user&#39;s instantaneous swimming direction is  1870 , the yaw angle can be noted as 90 degrees rather than 270 degrees to indicate there is 90 degrees counterclockwise difference from direction  1830  to direction  1870 . 
     In some embodiments, the user&#39;s motion characteristics, such as yaw angle and/or speed, can be directly observed by the proctor during the training sessions. In some embodiments, the user&#39;s motion characteristics are observed by motion sensors  240  of wearable device  100  as described in more detail below. Because the proctor also specifies the user&#39;s motion type (for example, swimming versus turning), after one or more training sessions, one can obtain significant amount of raw data detailing swimming behavior versus turning behavior. In some embodiments, the training session can be three to five minutes. In some embodiments, the training session can be a longer duration such as 10 to 20 minutes. In some embodiments, the training session can any suitable duration. The raw data can indicate the user&#39;s yaw angle at a given moment and corresponding motion type specified by the protector. For example, the raw data can be in a format as {time tag, yaw angle, motion type}. The raw data can also include other suitable information and can be in any other suitable format. In some embodiments, a proctor is not needed; instead, by analyzing the raw data from the accelerometer and/or gyroscope, it can be determined when the user was swimming and turning. As a result, in some embodiments, the learning data can be analyzed and tagged post session. 
     The set of training data can then be statistically determined based on the raw data. In one embodiment, the set of training data includes a first probability distribution of a plurality of yaw angles of the user while the user is turning, P (yaw|turning), a second probability distribution of the plurality of yaw angles of the user while the user is swimming, P (yaw|swimming), and a factor, K, indicating a ratio of a first likelihood indicating the user is turning to a second likelihood indicating the user is swimming. In some embodiments, the set of training data can also include any other suitable information. 
       FIG. 16A  illustrates probability distributions of a plurality of yaw angles of the user while the user is swimming and turning according to some embodiments of the present disclosure. The x-axis is yaw in degrees, and the y-axis is the probability mass functions (PMF) indicating that the user is swimming and the user is turning. In  FIG. 16A , the curve  1610  indicates the second probability distribution of a plurality of yaw angles of the user while the user is swimming, P(yaw|swimming). Also in  FIG. 16A , the curve  1620  indicates the first probability distribution of the plurality of yaw angles of the user while the user is turning, P(yaw|turning). In  FIG. 16A , P(yaw|swimming)&gt;P(yaw|turning) when the yaw angle is less than approximately 75 degrees. This suggests that when the user is swimming, the yaw angles are more likely to be less than around 75 degrees, and when the user is turning, the yaw angles are more likely to be more than around 75 degrees. Also in  FIG. 16A , P(yaw|swimming) has a maximum value at approximately 0 degree, and P (yaw|turning) has a maximum value at approximately 180 degrees. This suggests that when the user is swimming, the yaw angles are most likely around 0 degree, and when the user is turning, the yaw angles are most likely around 180 degrees. 
     In some embodiments, a factor, K, can indicate the ratio of a first likelihood indicating the user is swimming, P(turning) to a second likelihood indicating the user is turning, P(swimming), and can be expressed by Eq. 4.
 
 K=P (turning)/ P (swimming)  Eq. 4.
 
     In some embodiments, K can be estimated based on observation from the user&#39;s training sessions. For example, when the user swims in a 100 m pool, the user may be swimming for 50 seconds, and only be turning for 5 seconds. In this example, at any random time, the user is 10 times more likely to be swimming than turning, and K can be equal to 0.1. 
     Referring back to  FIG. 15 , at step  1520 , from the set of training data including P(yaw|swimming), P(yaw|turning), and K, a plurality of likelihood ratios, LR(yaw) can be computed. In one embodiment, LR(yaw) can be expressed in Eq. 5 below.
 
 LR (yaw)= P (turning|yaw)/ P (swimming|yaw)  Eq. 5.
 
     In Eq. 5, P(swimming|yaw) indicates the probability distribution of the user is swimming at the plurality of yaw angles. Likewise, P(turning|yaw) indicates the probability distribution of the user is turning at the plurality of yaw angles. P(swimming|yaw) and P(turning|yaw) can be further expressed in Eqs. 6 and 7, respectively.
 
 P (swimming|yaw)= P (yaw|swimming)* P (swimming)/ P (yaw)  Eq. 6
 
 P (turning|yaw)= P (yaw|turning)* P (turning)/ P (yaw)  Eq. 7
 
     From Eqs. 4, 5, 6, and 7, LR(yaw) can be further expressed in Eq. 8. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     Eq. 8 shows that LR(yaw) can be determined by K, P(yaw|swimming), and P(yaw|turning), which are included in the set of training data and can be all obtained from the raw data from the training sessions. 
     Alternatively, in some embodiments, LR(yaw) can be expressed in logarithmic scale as shown in Eqs. 9 and 10. 
     
       
         
           
             
               
                 
