A first order system unit step response is described by the equation

where *A* is the gain and is the time constant of
the system. The objective of this experiment is to estimate the values
of *A* and recursively from the sampled data.
That is, the estimates of *A* and are improved in real-time
as each new data point is measured.

Following the approach presented in [2] and [3],
we obtain a first-order Taylor series expansion of ()
about a point .
Then we minimize the
sum of squared differences between
the measured data
and the model in () with respect to the parameters
*A* and .
This process leads to the recursive algorithm described next.

The recursive algorithm begins with
an initial estimate of and .
The next values of *A* and are computed by solving
for the updates and in ()

where

and

The first order system used in the experiment is the RC
circuit shown in Figure .
The objective is to estimate the parameters *A* and
by observing the output voltage when the input
voltage is a unit step function.
In this circuit, and .
The parameter estimates are updated in real-time as each data
point is measured.
Data collection can be stopped when the estimates have converged.

Fri Jun 21 11:03:19 EDT 1996