Global Positioning System Reference
In-Depth Information
7.5
Movement and Inertial Sensing
Dynamics is the branch of physics that covers the motion of objects and includes
the variables of position, distance, velocity, and acceleration. These are all related
by the laws of motion or Newton's laws, which describe the movements of all
objects and are accurate for all but the most extreme situations when Einstein's
theory of relativity also needs to be included. Computer navigational systems
employ a “motion model” using a set of algorithms based on these mathematical
relationships (together with some calculus, which Newton also invented). The
model attempts to predict, using software, the real physical motions of objects.
Inputs to the models come from sensing, measurements, and a priori information
and the model is only as good as the underlying quality of the sensed information
and the degree of sophistication. It is possible, however, to improve quality by
using statistical filtering techniques, but the computational load of modeling and
filtering can be immense. One of the main reasons why Whereness is an emerging
opportunity is that is it dependent on improvements in computer science.
We have considered systems that measure distance by timing pulses and
geometry and velocity (i.e., speed in a given direction), but now we come to linear
acceleration and rotation. Acceleration is very easy to measure, especially with the
advent of accelerometer chips and rotation also with solid-state gyroscopes, but
the relevance of acceleration needs perhaps a little explanation.
Acceleration is the rate of change (with respect to time) of velocity and in
turn, velocity is the rate of change of distance. So it can be seen that if timed
measurements of distance, velocity, or acceleration are taken, the others can be, in
theory, determined. In mathematics, velocity is the first derivative of distance and
acceleration its second derivative. If rate of change of distance is differentiated,
velocity is obtained and again, if velocity is differentiated then acceleration is
found. Conversely (and of interest if we wish to use accelerometers), if the output
of an accelerometer is integrated with respect to time, we obtain velocity and if
velocity is integrated distance is found. These relationships were first computed
using analog computers that are adept at calculus and that guided the first
generations of electrically controlled weapons, but today we use digital algorithms
and processors that can model motion in real time.
Accelerometers can also be used to determine tilt by measuring the effects of
gravity as well as inertia. Gyroscopes (gyros) are used to detect turning moments
and direction of travel. Historically they were based on rotating flywheels and
were and continue to be used in aircraft and missile autopilots. There are now
families of solid-state miniature devices based on other techniques, (e.g., quartz
crystal tuning forks). These mimic halteres, which are nature's gyros and which
can be observed on the bodies of some insects such as the crane fly. As these
structures vibrate they tend to oppose rotation that can be detected by changes in
their oscillations. Along with accelerometers, gyros are now in consumer
electronics applications such as radio-controlled model aircraft and vehicle
navigation systems.
