AIDJEX Bulletin #40 - Polar Science Center - University of Washington

VELOCITY ERROES
As mentioned earlier, the February data were selected for detailed study
because the ice was nearly stationary then. Clearly, such data do not include
fix errors due to ice velocity itself. In the general situation when
the ice is moving there is an additional source of error.
The measurement equation which we used, relating the observer’s position
to the corrected Doppler counts, did not take into account velocity of the
observer. In principle the velocity can easily be included in the measurement
equation--in fact, it is standard practice for shipboard applications--
but we decided to ignore the velocity effect for several reasons. Ice
velocities are typically small and highly correlated between stations only
100 km apart. Thus the velocity errors in translocation will be small.
Also, we were not confident of a technique to estimate the ice velocity based
on the previous few fixes. The effect of velocity errors could have been
reduced by a suitable algorithm to, estimate the ice velocity and use it in
the fix solution.
The histogram of ice velocity (Fig. 10) shows that the velocity error
could occasionally exceed 20 cm sec-’ , with which, using the above guideline,
is associated a fix error of at least 100 m. The difference in velocity
between two stations will affect our translocation results. The velocity
difference was occasionally as large as 10 cm sec-’ (FiF. I), causing occasional
translocation errors of more than 50 m. Thus, we can see that at times
of extreme ice motion, the effect of velocity errors is somewhat larger than
the other sources of error in stand-alone and translocation position
measurements.
The errors in position due to velocity errors are roughly proportional
to the ice velocity itself (50 m per 10 cm sec-l). Likewise, the distance
traveled by the ice in a given tine (12 hours, say) is also proportional to
the velocity. Thus, the ratio of the measurement error to the actual motion
is independent of the ice velocity, and is about 0.02. While position errors
due to the ice velocity are not negligible, they degrade our estimates of ice
motion over periods of 12 hours or so by only approximately 2%.
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