                   
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     When LR(yaw) is expressed as P(turning|yaw)/P(swimming|yaw) as shown in Eq. 5, if a yaw angle makes the value of LR(yaw) greater than 1, then the user is more likely turning at this yaw angle; and if a yaw angle makes the value LR(yaw) less than 1, then the user is more likely swimming at this yaw angle. 
     Similarly, when LR(yaw) is expressed as log 10(P(turning|yaw)/P(swimming|yaw)) as shown in Eq. 10, if a yaw angle makes the value of LR(yaw) greater than 0, then the user is more likely turning at this yaw angle; and if a yaw angle makes the value LR(yaw) less than 0, then the user is more likely swimming at this yaw angle. 
       FIG. 16B  illustrates the values of LR(yaw) at the plurality of yaw angles when LR(yaw) is expressed in Eq. 10. The x-axis is yaw in degrees and the y-axis is the likelihood ratio. In  FIG. 16B , curve  1630  indicates where LR(yaw) is equal to 0. In  FIG. 16B , curve  1640  suggests that when the yaw angle is greater than approximately 75 degrees, LR(yaw) is generally greater than 0, and it means that the user is more likely turning; and when the yaw angle is less than approximately 75 degrees, LR(yaw) is generally less than 0, and it means that the user is more likely swimming. 
     As discussed above with respect to  FIG. 15 , at step  1510  and  1520 , the likelihood ratios of the user&#39;s motion at the plurality of yaw angles, LR(yaw), can be determined based on the set of training data. In some embodiments, a lookup table of LR(yaw) can be determined to show values of LR(yaw) at each yaw angle. When the user is in a future swimming session, as soon as a yaw angle of the user is received, a corresponding LR(yaw) value can then be retrieved from the lookup table, and a determination can be made regarding whether the user is swimming or turning in real time. The lookup table can always be fine-tuned and/or updated based on data from additional training sessions. 
     With reference to  FIG. 15 , at step  1530 , wearable device  100  can determine a real time yaw angle of the user based on motion information received from one or more sensors  240  of wearable device  100 . Step  1530  is further explained in  FIG. 17 .  FIG. 17  shows a flow chart illustrating a process  1700  of determining yaw angles of a user while swimming according to some embodiments of the present disclosure. In some embodiments, the process  1700  can be modified by, for example, having steps combined, divided, rearranged, changed, added, and/or removed. As described in more detail below, in some embodiments, the process  1700  can include three steps. At step  1710 , wearable device  100  receives motion information from one or more motion sensors  240 . At step  1720 , wearable device  100  determines a first set of rotational data of wearable device  100 . At step  1730 , wearable device  100  converts the first set of rational data into a second set of rotational data, which include yaw angles of the user. 
     At step  1710 , motion information may be received from one or more motion sensors  240  on wearable device  100 . In some embodiments, motion information may include three-dimensional rotational data of wearable device  100  from gyroscope  250 . In some embodiments, motion information may include three-dimensional accelerations of wearable device  100  from accelerometer  260 . 
     At step  1720 , wearable device  100  determines a first set of rotational data of wearable device  100  based on the motion information received from one or more motion sensors  240 . In some embodiments, the rotational data of wearable device  100  include how wearable device  100  rotates, such as angular position, angular velocity, and/or angular acceleration of wearable device  100 , with respect to a frame of reference. In some embodiments, if the rotational data of wearable device  100  is angular acceleration, then angular velocity and/or angular position can be obtained by integrating the angular acceleration over time. Likewise, if the rotational data of wearable device  100  is angular velocity, then angular position can be obtained by integrating the angular velocity over time. In some embodiments, the first set of rotational data is received from gyroscope  250  and is expressed in a body-fixed frame of reference with respect to wearable device  100 . 
     At step  1730 , wearable device  100  converts the first set of rotational data into a second set of rotational data. As described above, rotational data in the body-fixed frame of reference cannot readily indicate whether or not wearable device  100  undergoes movements with respect to external references. To address this issue, wearable device  100  converts the rotational data in the body-fixed frame of reference into rotational data in an inertial frame of reference using techniques appreciated by people skilled in the art such as the one discussed in “Kalman-filter-based orientation determination using inertial/magnetic sensors: observability analysis and performance evaluation,” Angelo Maria Sabatini, published Sep. 27, 2011, Sensors 2011, 11, 9182-9206. 
     Referring back to  FIG. 15  at step  1540 , the yaw angle obtained at step  1530  can be used by wearable device  100  to retrieve a corresponding value of LR(yaw). For example, the value of LR(yaw) can be retrieved from the lookup table of LR(yaw). 
     At step  1550 , based on the retrieved value of LR(yaw), wearable device  100  can determine whether the user is swimming or turning by comparing the retrieved value LR(yaw) with a threshold. Specifically, if LR(yaw) is expressed as in Eq. 5, the threshold can be set at 1: if the retrieved value of LR(yaw) is greater than 1, then the user is more likely swimming; and if the retrieved value LR(yaw) is less than 1, then the user is more likely turning. Similarly, if LR(yaw) is expressed as in Eq. 10, the threshold can be set at 0: if the retrieved value of LR(yaw) is greater than 0, then the user is more likely swimming; and if the retrieved value LR(yaw) is less than 0, then the user is more likely turning. 
     Classifying Swim Strokes 
     In some embodiments, the present disclosure describes a wearable device that may be configured to classify a user&#39;s swim stroke into one of four common styles, including, freestyle, backstroke, breaststroke, and butterfly. 
       FIG. 19  shows a flow chart illustrating a process  1900  for classifying a user&#39;s swim stroke style, according to some embodiments of the present disclosure. In some embodiments, the method can include the steps of: receiving information from a motion sensor and calculating a fundamental period (step  1910 ), determining a set of rotational data of wearable device  100  (step  1920 ), extracting a first set of features from the set of rotational data to perform a first tier analysis to classify backstroke and breaststroke and distinguish these stroke styles from freestyle and butterfly (step  1930 ) and extracting a second set of features from the set of rotational data to perform a second tier analysis to distinguish freestyle from butterfly (step  1940 ). In some embodiments, the process  1900  can be modified by, for example, having steps combined, divided, rearranged, changed, added, and/or removed. 
     At step  1910 , wearable device  100  samples output information from one or more motion sensors  240 . In some embodiments, the information can include any combination of gravity, acceleration, rotation or attitude. Based on the sampled information output from motion sensors  240 , a fundamental period can be calculated. For example, information from the one or more motion sensors  240  can be sampled at 14 Hz. Based on the stroke rate obtained from the stroke counter, wearable device  100  samples motion information for a period equivalent to two strokes. In some embodiments, if the sampled data does not show a sufficiently periodic signal, then the wearable device  100  resamples the motion sensor information until it receives a sufficiently periodic signal. Process  1900  for classifying a user&#39;s stroke can be performed on a per stroke basis, but can be reported to a user after the user completes a lap or some other defined period for reporting the data. 
     At step  1920 , wearable device  100  determines a set of rotational data, including acceleration data, of wearable device  100  in up to three-dimensions based on the information received from one or more motion sensors  240 . In some embodiments, the rotational data of wearable device  100  include how wearable device  100  rotates, such as angular position, angular velocity, and/or angular acceleration of wearable device  100 , with respect to a frame of reference. In some embodiments, if the rotational data of wearable device  100  is angular acceleration, then angular velocity and/or angular position can be obtained by integrating the angular acceleration over time. Likewise, if the rotational data of wearable device  100  is angular velocity, then angular position can be obtained by integrating the angular velocity over time. In some embodiments, the set of rotational data is received from gyroscope  250  and is expressed in a body-fixed frame of reference with respect to wearable device  100 . In some embodiments, the acceleration data is received from accelerometer  260  and is also expressed in a body-fixed frame of reference with respect to wearable device  100 . 
       FIG. 20  shows a series of graphs  2000 ,  2010 ,  2020 ,  2030 , that depict exemplary 3D paths of the wearable device  100 , as worn by a user during a swimming session. Specifically, each graph corresponds to one of the four swim stroke styles (i.e., graph  2000  corresponds to freestyle, graph  2010  corresponds to backstroke, graph  2020  corresponds to breaststroke and graph  2030  corresponds to butterfly) and depicts the 3D path of wearable device  100  for 30 strokes of that stroke style. Each graph includes three axes: an axis that represents the orientation of the face of the wearable device, an axis that represents the orientation of the crown of the wearable device, and an axis that represents the orientation of the band of the wearable device. Each axis ranges from 1, which represents pointing down to the ground, to −1, which represents pointing up towards the sky. As indicated by graphs  2000 ,  2010 ,  2020  and  2030 , both breaststroke (graph  2020 ) and backstroke (graph  2010 ) exhibit unique orbits that make them easy to differentiate from freestyle (graph  2000 ) and butterfly (graph  2030 ). However, freestyle and butterfly exhibit similar 3D paths that make them more difficult to distinguish from each other. Accordingly, in some embodiments of the disclosed subject matter, a two tier analysis can be performed. During the first tier of analysis, as described below in connection with step  1930 , features are extracted from the set of rotational data to identify breaststroke and backstroke, and distinguish these stroke styles from butterfly and freestyle. If the stroke is identified as breaststroke or backstroke, then a second level of analysis does not have to be performed. Otherwise, if breaststroke and backstroke are ruled out, then a second tier analysis can be performed on the set of rotational data, as described below in connection with step  1940 , to identify whether the stroke is freestyle or butterfly. In some embodiments, a second tier analysis can be performed regardless of the results of the first tier analysis. 
     At step  1930 , a first tier analysis can be performed by analyzing certain features from the set of rotational data to identify backstroke and breaststroke and distinguish these stroke styles from butterfly and freestyle. According to some embodiments of the disclosed subject matter, at least three features can be used to identify backstroke and breaststroke and distinguish these stroke styles from butterfly and freestyle. These three features can include (1) mean crown orientation during the fastest part of user&#39;s stroke; (2) correlation of user&#39;s arm and wrist rotation; and (3) how much rotation about the crown contributes to the total angular velocity. These foregoing features are not intended to differentiate freestyle from butterfly. 
     According to some embodiments, as depicted by the graph  2100  in  FIG. 21 , two of the three features of the first tier analysis are graphed for each of the different swim styles. Specifically, the y-axis represents the correlation of the arm and wrist rotation during the fastest part of the stroke, ranging from −1 (negative correlation, where the wrist and arm rotate in different directions), 0 (no correlation) to 1 (positive correlation, where the wrist and arm rotate in the same direction). As shown in the upper left portion of the graph, the backstroke exhibits a positive correlation of the arm and wrist rotations (i.e., the wrist rotates inward, then the arm rotates downward), while the breaststroke exhibits negative correlation of the arm and wrist rotations (i.e., the wrist rotates outward, then the arm rotates downward). Further, the x-axis of graph  2100 , represents the mean crown orientation of the wearable device  100  (which is a proxy for the orientation of a user&#39;s fingertips) during the fastest part of the stroke, ranging from −1, where user&#39;s fingertips (or the crown) faces up towards the sky, to 1, where the user&#39;s fingertips (or crown) is oriented downwards, facing the earth. As depicted in graph  2100 , during the fastest part of the backstroke  2110  (i.e., during the recovery phase when the hand is out of the water and making an arc towards the sky), the user&#39;s fingertips face upwards towards the sky, while breaststroke  2140 , the user&#39;s fingertips face downwards towards the earth when the hand is moving fastest. 
     Also shown in graph  2100 , in  FIG. 21 , the butterfly  2130  and freestyle  2120  strokes exhibit similar correlation between arm and wrist rotation (i.e., both exhibit a positive correlation of the arm and wrist rotations), as well as similar crown orientations during the fastest part of the strokes (i.e., fingertips facing downwards towards the earth), making these strokes difficult to distinguish from each other based on these two features. In contrast, the backstroke is easily distinguishable based on (1) a negative arm-wrist correlation and (2) the mean crown orientation facing up towards the sky during the fastest part of the stroke. The breaststroke is also easily distinguishable based on (1) a positive arm-wrist correlation and (2) the mean crown orientation facing downwards during the fastest part of the stroke. 
     The next series of graphs shown in  FIG. 22 , focus on the mean crown orientation feature, discussed above in connection with  FIG. 21 . Specifically, the series of graphs shown in  FIG. 22 , depict the mean crown orientation with respect to gravity, weighted by the faster parts of the stroke. This feature is a proxy for the direction that the user&#39;s fingertips are pointing when the user&#39;s arm is moving the fastest. The mean crown orientation feature can be expressed by the following equation:
 
