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The final method is fully non-linear optimization. In this approach the Nelder-Mead
simplex algorithm is used to adjust the four parameters to achieve an optimal result. First, define
MX and MY, the corrected measurements:
S
O
CORRECTED
S
O
CORRECTED
Y
YHY
HYMY
X
XHX
HXMX
==
==
()
2
1
2
22
1
+=
j
jjN
MYMXE
Then define a measure, E
N,
of the collective deviation of the corrected measurements from the
unit circle. The algorithm iteratively adjusts the four parameters until the collective deviation, E
N
,
is minimized. Running the algorithm more than once, with the previous result as an initial value,
is recommended.
NOTE
A description of the algorithm can be found in Section 10.4 of Numerical Recipes in C, Press,
W.H., Flannery, B. P., Teukolsky, S. A., Vetterling, W.T., Cambridge University Press,
Cambridge, 1988.
The result of the non-linear optimization is shown in Figure 8-14, “Non-Linear
Optimization”. The numerical results are similar to those obtained by vector averaging and
scaling with maximum values.
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