October 2011
Intermediate to advanced
749 pages
23h 36m
English
Content preview from Optimal Estimation of Dynamic Systems, 2nd Edition
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600 Optimal Estimation of Dynamic Systems
The matrix Γ is obtained from integration of Equation (A.123):
Γ =
IΔt +
1
2!
FΔt
2
+
1
3!
F
2
Δt
3
+ ···
B (A.124)
Adequate results can be obtained in most cases using only a few of the terms in the
series expansion. For the matrices in example A.5, using three terms in the series
expansion yields
Φ =
0.9048 0
0.0952 1
, Γ =
0.0952
0.0048
(A.125)
The series results for Φ and Γ are accurate to within four significant digits. Results
vary with sampling interval. As a general rule of thumb, if the sampling interval is
below Nyquist’s upper limit, then three to four terms in the series expansion gives
accurate results.
20
The concep ...
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