mean_ gx _ w 1=sum(gravity_ x *total_user_acceleration)/sum(total_user_acceleration)   Eq. 11.
 
     The series of graphs depicted in  FIG. 22 , correspond to the crown orientation for each of the different swim stroke styles (i.e., graph  2200  corresponds to freestyle, graph  2210  corresponds to breaststroke, graph  2220  corresponds to backstroke and graph  2230  corresponds to butterfly). The y-axis of each of the graphs represents crown orientation z, where −1=crown facing up towards the sky, 0=the crown facing parallel to the horizon, and 1=crown facing down towards the earth. The x-axis of each of the graphs represents time in seconds. 
     The crown orientation feature can be used to identify backstroke and breaststroke and distinguish these stroke styles from the other swim stroke styles. As shown in graph  2220 , the user&#39;s fingertips in backstroke trace an arc from the horizon to the sky and back to horizon, when the user&#39;s arm is out of the water and moving fast. Unlike the other swim stroke styles, the orientation of the crown in backstroke is above the horizon for half the stroke and faces the sky during points of high acceleration. 
     For breaststroke, as depicted in graph  2210 , the crown goes above the horizon during the quiescent portions of the stroke and faces downward during the fastest parts of the stroke. For both freestyle (graph  2200 ) and butterfly (graph  2230 ), the crown rarely goes above the horizon and faces parallel to the horizon during the fastest parts of these strokes, making these strokes hard to distinguish from each other based on this feature. 
     According to some embodiments of the disclosed subject matter,  FIG. 23  is another method for graphically depicting the crown orientation feature for the different swim stroke styles. In this embodiment, the x-axis of graph  2300  represents the crown orientation during the fastest part of the stroke (−1=the crown faces up towards the sky, 0=the crown faces parallel to the horizon, 1 the crown faces down towards the earth), and the y-axis represents the number of strokes taken over a large population of swimmers of varying skill. Specifically, graph  2300  shows the crown orientation distribution for the different stroke styles: backstroke (depicted by curve  2310  made up of triangles), butterfly (depicted by curve  2320  made up of circles), freestyle (depicted by curve  2330  made up of squares) and breaststroke (depicted by curve  2340  made up of stars). As shown in graph  2300 , using the crown orientation feature, backstroke is most easily distinguishable from the other stroke styles. 
     The next series of graphs shown in  FIG. 24 , focus on the wrist-arm correlation feature, as discussed above in connection with  FIG. 21 . Each graph corresponds to a different swim stroke style (i.e., graph  2400  corresponds to butterfly, graph  2410  corresponds to backstroke, graph  2420  corresponds to breaststroke and graph  2430  corresponds to freestyle). Specifically, the series of graphs shown in  FIG. 24 , depict how the position of the top of the band (gravity_y) rotates around the axis perpendicular to the forearm (rotation_y) in relation to the rotation of the forearm. This feature can be expressed by the following equation:
 
gray_rotation_norm_ cfpy _ w 1=weighted Pearson correlation between gravity_ y  and rotation_ y   Eq. 12.
 
