Create a new experiment by clicking New Experiment on the Parameter Estimation tab. Name it EstimationData. Then import the I/O data, xdata1 and ydata1, and the time vector, time1, into the experiment. To do this open the experiment editor by right-clicking EstimationData and selecting Edit.... Type [time1,ydata1] in the output dialog box and [time1,xdata1] in the input dialog box in the experiment editor. For more information, see Import Data for Parameter Estimation. After you import the data the experiment looks as follows:

Run an initial simulation to view the I/O data, simulated output, and the initial table values. To do so, type the following commands at the MATLAB prompt:

sim('lookup_regular')
figure(1); plot(xdata1,ydata1, 'm*', xout, yout,'b^')
hold on; plot(linspace(0,6.5,10), table, 'k', 'LineWidth', 2);
legend('Measured data','Initial simulation data','Initial table values');

The x-axis and y-axis of the figure represent the input and output data, respectively. The figure shows the following plots:

You can see that the initial table values and simulated data do not match with the measured data.

To select the table values to estimate, on the Parameter Estimation tab, click the Select Parameters button to open the Edit:Estimated Parameters dialog. In the Parameters Tuned for all Experiments panel, click Select parameters to launch the Select Model Variables dialog. Check the box next to table, and click OK.

The Edit:Estimated Parameters window now looks as follows. The table values are selected for estimation by default.

On the Parameter Estimation tab, click Select Experiments. EstimationData is selected for estimation by default. If not, check the box under the Estimation column, and click Close.

To estimate the table values using the default settings, on the Parameter Estimation tab, click Estimate to open the Parameter Trajectory plot and Estimation Progress Report window. The Parameter Trajectory plot shows the change in the parameter values at each iteration.

After the estimation converges, the Parameter Trajectory plot looks like this:

The Estimation Progress Report shows the iteration number, number of times the objective function is evaluated, and the value of the cost function at the end of each iteration. After the estimation converges, the Estimation Progress Report looks like this:

The estimated parameters are saved in EstimatedParams in the Results section of the data browser pane on the left. To view the results, right-click on EstimatedParams and then select Open. The report resembles the following.

This report includes the estimated parameter values, the final value of the cost function, and other optimization results. You can see that the optimization stopped when the size of the gradient, 1.18e-14 was less than the criteria value, 1e-3.

Create a new experiment to use for validation. Name it ValidationData. Import the validation I/O data, xdata2 and ydata2, and time vector, time2 in the ValidationData experiment. To do this open the experiment editor by right-clicking ValidationData and selecting Edit.... Then, type [time2,ydata2] in the output dialog box and [time2,xdata2] in the input dialog box in the experiment editor. For more information, see Import Data for Parameter Estimation.

To select the experiment for validation, on the Parameter Estimation tab, click Select Experiments. The ValidationData experiment is selected for estimation by default. Deselect the box for estimation and check it for validation.

To select results to use, on the Validation tab, click Select Results to Validate. Deselect Use current parameter values and select EstimatedParams, and click OK.

The Parameter Estimator, by default, displays the experiment plot after validation. Add the residuals plot by checking the corresponding box on the Validation tab.

To start validation, on the Validation tab, click Validate.

Examine the plots