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Recursive Parameter Estimation Algorithm

The recursive algorithm is implemented using the following steps.

  1. Make initial estimates tex2html_wrap_inline237 and tex2html_wrap_inline239 .
  2. Solve equation (gif) for tex2html_wrap_inline245 and tex2html_wrap_inline247 using the first three measurements, tex2html_wrap_inline269 , and tex2html_wrap_inline271 and with N=3.
  3. Obtain the new estimates of A and tex2html_wrap_inline223 by forming tex2html_wrap_inline279 and tex2html_wrap_inline281 . If either value of A or tex2html_wrap_inline223 is negative, then use the previous value.
  4. Measure the next data point, increment N, and evaluate tex2html_wrap_inline289 in (gif) and tex2html_wrap_inline291 in (gif) for tex2html_wrap_inline293 using the new values for A and tex2html_wrap_inline223 .
  5. Solve equation (gif) for tex2html_wrap_inline245 and tex2html_wrap_inline247 , 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 (gif). The algorithm is stopped when tex2html_wrap_inline245 and tex2html_wrap_inline247 are small.

A variation of the above algorithm is to always use the initial values tex2html_wrap_inline307 and tex2html_wrap_inline309 in the equations (gif), (gif), (gif), 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