Accelerometer Limitations
There are
various types of accelerometers but the force balance pendulous
accelerometer and piezoelectric accelerometer are the most common. The
pendulous accelerometer has excellent performance but unfortunately is
relatively large and expensive. The piezoelectric accelerometer is less
expensive and can fit on one's hand but cannot measure either static
accelerations or ones occurring at the low frequencies commonly found
in human motion.
All of these linear accelerometers measure, of course,
the acceleration which represents the actual dynamics of a moving body,
but may also be contaminated by components of earth's gravity which may
also be sensed.
An accelerometer sitting stationary on the Earth with
its sensitive axis pointing vertically will give an output signal
equivalent to one g, or 32.2 ft/sec squared (9.8 m/sec squared),
assuming that it responds to static acceleration inputs. If this
accelerometer is rotated 90 degrees and left stationary with its
sensitive axis pointing parallel to the surface of the Earth, it will
produce an output signal equivalent to zero g's.
If one orients this accelerometer so that its
sensitive axis is pointing down, it will yield a minus one g signal and
so on. In each of these cases, the accelerometer has not been moving
but is yielding an output suggesting that there have been some dynamic
motions.
Of course, if one rotated the sensitive axis of the
accelerometer to a new position only a few degrees (theta) from the
horizontal, it would produce a small indicated acceleration
(mathematically: g(sine theta)). Note that its output now would be
entirely position dependent.
If one slowly moved the sensitive axis of the
accelerometer to a new position only a few degrees above and to a few
degrees below the horizontal plane one would see an oscillating
acceleration output no matter how slowly you rotated the accelerometer.
Again, the magnitude of the output would be completely dependent on the
angular position. Often, this varying output is interpreted as a
measure of the dynamics of a hand tremor when it is actually the error
contributed by Earth's gravity.
One cannot filter out low frequency accelerometer
signals and expect to eliminate the gravitational component since that
component will most often occur at the frequency of the movement, the
tremor frequency for example.
When the motion of the accelerometer is random, it
will measure the linear sum of true dynamic accelerations and those due
to Earth's gravity. It cannot differentiate or distinguish one from the
other, and there is no way of filtering its output to eliminate the
signal due to Earth's gravity.
Only in the unlikely situation that the measured
motion was in a perfect straight line would it be possible to eliminate
the gravity "noise" component since it would be a constant. In this
unusual circumstance one could be left with the true dynamic
acceleration (the rate of change of velocity). If the direction on
movement is not precisely known, the contribution of Earth's gravity
cannot be removed unless numerous other sensors are utilized in
addition to the one accelerometer; even a triaxis accelerometer package
would not be sufficient.
With relatively small dynamic motions such as in human
tremors, the magnitude of the accelerations due to dynamics may be of
the same relative size as those due to small changes in the orientation
of the sensitive axis, by coupling to Earth's gravity.
Unless a tremor is restricted to a perfect straight
line, the orientation input for just a few degrees of rotation will
mask the true dynamics of the tremor. For example, a tremor of plus and
minus 0.1 g would easily be in error by as much as 100% due to a
rotation of just plus and minus 5.7 degrees.
Only a large inertial measurement system containing
more accelerometers and gyros can separate the dynamic motions from the
errors due to angular position. Such a system would be significantly
larger than most hands, arms, legs, etc. that it was to measure.
In
conclusion:
It is technically impossible to quantify typical
tremors with a simple accelerometer since the best such a sensor could
do is to occasionally capture the high frequency components (not the
magnitude) of a tremor.
Since human skeletal components are basically hinged
together, their
relative motions are primarily rotational. A gyroscope that measures
angular rotation rates is thus fundamentally superior and hence the
sensor of choice.
The
choice is clear: Motus
The miniature Motus gyro is insensitive to linear
accelerations and also insensitive to Earth's gravitation. It measures
the true dynamics (angular rotation rates) of an object and is not
confused by orientation changes.