     As shown below, the correlation can be weighted by the total angular velocity at each point to discount clusters that occur during the slower portions of the stroke: 
     Weighted mean: 
     
       
         
           
             
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     The series of graphs in  FIG. 24  include an x-axis, which represents the number of samples at a sampling rate of 14 Hz and the y-axis represents motion in a clockwise motion (2.5) or a counter clockwise motion (−2.5). The series of graphs shown in  FIG. 24  are normalized so that they are on the same scale. Specifically, each signal is divided by its standard deviation to normalize their respective magnitude for visualization purposes. Each graph shows two curves: one curve, indicated by a dashed line, represents wrist rotation (i.e., orientation of the top of the band (gravity_y) with rotation around the axis perpendicular to the forearm) and another curve, indicated by a solid line, represents the forearm rotation (rotation_y). 
     Analyzing the wrist-forearm correlation for each of the swim stroke styles, shows a positive wrist-forearm correlation for all the swim stroke styles, except for the breaststroke. The breaststroke exhibits a negative wrist-forearm correlation. Specifically, for the breaststroke (graph  2420 ), the wrist rotates outward, then the arm rotates downward. For all the other strokes, as shown by graphs  2400  (butterfly),  2410  (backstroke) and  2430  (freestyle), the wrist rotates inward, then the arm rotates downward (i.e., positive correlation). Accordingly, this wrist-forearm correlation feature can be used to identify the breaststroke and differentiate it from the other stroke styles. 
     Another way to graphically depict the correlation of arm and wrist rotation feature is shown by graph  2500  in  FIG. 25 . The x-axis represents the correlation of the arm and wrist rotations, where −1 indicates a negative correlation, 0 indicates no correlation and −1 indicates a positive correlation. The y-axis represent the number of strokes from a large population of swimmers of varying ability. Specifically, graph  2500  depicts the distribution of the correlation of the arm and wrist rotations for the different stroke styles: breaststroke (depicted by curve  2510  made up of stars), freestyle (depicted by curve  2520  made up of squares), backstroke (depicted by curve  2530  made up of triangles) and butterfly (depicted by curve  2540  made up of circles). As shown in graph  2500 , using the correlation of the arm and wrist rotation feature, it is easy to distinguish the breaststroke from the other stroke styles. 
     The series of graphs shown in  FIG. 26  focus on a third feature that can be used in the first tier analysis, according to some embodiments of the disclosed subject matter, to identify and separate backstroke and breaststroke from freestyle and butterfly. Specifically, this feature analyzes how much the rotation about the crown contributes to the total angular velocity (and the sign). 
     The series of graphs shown in  FIG. 26  include a y-axis, which represents normalized angular velocity about the crown and an x-axis which represents the number of samples, at a sampling rate of 14 Hz. The graphs for freestyle ( 2600 ) and butterfly ( 2620 ) show a negative rotational mean for Equation 3, which captures fast inward rotation during freestyle and butterfly when the user&#39;s arm is out of the water. The graphs for breaststroke ( 2610 ) and backstroke ( 2630 ), on the other hand, show a positive rotational mean. 
     Another way to graphically depict the relative angular velocity about the crown feature is shown by graph  2700  in  FIG. 27 . The x-axis represents the relative angular velocity about the crown. The y-axis represents the number of strokes from a large population of swimmers with varying skill levels. The graph depicts the distribution for the relative angular velocity about the crown for the different stroke styles. As shown in graph  2700 , using the relative angular velocity about the crown feature, it is easy to separate backstroke (depicted by curve  2710  made up of triangles) and breaststroke (depicted by curve  2720  made up of stars) from freestyle (depicted by curve  2730  made up of square) and butterfly (depicted by curve  2740  made up of circles). 
     The three features detailed above for the first tier analysis may be used in a three-way logistic regression and weighted by their usefulness in classifying a swim stroke style. It is understood that the present disclosure is not limited to a three-way logistic regression and any classifier could be used here, e.g., linear discriminant analysis (LDA), support vector machine (SVM), Neural Networks, etc., to yield similar results. In some embodiments, the arm-wrist correlation feature and the mean crown orientation feature are assigned greater weight than the rotation about the crown feature. It is understood that the three features discussed above are exemplary, and other suitable features may be used as well. 
     At step  1940 , after a first tier analysis is performed on the set of rotational data, a second tier analysis can be performed and certain features from the set of rotational data can be examined to distinguish freestyle from butterfly. In some embodiments, nine features can be used during the second tier analysis to distinguish between butterfly and freestyle. 
     A first feature that can be used is relative arm rotation about the band during the pull phase, which can be expressed by the following equation:
 
RMS (rotation  y  during pull phase)/RMS (rotation  y  during entire stroke), where RMS is root mean square  Eq. 13.
 
     The ratio for the relative arm rotation features tends to be higher for butterfly, because butterfly, in comparison to freestyle, tends to have more (stronger) rotation around the band of wearable device  100  during the pull phase, but similar or less rotation around the band during the recovery phase. During the recovery phase of butterfly, the palms tend to stay more parallel to the horizon than during freestyle which results in less rotation about the band during recovery. Since the hands are more parallel during recovery in butterfly, the rotation tends to be around the face (less rotation around the band). For freestyle, the hands are less parallel so there is more rotation around the band. 
     A second feature that can be used is the moment arm feature range(uxz)/range(wy), where:
 
 uxz =sqrt(sum(user_ x 2+user_ z 2), wy =abs(rotation_ y ),range( x )=max( x )−min( x )   Eq. 14.
 
     The moment arm feature captures the longer moment arm (i.e., arms outstretched) during butterfly, in comparison to freestyle. This feature compares rotation around the band (i.e., axis y) to the linear acceleration in the plane perpendicular to the band. The longer the moment arm, the more linear acceleration relative to rotation there will be. 
     Graph  2800  depicted in  FIG. 28 , graphs the first and second feature discussed above. Specifically, graph  2800  includes an x-axis, which represents the moment arm feature and a y-axis, which represents relative arm rotation magnitude during the pull phase. As shown by graph  1500 , these two features are important in distinguishing butterfly from freestyle. 
     A third feature that can be used to distinguish butterfly ( 2810 ) from freestyle ( 2820 ) is the ratio of acceleration z to rotation y. This is another version of moment arm and can be expressed by
 
 uz/wy , where  uz =sum(abs(rotation_ y )), uz +sum(abs(user_ z ))  Eq. 15.
 
     A fourth feature that can be used to distinguish butterfly from freestyle is mean gravity crown weighted by acceleration, similar to the feature used during the first tier analysis, discussed above in connection with  FIGS. 21-23 . This feature measures the orientation of the crown (which is a proxy for the orientation of user&#39;s fingertips during the stroke). It is weighted by the faster parts of the stroke to give more weight to the recovery phase of the stroke. In butterfly, the crown orientation with respect to gravity is close to zero, which captures that the user&#39;s hands stay more parallel to the horizon during butterfly, in comparison to freestyle. 
     A fifth feature that can be used to distinguish butterfly from freestyle is the correlation between gravity_y (top of band orientation) and rotation_y (rotation around the band) and can be measured by the equation: 
     
       
         
           
             
               
                 
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     Specifically, this feature measures how the wrist and arm rotate together during the stroke. The wrist and arm correlation is lower for butterfly than freestyle, indicating that there are more times during the butterfly stroke where the arm is rotating, but the wrist is not. This feature also captures that the hands stay more parallel to the horizon during butterfly (i.e., arms swing around with less wrist rotation), in comparison to freestyle. 
     A sixth feature that can be used to distinguish butterfly from freestyle is RMS of crown rotation, which can be expressed by the equation:
 
RMS(rotation_ x )  Eq. 17.
 
