Using Gravity to Estimate Accelerometer Orientation
`David Mizell
`Cray, Inc.
`Work performed while the author was at Intel Research Seattle
`
`Abstract
`
`Several wearable computing or ubiquitous
`computing research projects have detected and
`distinguished user motion activities by attaching
`accelerometers
`in known positions and
`orientations on the user’s body. This paper
`observes that the orientation constraint can
`probably be relaxed. An estimate of the constant
`gravity vector can be obtained by averaging
`accelerometer samples. This gravity vector
`estimate in turn enables estimation of the
`vertical component and the magnitude of the
`horizontal component of the user’s motion,
`independently of how
`the
`three-axis
`accelerometer system is oriented.
`
`1. Introduction
`
`Most previous work on detecting or measuring
`user motion activities using body-worn
`accelerometers
`[1 – 7] attached
`the
`accelerometers to the body in a known position
`and orientation relative to the body. The
`research issue addressed in this work is the
`following: in the absence of information about
`how a device containing a
`three-axis
`accelerometer is being carried by the user, can
`we still make reliable inferences about the user’s
`activities or actions?
`
`2. Orientation-independent acceleration
`information
`
`Our hardware configuration employed two
`Analog Devices, Inc. ADXL202 evaluation
`boards hot-glued together at a 90-degree angle to
`provide three orthogonal acceleration axes. We
`needed all three because of our assumption that
`the orientation of the device is not known.
`Acceleration measurements on each of the three
`axes were sampled at 100Hz and collected on an
`iPAQ, which experimental subjects could carry
`with them.
`
`Our approach for obtaining orientation-
`independent acceleration information makes use
`of the fact that MEMS accelerometers measure
`gravitational (“static”) acceleration as well as
`
`(“dynamic”) acclerations caused by the wearer’s
`motion. The pull of gravity downward along
`some accelerometer axis manifests itself in the
`accelerometer output as an acceleration in the
`opposite direction along that same axis.
`
`Fig. 1. Relevant coordinate systems
`
`There are two relevant coordinate systems, as
`shown in Figure 1. The three-axis accelerometer
`configuration is in some arbitrary orientation on
`the wearer’s body. The three accelerometer axes
`are denoted in the figure as x, y, and z. Ideally,
`we would like to know acceleration information
`in terms of a coordinate system oriented to the
`user and his forward motion. In the figure, these
`axes are denoted v (for vertical), f (for the
`direction of horizontal forward motion), and s is
`a (usually of less interest) horizontal axis
`orthogonal to the direction of motion.
`
`The algorithm works as follows: for a chosen
`sampling interval, typically a few seconds,
`obtain an estimate of the gravity component on
`each axis by averaging all the readings in the
`interval on that axis. That is, we are estimating
`the vertical acceleration vector v corresponding
`to gravity as v = ( vx, vy, vz ), where vx, vy and vz
`are averages of all the measurements on those
`respective axes for the sampling interval.
`
`Let a = (ax, ay, az) be the vector made up of the
`three acceleration measurements taken at a given
`point in the sampling interval. We assume for
`the sake of simplicity
`that
`the
`three
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`Proceedings of the Seventh IEEE International Symposium on Wearable Computers (ISWC’03)
`1530-0811/03 $ 17.00 © 2003 IEEE
`
`
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`SAMSUNG EXHIBIT 1007
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`measurements are taken simultaneously. We set
`d = ( ax – vx, ay – vy, az – vz ) to represent the
`dynamic component of a, that caused by the
`user’s motion rather than gravity. Then, using
`vector dot products, we can compute the
`projection p of d upon the vertical axis v as
`vd
`p
`v
`=
`vv
`component of the dynamic acceleration vector d.
`Next, since a 3D vector is the sum of its vertical
`and horizontal components, we can compute the
`horizontal component of
`the dynamic
`acceleration by vector subtraction, as h = d – p.
