What Is Recursive Estimation?

Many real-world applications, such as adaptive control, adaptive filtering, and adaptive prediction, require a model of the system to be available online while the system is in operation. Estimating models for batches of input-output data is useful for addressing the following types of questions regarding system operation:

  • Which input should be applied at the next sampling instant?

  • How should the parameters of a matched filter be tuned?

  • What are the predictions of the next few outputs?

  • Has a failure occurred? If so, what type of failure?

You might also use online models to investigate time variations in system and signal properties.

The methods for computing online models are called recursive identification methods. Recursive algorithms are also called recursive parameter estimation, adaptive parameter estimation, sequential estimation, and online algorithms.

For more information, see Recursive Estimation and Data Segmentation Techniques in System Identification Toolbox™. For detailed information about recursive parameter estimation algorithms, see the corresponding chapter in System Identification: Theory for the User by Lennart Ljung (Prentice Hall PTR, Upper Saddle River, NJ, 1999).

At the command line, you can recursively estimate linear polynomial models, such as ARX, ARMAX, Box-Jenkins, and Output-Error models. For time-series data containing no inputs and a single output, you can estimate AR (autoregressive) and ARMA (autoregressive and moving average) single-output models.

For information about performing online estimation in Simulink®, see Online Estimation.

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