     This feature captures the stronger rotational energy exhibited by butterfly, in comparison to freestyle. 
     A seventh feature that can be used to distinguish butterfly from freestyle is minimum rotation around the crown, which can be expressed by the equation:
 
min(rotation_ x )  Eq. 18.
 
     This feature also captures the stronger rotational energy exhibited by butterfly, in comparison to freestyle. 
     An eighth feature that can be used to distinguish butterfly from freestyle is maximum rotation around the band, which can be expressed by the equation:
 
max(rotation_ y )  Eq. 19.
 
     This feature also captures the stronger rotational energy exhibited by butterfly, in comparison to freestyle. 
     A ninth feature that can be used to distinguish butterfly from freestyle is maximum rotation x over y, which can be expressed by the equation:
 
max(abs(rotation_ x )/max(abs(rotation_ y ))  Eq. 20.
 
     This feature also captures the stronger rotational energy exhibited by butterfly, in comparison to freestyle. 
     These nine features can be used together in a two-way logistic regression to distinguish butterfly from freestyle and can be weighted, based on their usefulness in distinguishing butterfly from freestyle. It is understood that most classifiers (SVM, LDA, etc.) will perform similarly with this same feature set. It is further understood that the nine features discussed above are exemplary, and other suitable features may be used as well. In some embodiments, the nine features of the second tier analysis, have the following order of usefulness, ranked from greatest to least: 
                                 Rank   Feature                  1   Relative arm rotation during the pull phase       2   Range ration of ZX acceleration to rotation y       3   Ratio of acceleration z to rotation y       4   Max. rotation around band       5   Max. rotation X over Y       6   Mean gravity crown weighted by acceleration       7   Correlation between gravity_y (top of band orientation) compared           to rotation_y (rotation around band).       8   RMS of crown rotation       9   Min. rotation around crown                    
Determining Swim Stroke Phase
 
     The present disclosure describes a wearable device that may be configured to determine a user&#39;s swim stroke phase. As shown in  FIGS. 29A-29B  a swim stroke (e.g., butterfly  2925 , freestyle  2930 , backstroke  2935  and breaststroke  2940 ) can be broken down into four phases: glide  2905 , pull  2910 , transition  2915  and recovery  2920 . Each phase exhibits certain characteristics unique to that phase. For example, glide phase  2905 —when the user&#39;s arms are stretched out in front of him in the direction of travel—is typically the most quiescent portion of the stroke. This phase exhibits the least amount of user acceleration and most stable wrist orientation compared to the other three phases of the stroke. The next phase (i.e., pull phase  2910 ) occurs when the user&#39;s hand is underwater and propels the swimmer forward. This phase shows increased acceleration from glide phase  2905  and a change in orientation of the swimmer&#39;s fingertips. For butterfly, freestyle, and backstroke the fingertips tend to point down through this phase. For backstroke, the fingertips will be more parallel to the horizon during the pull phase. The third phase shown in  FIGS. 29A-29B  is transition phase  2915 , the phase between pull phase  2910  and recovery phase  2920 . In transition phase  2915 , the orientation of the swimmer&#39;s fingertips is opposite to the direction of travel and will exhibit the maximum angle between direction of travel and current orientation of the user&#39;s fingertips. This phase commonly has the shortest duration. Finally, recovery phase  2920 , when the swimmer brings his hand back around to the direction of travel, will usually exhibit the most acceleration. For butterfly, freestyle and backstroke the hand is out of the water during the recovery phase. For breaststroke the hand remains in the water. The recovery phase will usually exhibit the most acceleration across all stroke styles, but the difference will be less pronounced for breaststroke. It is understood that the strokes provided above are exemplary, and that it is contemplated that other strokes can be broken down into similar phases. 
       FIG. 30  is a flow chart illustrating a process  3000  for determining a user&#39;s swim stroke phase, according to some embodiments of the present disclosure. In some embodiments, the method can includes the steps of: receiving information from a motion sensor (step  3010 ), determining a first set of rotational data, including acceleration data, of wearable device  100  (step  3020 ), converting the first set of rotational data into a second set of rotational data (step  3030 ), determine certain phases based on the second set of data (steps  3040 ,  3050 ) and analyze phase characteristics (step  3060 ). In some embodiments, the process  3000  can be modified by, for example, having steps combined, divided, rearranged, changed, added, and/or removed. 
     At step  3010 , wearable device  100  receives information from one or more motion sensors  340 . In some embodiments, the information can include any combination of gravity, acceleration, rotation or attitude. Based on the information output from motion sensors  240 , a fundamental period can be calculated. If it is determined that the user is not swimming, in some embodiments, the wearable device  100  will not determine the stroke phase. 
     The information output from one or more motion sensors  240  can be filtered using a low pass filter with a cutoff frequency based on a time constant that is proportional to a period slightly greater than the period that the user needs to complete a stroke. 
     The time period can be set by a user or the time period can be fixed. In some embodiments, the time period is proportional to a period greater than the period that an average user needs to complete a single stroke. In some embodiments, the wearable device  100  can dynamically set the time period based on average duration of user&#39;s strokes detected by wearable device  100 . For example, if it takes a user three seconds to finish a stroke, then the time period can be set to six seconds. 
     At step  3020 , wearable device  100  determines a first set of rotational data, including acceleration data, of wearable device  100  in up to three-dimensions based on the information received from one or more motion sensors  240 . In some embodiments, the rotational data of wearable device  100  include how wearable device  100  rotates, such as angular position, angular velocity, and/or angular acceleration of wearable device  100 , with respect to a frame of reference. In some embodiments, if the rotational data of wearable device  100  is angular acceleration, then angular velocity and/or angular position can be obtained by integrating the angular acceleration over time. Likewise, if the rotational data of wearable device  100  is angular velocity, then angular position can be obtained by integrating the angular velocity over time. In some embodiments, the first set of rotational data is received from gyroscope  250  and is expressed in a body-fixed frame of reference with respect to wearable device  100 . In some embodiments, acceleration data is received from accelerometer  260  and is also expressed in a body-fixed frame of reference with respect to wearable device  100 . 
     At step  3030 , wearable device  100  converts the first set of rotational data, including acceleration data, into a second set of rotational data. As described above, the rotational data in the body-fixed frame of reference cannot readily indicate whether or not wearable device  100  undergoes movements with respect to external references. To address this issue, wearable device  100  converts the rotational data, including acceleration data, in the body-fixed frame of reference into rotational data in an inertial frame of reference using techniques appreciated by people skilled in the art such as the one discussed in “Kalman-filter-based orientation determination using inertial/magnetic sensors: observability analysis and performance evaluation,” Angelo Maria Sabatini, published Sep. 27, 2011, Sensors 2011, 11, 9182-9206. 
       FIGS. 31A-31D  illustrate rotational data, including acceleration data, of wearable device  100  in the inertial frame of reference over a period of time according to some embodiments of the present disclosure. Specifically,  FIGS. 31A-31D  illustrate a set of rotational data, including acceleration data, for wearable device  100  worn on a swimmer&#39;s wrist during a swimming session that has been converted from a body fixed from of reference to an inertial frame of reference. The x-axis represents the time period of the signal received from the one or more motions sensors  240  and is measured in ( 1/100ths of a second) and the y-axis represents acceleration normalized by gravity and is measured in m/s 2 . User acceleration is represented by curved line  3110  and the yaw angle is represented by curved line  3120 . The yaw angle corresponds to the crown orientation of wearable device  100  (i.e. the direction of the user&#39;s fingertips). 
     In some embodiments, the pitch angle, represented by curved line  3145  (shown in yellow), can also be used to determine the different phases. For example, the pitch angle will show a transition from near 0 (glide) to an angle greater than 0 (pull) and then back to zero (recovery). For example, it can be inferred that the hand is opposite by tracking states when pitch is close to zero along with acceleration:
         State #1 (glide): Pitch is near zero and lowest acceleration   State #2 (pull): Pitch transitions from near zero to non-zero back to near zero=   State #3 (transition): Pitch is near zero again   State #4 (recovery): Pitch maybe non-zero or zero here (depending on the stroke type and the user), but acceleration should generally be higher than other 3 phases.       