`
`
`
`••
`
`
`
`. In other words, p is the vertical
`
`implementing early prototype hardware. Kurt
`Partridge and Waylon Brunette of UW provided
`valuable debugging help. A special thanks goes
`to Prof. W. Dan Curtis of Central Washington
`University for vastly clarifying the author’s
`mathematics.
`
`References
`
`[1] Aminian, K, et al, “Motion Analysis in
`Clinical Practice Using Ambulatory
`Acclerometry,” in Lecture Notes in
`Artificial Intelligence 1537, Modeling and
`Motion Capture Techniques for Virtual
`Environments, 1998.
`
`[2] Farringdon, J., et al, “Wearable Sensor
`Badge & Sensor Jacket for Context
`Awareness,” in Proceedings, Third
`International Symposium on Wearable
`Computers, San Francisco, CA, IEEE
`Computer Society, 1999, ISBM 0-7695-
`0428-0, pp.107-113.
`
`[3] Lee, C-Y. and Lee, J-J., “Estimation of
`Walking Behavior Using Accelerometers
`in Gait Rehabilitation,” International
`Journal of Human-Friendly Welfare
`Robotic Systems, June 2002, Vol. 3, No. 2,
`ISSN 1598-3250, pp. 32-35.
`
`[4] Lee, S. and Mase, K., “Activity and
`Location Recognition Using Wearable
`Sensors,” IEEE Pervasive Computing,
`July-September 2002, Vol. 1 No. 3, pp.
`24-32.
`
`[5] Morris, J., “Acclerometry – A Technique
`for the Measurement of Human Body
`Movements,” in Journal of Biomechanics,
`Vol. 7, 1974, pp. 157-159.
`
`[6] Randell, C., and Muller, H., “Context
`Awareness by Analysing Accelerometer
`Data,”
`in P r o c e e d i n g s ,
`F o u r t h
`International Symposium on Wearable
`Computers, Atlanta, GA, IEEE Computer
`Society, 2000, ISBN 0-7695-0795-6, pp.
`175-176.
`
`[7] Van Laerhoven, K., and Cakmakci, O.,
`“What Shall We Teach Our Pants?”, in
`Proceedings, Fourth
`International
`Symposium on Wearable Computers,
`Atlanta, GA, IEEE Computer Society,
`2000, ISBN 0-7695-0795-6, pp. 77-83.
`
`However, as opposed to the vertical case, we
`don’t know the orientation of h relative to f, the
`horizontal axis we’d like to have it projected
`upon. Furthermore, it appears impossible to
`detect. There
`is no dominating static
`acceleration as there is in the vertical case.
`Accordingly, we simply compute the magnitude
`of the horizontal component of the dynamic
`accelerations, concluding that that is the best we
`can expect to do.
`
`The result of the algorithm performed across a
`sampling interval is a pair of waveforms,
`estimates of the vertical components and the
`magnitude of the horizontal components of the
`dynamic accelerations, each of which is
`independent of the orientation of the mobile
`device containing the accelerometers.
`
`3. Conclusions
`
`Our results indicate that a three-axis MEMS
`accelerometer system might be useful in
`detecting and distinguishing several user motion
`activities, such as walking, running, climbing or
`descending stairs, or riding in a vehicle – in spite
`of the fact that the position and orientation of the
`device are not known. We conjecture that the
`vertical acceleration component is sufficient
`information for most such activity detection.
`
`Acknowledgements
`
`The author wishes to thank Jonathan Lester of
`the University of Washington for the hardware
`implementations for this work, and Mike
`Perkowitz of Intel Research Seattle for his
`implementation of the iPAQ data capture
`software, and both of them for their help with the
`experiments. Saurav Chatterjee of the University
`of Washington was
`instrumental
`in
`
`Proceedings of the Seventh IEEE International Symposium on Wearable Computers (ISWC’03)
`1530-0811/03 $ 17.00 © 2003 IEEE
`
`Page 2 of 2
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