Accelerating the pace of engineering and science

# Documentation

## Validate Online Estimation Results

Use the following approaches to validate an online estimation performed using the Recursive Least Squares Estimator or Recursive Polynomial Model Estimator block:

• Examine the estimation error (residuals), which is the difference between the measured and estimated outputs. For systems whose parameters are constant or vary slowly with respect to time, the estimation generally takes some time to converge (settle). During this initial period, the estimation error can be high. However, after the estimation converges, a low estimation error value gives confidence in the estimated values.

You can also analyze the residuals using techniques such as the whiteness test and the independence test. For such analysis, use the measured data and estimation error collected after the parameter values have settled to approximately constant values. For more information regarding these tests, see What Is Residual Analysis?

To obtain the estimation error, in the Algorithm and Block Options tab of the online estimation block's dialog, select the Output estimation error check box. The software adds an Error outport to the block, which you can monitor using a Scope block. This outport provides the one-step-ahead estimation error, e(t) = y(t)–yest(t). For the time step, t, y and yest are the measured and estimated outputs, respectively.

• Examine the parameter covariance matrix, which measures the estimation uncertainty. A smaller covariance value gives confidence in the estimated values.

To obtain the parameter covariance, in the Algorithm and Block Options tab of the online estimation block's dialog, select the Output parameter covariance matrix check box. The software adds a Covariance outport to the block, which you can monitor using a Display block. This outport provides the parameter covariance matrix.

• Simulate the estimated model and compare the simulated and measured outputs. That is, feed the measured input into a model that uses the estimated parameter values. Then, compare this system's output with the measured output. The simulated output closely matching the measured output gives confidence in the estimated values.

If the validation indicates low confidence in the estimation, then see Troubleshooting Online Estimation for ideas on improving the quality of the fit.