     Each of  FIGS. 31A-31D  highlights a different phase of a user&#39;s swim stroke based on the rotational data. At step  3040 , according to some embodiments, the glide phase of the swim stroke can be determined by finding the minimum L2 norm of user&#39;s acceleration, over one stroke, as shown in  FIG. 31A . The lowest point along the acceleration curve  3110 , which corresponds to the least amount of acceleration, is indicated by  3130  and represents the midpoint of the glide phase. The beginning of the glide phase can be defined as 10% of the maximum acceleration before the midpoint, and the end of the glide phase can be defined as 10% of the maximum acceleration after the midpoint (e.g., the length of the acceleration curve  3110  between points A and B). Once the minimum acceleration is determined, the reference yaw angle  3140  (i.e., when the yaw angle is 0°) is determined relative to the minimum acceleration point. The reference yaw angle  3140  is the point along the yaw angle curve  3120  directly beneath the lowest acceleration point. 
     In another embodiment, the duration of the glide is calculated based on the portion of the acceleration curve within 10 degrees of the yaw reference angle. 
     At step  3040 , the transition phase is determined based on the maximum yaw angle  3150 , as shown in  FIG. 31B , in relation to the reference yaw angle  3140 . The duration of the transition period (i.e., the portions of the curves between points C and D) is within 10 degrees of the maximum yaw angle. The maximum yaw angle  3150  represents the orientation of the swimmer&#39;s fingertips when they are most opposite to the direction of travel. In other words, the point along the curve that shows the maximum angle between the direction of travel and current orientation of the swimmer&#39;s finger tips. 
     Once the glide and transition phases of the swim stroke are identified, then the recovery and pull phases can be determined based on the start and end of the glide and transition phases (step  3050 ). For example, the pull phase, as shown in  FIG. 31C  between points B and C and B′ and C′, is simply the portions of the acceleration curve  3110  and the yaw angle curve  3120  between the end of the glide phase and the start of the transition. And the recovery phase, as shown in  FIG. 31D  between points D and E and D′ and E′, is the portions of the acceleration curve  3110  and the yaw angle curve  3120  between the end of the transition phase and the start of the new glide phase (i.e., the old glide phase plus one period). The recovery period usually shows the greatest acceleration. 
     At step  3060 , once the different phases for a swim stroke are identified, the characteristics of the individual phases can be identified and analyzed. In some embodiments, characteristics of a particular phase that differ among stroke types can be used to classify the stroke. For example, a longer arm sweep during the recovery phase is typically associated with the butterfly stroke, in comparison to the freestyle stroke. Therefore the measured arm sweep during the recovery phase can be used to distinguish between the butterfly stroke and the freestyle stroke. In another example, a longer transition phase is typically associated with the freestyle stroke, in comparison to the butterfly stroke, and thus, can be used to identify the freestyle stroke. In another example butterfly can be differentiated from freestyle based on rotational energy about the y-axis during the pull phases relative to all the rotational y-axis energy over all the phases. This can be calculated by the following formula:
 
Relative Pull Rotation  Y =RMS (rotation- y  during pull)/RMS (rotation- y  over all phases)
 
     RMS: root-mean-square 
     The ratio tends to be higher for butterfly compared with freestyle. Butterfly tends to have more (stronger) rotation around the band during the pull phase, but similar or less rotation around the band during the recovery (phase as the arms tend to be more parallel to the horizon throughout the recovery) than freestyle. These are just a few examples and it is understood that other distinguishing phase characteristics can be used to classify a swim stroke. 
       FIG. 32A  graphs the acceleration and yaw data for the four phases of a butterfly stroke and  FIG. 32B  graphs the four phases of a freestyle stroke. The x-axis represents the time period of the signal received from the one or more motions sensors  240  and is measured in seconds, and the y-axis represents acceleration normalized by gravity and is measured in m/s 2 . User acceleration data is represented by the gray shaded portions of the graph and the yaw angle data is represented by the dark curved line. 
     In both  FIGS. 32A and 32B , the glide, pull, transition, and recovery phases are labeled. Comparing the phases of the butterfly stroke shown in  FIG. 32A  with like phases of the freestyle stroke shown in  FIG. 32B , the following differences between like phases are apparent: 
     
       
         
           
               
               
               
             
               
                   
               
               
                   
                 Butterfly stroke (as shown in 
                 Freestyle stroke (as shown in 
               
               
                 Phase 
                 FIG. 32A) 
                 FIG. 32B) 
               
               
                   
               
             
            
               
                 Transition phase 
                 Less dwell (i.e., shorter duration - 
                 More dwell (i.e., longer duration - 
               
               
                   
                 the yaw angle has a sharper peak 
                 the yaw angle tends to stay close to 
               
               
                   
                 and does not stay near the 
                 the maximum yaw angle for 
               
               
                   
                 maximum for very long). 
                 longer). 
               
