Create a variable to store u t This variable is updated at each time step.

## Recursive Identification and Parameter Estimation

Estimate the parameters and output using step and input-output data, maintaining the current regressor pair in H. Invoke the step function implicitly by calling the obj system object with input arguments. System object for online parameter estimation, created using one of the following commands:. The step command updates parameters of the model using the recursive estimation algorithm specified in obj and the incoming input-output data. Input data acquired in real time, specified as a scalar or vector of real values depending on the type of System object.

Estimated model parameters, returned as vectors of real values. The number of estimated parameters, and so the step syntax, depend on the type of System object:. Polynomials A q and C q coefficients.

Polynomials A q and B q coefficients. Polynomials A q , B q , and C q coefficients.

Polynomials B q and F q. Polynomials B q , C q , D q , and F q coefficients.

Estimated output, returned as a real scalar. The output is estimated using input-output estimation data, current parameter values, and recursive estimation algorithm specified in obj.

## Recursive Identification and Parameter Estimation: Han-Fu Chen, Wenxiao Zhao - Book | Rahva Raamat

Starting in Rb, instead of using the step command to update model parameter estimates, you can call the System object with input arguments, as if it were a function. A modified version of this example exists on your system. Do you want to open this version instead? Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:.

Select the China site in Chinese or English for best site performance. However, they typically have better convergence properties. The following set of equations summarizes the forgetting factor adaptation algorithm:. The software ensures P t is a positive-definite matrix by using a square-root algorithm to update it [2]. The software computes P assuming that the residuals difference between estimated and measured outputs are white noise, and the variance of these residuals is 1.

Q t is obtained by minimizing the following function at time t :. See section For more information about the Kalman filter algorithm, see Kalman Filter.

The following set of equations summarizes the Kalman filter adaptation algorithm:. Where, R 1 is the covariance matrix of parameter changes that you specify. R 2 is the variance of the innovations e t in the following equation:. This scaling does not affect the parameter estimates. In the linear regression case, the gradient methods are also known as the least mean squares LMS methods.

### 1st Edition

The following set of equations summarizes the unnormalized gradient and normalized gradient adaptation algorithm:. In the unnormalized gradient approach, Q t is given by:. In the normalized gradient approach, Q t is given by:. If the gradient is close to zero, this can cause jumps in the estimated parameters. To prevent these jumps, a bias term is introduced in the scaling factor. These choices of Q t for the gradient algorithms update the parameters in the negative gradient direction, where the gradient is computed with respect to the parameters.

### Matlab simulink online

See pg. This approach is also known as sliding-window estimation. Finite-history estimation approaches minimize prediction errors for the last N time steps. In contrast, infinite-history estimation methods minimize prediction errors starting from the beginning of the simulation. The software solves this linear regression problem using QR factoring with column pivoting. System Identification: Theory for the User. Choose a web site to get translated content where available and see local events and offers.