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

unknown position, velocity, and acceleration of each station.
system as described by X is assumed to satisfy
The physical
.Yn+l = 4 (n+l ,n> xn + r (n+l ,n) w, ,
where
Here 4 and r are known matrices involving (t,+l - t,) and W, is an unknown
random white noise. The covariance of w is assumed to be &.
Z, contains the measured coordinates of each station which obtained a
fix from the nth satellite pass. The measurements satisfy
where
Z, = Hn Xn -+ V,,
‘in is the known relationship between the 2, and the Xn, and Vn is unknown
random white measurement error with known covariance 8. Under these assump-
tions, one can find best estimates €or X,
given a sequence of measurerents
52, i = 1,2, ..., €17 (see Thorndike and Cheung [1377] for details ).
Of particular interest here is the definition of the measurement error
covariance matrix R.
Consider the situation in which two stations A and B
tracked the same satellite pass. Then the measurement Z (looking at only one
coordinate direction) has the form
For times that the ice was moving, the estimation errors are up to twice as
large as shown, since the raw data then include additional errors due to
neglecting the ice velocity.
Other data processing approaches could produce better accuracy with
additional effort: treatment of velocity effects; use of passes tracked by
the second receiver at each camp in position estimates; editing of the translocation
data as well as the geographic data; incorporating models for the
various error functions; and tighter tuning of the physical parameters that
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