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Estimating the Derivative

As no direct measurements of the continuous derivative exist, it must be estimated from the samples. This is done using a simple difference form:

\begin{displaymath}
S_t'(\ensuremath{\mathbf{x}}) = \frac{S_t(\ensuremath{\mathb...
...suremath{\mathbf{d}})}
{2 \Vert \ensuremath{\mathbf{d}}\Vert}.
\end{displaymath} (40)

The direction of the derivative is specified by the direction of the difference vector $\ensuremath{\mathbf{d}}$.

It is assumed that this approximation ( $S_t'(\ensuremath{\mathbf{x}}) \approx
\frac{\partial S_t(\ensuremath{\mathbf{x}})}{\partial x}$) is sufficiently accurate so that estimation described in equation 36 is not significantly biased.



Mark Jenkinson 2001-11-07