               
                 Recovery phase 
                 Faster arm sweep 
                 Slower arm sweep 
               
               
                 Glide phase 
                 Swimmer&#39;s arm is less quiescent 
                 Swimmer&#39;s arm is more quiescent 
               
               
                   
                 (i.e., shows more acceleration and 
                 (i.e., shows less acceleration and 
               
               
                   
                 change in orientation) 
                 change in orientation) 
               
               
                   
               
            
           
         
       
     
     The table shown above illustrates some example differences between like phases of the freestyle and butterfly strokes. Those skilled in the art will appreciate that other differences between like phases of the freestyle and butterfly strokes exist and can be used to distinguish the two strokes. 
     In another application of the subject invention, determining the particular phase can help suppress false positives during turn detection/lap counting. For example, only the yaw angle during the glide phase can be considered for the purpose of detecting a turn. This would ensure that the angles considered for turn detection are when the hand is mostly facing in the direction of travel and therefore help to reduce the effects of any yaw change due to intra-stroke dynamics. In other words, if the yaw angle is tracked over the entire stroke, then it will be between 0 and 180 degrees from the glide to transition phase, which could get confused as a turn unless stroke dynamics are filtered out. However, if yaw is tracked only during the glide phase, then a 180 degree change in yaw during the glide phase between two consecutive strokes is more likely a real turn. 
     In another application, phase determination can help determine true swim strokes. For example, the duration of a user&#39;s stroke phase can be compared to the duration of a model stroke phase to determine whether the user executed an actual stroke. Similarly, other characteristics including acceleration and wrist orientation for a particular phase can be used to compare with like characteristics of a model stroke phase to determine whether the user executed an actual stroke. In another example, a user&#39;s stroke can be examined to determine whether all four phases of a stroke were executed in the correct sequence to determine whether the user executed an actual stroke. 
     The model strokes can be customized for a particular swimmer based on gender, age, or swimming level and/or other suitable characteristic. In some embodiments, the model strokes are observed from training sessions of the swimmer. 
     Determining Orbit Consistency 
     The present disclosure describes several ways to determine consistency of a user&#39;s stroke orbits while the user is swimming. For example,  FIG. 33  shows a flow chart illustrating a process  3300  of determining a user&#39;s stroke orbit consistency during a swimming session according to some embodiments of the present disclosure. In some embodiments, the process  3300  can be modified by, for example, having steps combined, divided, rearranged, changed, added, and/or removed. As described in more details below, in some embodiments, the process  3300  can include five steps. At step  3310 , wearable device  100  receives motion information from one or more motion sensors  240 . At step  3320 , wearable device  100  determines a set of rotational data of wearable device  100 . At step  3330 , wearable device  100  determines a first direction along which the set of rotational data have the least variance in a first past period. At step  3340 , wearable device  100  determines a second direction along which the set of rotational data have the least variance in a second past period. At step  3350 , wearable device  100  determines a difference between the first direction and the second direction to determine consistency of the user&#39;s stroke orbits. 
     At step  3330 , wearable device  100  determines a first direction along which the set of rotational data have the least variance in a first past period. In some embodiments, the first past period can be relatively short. As a non-limiting example, the first past period can be 10 seconds, and step  3330  can be performed every 10 seconds. In some embodiments, the direction along which the set of rotational data have the least variance can be determined using principal component analysis appreciated by people skilled in the art. For example, with reference to  FIG. 34 ,  FIG. 34  shows an orbit  3410  of a user&#39;s stroke in a three dimensional space with three axes x, y, and z. In  FIG. 34 , orbit  3410  has an oval shape and is along the x-y plane. Positions along orbit  3410  have variance along the x-axis and the y-axis, but they do not have any variance along the z-axis because every position of orbit  3410  has a zero component along the z-axis. Using principal component analysis, the third principal component of the orbit  3410  will be the direction  3420 , which is parallel with the z-axis and perpendicular to the x-y meaning. One physical meaning of the third principal component  3420  is that it indicates an axis of rotation of orbit  3410 . In this example, if orbit  3410  is the orbit of the set of rotational data in the first past period, then direction  3420  is the first direction determined at step  3330 . If the first past period is set at 10 seconds, then there will be a new first direction for the orbit of the set of rotational data in every past 10 seconds. In an ideal scenario when a user has a perfect repetition of strokes, the first directions determined every 10 seconds will be the same since the orbits of the set of rotational data will be overlapped over time. In a real swimming session, however, a user is not likely to maintain a perfect repetition of strokes, and the first directions determined in every first past period will be varied. One way to indicate a user&#39;s consistency of stroke movements is to measure deviation between a current first direction and an average first direction over a longer past period, such as, for example, 3 minutes or any suitable period. 
     Referring back to  FIG. 33 , at step  3340 , wearable device  100  determines a second direction along which the set of rotational data have the least variance in a second past period. In some embodiments, the second direction can be determined by the same way as the first direction is determined at step  3330 . As described above, in some embodiments, the second past period is longer than the first past period used at step  3330 . For example, if the first past period is 10 seconds, then the second past period can be 3 minutes in some embodiments. Since 3 minutes are 180 seconds, in every 3 minutes, one second direction and 18 first directions can be determined, and the second direction is the average first directions determined in the past 3 minutes. 
       FIG. 35  illustrates orbits of a user&#39;s strokes according to some embodiments of the present disclosure. In  FIG. 35, 3510  indicates a user&#39;s stroke orbits for a particular swimming session. Unlike orbit  3410  in  FIG. 34 , orbits  3510  are not perfectly repetitive and represent a more realistic stroke movement of a user while swimming. In  FIG. 35 , lines  3520  represent directions of the third principal components of orbits  3510  over a relatively shorter period of time, and dashed line  3530  represents direction of the third principal component of orbits  3510  over a relatively longer period of time. For example, orbits  3510  can be the set of rotational data of a user while swimming over 3 minutes. Then in one embodiment, step  3330  described in  FIG. 33  can be performed every 10 seconds to determine the third principal components of portions of orbit  3510  for every 10 seconds. The results can be the lines  3520 , which are directions along which portions of orbits  3510  have the least variance for every 10 seconds. And step  3340  described in  FIG. 33  can be performed to determine the third principal component of orbits  3510  over the entire 3 minutes. The result can be the dashed line  3530 , which is the direction along which orbits  3510  have the least variance over the entire 3 minutes. If orbits  3510  are perfectly repetitive every 10 seconds, then the lines  3520  would align exactly with the dashed line  3530 . From  FIG. 35 , the deviations between the lines  3520  and the dashed line  3530  provide a visual indication of how orbits  3510  wobble over time, which provides a measure of consistency of the user&#39;s stroke. 
     Referring back to  FIG. 33 , at step  3350 , wearable device  100  determines a difference between the first direction and the second direction. In some embodiments, the second past period is longer than the first past period, and the second direction can be considered as an average of multiple first directions in the past. In those embodiments, the difference obtained at step  3350  indicates how the direction of axis of rotation of a user&#39;s short term stroke orbits deviate from the direction of axis of rotation of the user&#39;s long term/average stroke orbits. In some embodiments, a small magnitude of the difference indicates a high level of orbit consistency of the user during the first past period, and a large magnitude of the difference indicates a low level of orbit consistency of the user during the first past period. A high level of orbit consistency may indicate, among others, the user has higher swimming skill, higher efficiency, and/or less fatigue. A low level of orbit consistency may indicate the opposite. 
       FIG. 36  illustrates running differences between the direction of axis of rotation of users&#39; short term stroke orbits and the direction of axis of rotation of the users&#39; long term/average stroke orbits at different sampling points according to some embodiments of the present disclosure.  FIG. 36  shows data processed by different filters, where  3601  represents extended Kalman filter, and  3602  represents complementary filter. In  FIG. 36 , the x-axis indicates the sampling points, which are sampled at every 0.01 seconds. The y-axis indicates the angle between average axis of rotation and an instantaneous axis of rotation for each orbit of strokes. Although the sampling period in  FIG. 36  is 0.1 seconds, the sampling period can be any other suitable value, such as between 0.002 and 0.1 seconds, in other cases. As discussed above, in some embodiments, the instantaneous axis of rotation can be obtained by determining the third principal component of the user&#39;s stroke orbits of strokes over a relatively short period. In some embodiments, such short period can be enough time to get at least one to two orbits. For example, the short period can be five to ten seconds. In some embodiments, other suitable values can be used. The average axis of rotation can be obtained by determining the third principal component of the user&#39;s stroke orbits of strokes over a relatively long period. In  FIG. 36 , if the angle is 0 degrees, then there is no variation between the average axis of rotation and the instantaneous axis of rotation, which means the consistency level of the user&#39;s stroke orbits is high. The farther the angle is from 0 degrees, the less consistent the user&#39;s strokes. In some embodiments, a low consistency level of the user&#39;s stroke can indicate that the user is of low swimming skills, of low swimming efficiency, being tired, and/or having health related issues. 
     In some embodiments, in addition to or instead of using principal component analysis, a user&#39;s consistency of strokes can be determined using spatial entropy analysis. For example,  FIG. 37  shows a flow chart illustrating a process  3700  of determining a user&#39;s stroke orbit consistency during a swimming session according to some embodiments of the present disclosure. In some embodiments, the process  3700  can be modified by, for example, having steps combined, divided, rearranged, changed, added, and/or removed. As described in more detail below, in some embodiments, the process  3700  can include four steps. At step  3710 , wearable device  100  receives motion information from one or more motion sensors  240 . At step  3720 , wearable device  100  determines a set of rotational data of wearable device  100 . At step  3730 , wearable device  100  determines a histogram of the user&#39;s stroke orbits based on the set of rotational data. At step  3740 , wearable device  100  determines a level of entropy of the histogram. 
     At step  3730 , wearable device  100  determines a histogram of the user&#39;s stroke orbits based on the set of rotational data. In one embodiment, the histogram can be a heat map of the user&#39;s stroke orbit. For example,  FIG. 38  illustrates a heat map of a user&#39;s stroke orbits according to some embodiments of the present disclosure. In  FIG. 38 , the heat map is expressed in a two dimensional histogram  3800  representing a horizontal coordinate system that is appreciated by people skilled in the art. The horizontal axis of the histogram  3800  is the azimuth coordinates of the horizontal coordinate system, where the azimuth coordinates can be denoted as Φ ranging from 0 degrees to 360 degrees. The vertical axis of the histogram  3800  is the elevation coordinates of the horizontal coordinate system, where the elevation coordinates can be denoted as Θ ranging from 0 degrees to 180 degrees, where in one embodiment the 0 degrees correspond to the zenith of the horizontal coordinate system and the 180 degrees correspond to the nadir of the horizontal coordinate system. The histogram  3800  shows how the user&#39;s stroke orbits correspond to the multiple Φ-Θ bins: each Φ-Θ bin can have a stroke possibility that indicates how likely that bin corresponds to the user&#39;s stroke orbits. If the user&#39;s stroke orbits frequently correspond to a bin, then that bin can have a higher value of stroke possibility, which corresponds to a lighter color in  FIG. 38 , such as bins  3810  and  3820 ; if the user&#39;s stroke orbits less frequently correspond to a bin, then that bin can have a lower value of stroke possibility, which corresponds to a darker color in  FIG. 38 . 
     At step  3740 , wearable device  100  determines a level of entropy of the histogram. In one embodiment, the level of entropy can be calculated as the absolute value of the summation of stroke possibilities of each Φ-Θ bin as expressed in Eq. 21.
 
