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The recursive algorithm is implemented using the following steps.
Three measurements are used in step 2 so that the estimates are not
adversely affected by a single noisy measurement.
Step 3 prohibits
negative parameter values because they
are impossible in the model ().
The algorithm is stopped when and are small.
- Make initial estimates and .
- Solve equation () for and
using the first three measurements, , and
and with N=3.
- Obtain the new estimates of A and by forming
If either value of A or is negative,
then use the previous value.
- Measure the next data point, increment N, and
evaluate in ()
and in () for using
the new values for A and .
- Solve equation () for and ,
and go to step 3
until the stopping
criteria is reached.
A variation of the above algorithm is to always use the initial
values and in the equations (),
(), (), resulting in a much simpler
with less real-time computation.
However, convergence of this variation is much more dependent
on the choice of initial conditions.
Students can investigate this tradeoff between computational
Fri Jun 21 11:03:19 EDT 1996