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Accuracy
In this section we want to examine which factors influence the
accuracy of the system. For this, we have to examine errors that can
occur during the measurement of
and
. From a measurement point of view the two are
identical, since they are both an amount of time elapsed between two
beam sightings. Therefore we will use as a genus for the two and
as the absolute error of . The following list contains
possible causes for measurement errors:
- Vibrations: Due to their fast rotation, the mirrors and
thus the reflected beams suffer from small vibrations, resulting in a
small angle of beam spread, which is about in
our prototype. Assuming
(since
), the resulting error is
for an observer
located at distance from the lighthouse rotation axis and at height
over the lighthouse center.
- Lower bound on time
for one mirror rotation:
Since we can measure elapsed time only when the rotating laser beam hits
the photo detector, the accuracy of
and
is limited by the speed of the rotating mirrors (i.e.,
).
The resulting error is
.
- Flutter of platform rotation: The relative error in lighthouse
rotation speed
causes an error in .
is mainly caused by the flutter of the motor
driving the lighthouse platform. The motor used in our prototype
has a flutter of 0.1%. The resulting error is
.
- Variable delays: There is a variable time offset between the
laser beam hitting the photo detector and the interrupt handler
reading the clock. On the path from the photo detector to the
interrupt handler are many sources of variable delay, such as
hardware and interrupt latency. The actual value of this error
pretty much depends on what is currently happening on the computer,
but is typically small compared to the other sources of errors.
- Clock resolution: The minimum time unit
that
can be measured by the clock limits the time resolution for
measurement of . The Linux laptop we used has
s. On the ATMEL we used a 16-bit counter
to implement a clock with
s. The resulting
error is
.
- Clock drift: The maximum relative error
in
the clock rate also causes an error in . A typical value is
both on Linux and the ATMEL. The
resulting error is
.
In our prototype systems, the clearly dominating errors are caused
by vibrations, limited
, and flutter of platform
rotation. The use of deflectable MEMS mirrors can both drastically
reduce vibrations and
. The flutter of platform
rotation can be reduced to about 0.01% by using electronically
stabilized motors as used, for example, in turntable drives. By this,
we expect a possible reduction of by a factor of about 10.
Note, however, that the errors resulting from these three main sources
can be modeled by a Gaussian noise source. This means that averaging
over a large number of measurements helps to reduce the error.
Next: Range
Up: System Analysis
Previous: System Analysis
Kay Roemer
2003-02-26