 E=|Σ   Φ=0   360 Σ Θ=0   180   PΦ,Θ|   Eq. 21
 
     In Eq. 1, P indicates an empirical probability measure of an orbit having a point in an Φ-Θ bin, and E indicates the entropy level. In some embodiments, the entropy indicates the degree to which the probability measure of the orbit is spread out over different Φ-Θ bin. In  FIG. 38 , a perfectly consistent stroke would have a minimum number of Φ-Θ bins occupied, and thus has a lower entropy level. On the other hand, a very inconsistent stroke would have many Φ-Θ bins occupied, and thus has a higher entropy level. For example, a uniformly random process across all Φ-Θ bins would be the most inconsistent stroke orbits and would yield maximum entropy. Therefore, the consistency level of the user&#39;s stroke orbits can be characterized by the entropy level: the lower the entropy level, the more consistent the user&#39;s stroke orbits. In some embodiments, the level of entropy of the histogram refers to the level of variance of the histogram. If the histogram is concentrated on a small number of Φ-Θ bins, then the level of variance is low. If the histogram is spread over a large number of Φ-Θ bins, then the level of variance is high. In some embodiments,  FIG. 38  can be viewed as a 2-D histogram normalized by the total number of samples. 
     It is to be understood that the present disclosure is not limited in its application to the details of construction and to the arrangements of the components set forth in the description or illustrated in the drawings. The present disclosure is capable of other embodiments and of being practiced and carried out in various ways. In addition, it is to be understood that the phraseology and terminology employed herein are for the purpose of description and should not be regarded as limiting. For example, the techniques described in the present disclosure are not limited to identifying true swim strokes or classifying swim stroke type based on amount of arm extension. Other applications include using amount of arm extension for gait analysis for pedestrian activities or for repetition counting for weight training activities. 
     As such, those skilled in the art will appreciate that the conception, upon which this disclosure is based, may readily be utilized as a basis for the designing of other structures, systems, methods and media for carrying out the several purposes of the present disclosure. It is important, therefore, that the claims be regarded as including such equivalent constructions insofar as they do not depart from the spirit and scope of the present disclosure. 
     Although the present disclosure has been described and illustrated in the foregoing exemplary embodiments, it is understood that the present disclosure has been made only by way of example, and that numerous changes in the details of implementation of the present disclosure may be made without departing from the spirit and scope of the present disclosure, which is limited only by the claims which follow.

Metadata:
Filing Date: 20170831
Publication Date: 20210831
Grant Date: 20210831
Priority Date: 20160831
Inventors: MERMEL, CRAIG H.
RAGHURAM, KARTHIK JAYARAMAN
PHAM, HUNG A.
HOWELL, ADAM S.
OCHS, JAMES P.
SINGH ALVARADO, ALEXANDER
CHOW, SUNNY K.
HUANG, RONALD K.
DERVISOGLU, GUNES
WATERS, KENNETH
Assignee: APPLE INC
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Family ID: 61241247