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# Recursive Parameter Estimation Algorithm

The recursive algorithm is implemented using the following steps.

1. Make initial estimates and .
2. Solve equation () for and using the first three measurements, , and and with N=3.
3. Obtain the new estimates of A and by forming and . If either value of A or is negative, then use the previous value.
4. Measure the next data point, increment N, and evaluate in () and in () for using the new values for A and .
5. Solve equation () for and , and go to step 3 until the stopping criteria is reached.
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.

A variation of the above algorithm is to always use the initial values and in the equations (), (), (), resulting in a much simpler implementation 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 complexity and convergence.

Kozick Rich
Fri Jun 21 11:03:19 EDT 1996