SI Recursively Estimate ARX Model VI

Owning Palette: Recursive Model Estimation VIs

Requires: Advanced Signal Processing Toolkit or Control Design and Simulation Module

Estimates the parameters of an ARX model using a recursive method. Wire data to the stimulus signal and response signal inputs to determine the polymorphic instance to use or manually select the instance.

Example

SI Recursively Estimate ARX Model (SISO Waveform)

	initialize specifies whether to initialize the internal state of the VI. This VI performs calculations that are dependent on all previous data since you last ran the VI or since you set initialize to TRUE. When initialize is TRUE, this VI restarts the calculation dependency. The default is FALSE.
	recursive method specifies the recursive estimation method to use. 0 RLS (default)—Recursive least squares method 1 KF—Kalman filter method 2 NLMS—Normalized least mean squares method 3 LMS—Least mean squares method
	stimulus signal specifies the input waveform of the stimulus signal.
	response signal specifies the input waveform of the response signal.
	orders of ARX model specifies the orders and delay of the ARX model. A order specifies the order of the A coefficients of the system model. The value of A order must be greater than or equal to 0. B order specifies the order of the B coefficients of the system model. The value of B order must be greater than or equal to 1. delay specifies the delay k of the system model. The value of delay must be greater than or equal to 0.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	ref value specifies the reference value for the recursive estimation algorithms. When recursive method is KF, ref value is the drift matrix. This method uses the drift matrix to prevent the gradient from approaching zero in the identification process. The gradient indicates the changes of the model coefficients. When recursive method is RLS, this VI uses the value in the first row and the first column of ref value as the forgetting factor. The forgetting factor specifies the percentage of information this VI uses from previous estimation calculations. The range of the forgetting factor is between 0 and 1. For example, if you set the forgetting factor to 0.5, this VI uses 50% of information from previous estimation. If you want to estimate a time-invariant system, you can set the forgetting factor between 0.98 and less than 1. If you want to estimate a time-variant system, you can set a smaller forgetting factor. Then, this VI can have a better ability to track the changes of the system coefficients. When recursive method is NLMS or LMS, this VI uses the value in the first row and the first column of ref value as the step size. The value of the step size is proportional to the convergence rate. The larger the step size, the faster the convergence. However, the algorithm can become unstable if the step size gets too large. An appropriate step size depends on the model type, order, and input signal.
	system model out returns information about the model structure, nominal or estimated parameters, identification result, and so on. Use the Model Management VIs to retrieve the information system model out contains. Note  You can use a customized system model probe to view model information that flows through system model wires when you debug a block diagram created with the System Identification VIs. Right-click a system model wire and select Custom Probe»SI System Model from the shortcut menu to use the system model probe.
	predicted response returns the predicted response output from the current estimated system model. The difference between the values of predicted response and response signal is the measure of the recursive estimation.
	coefficients of ARX model returns the coefficients of the ARX model. A returns the A coefficients of the system model. B returns the B coefficients of the system model.
	error out contains error information. This output provides standard error out functionality.

SI Recursively Estimate ARX Model (SISO Array)

	initialize specifies whether to initialize the internal state of the VI. This VI performs calculations that are dependent on all previous data since you last ran the VI or since you set initialize to TRUE. When initialize is TRUE, this VI restarts the calculation dependency. The default is FALSE.
	recursive method specifies the recursive estimation method to use. 0 RLS (default)—Recursive least squares method 1 KF—Kalman filter method 2 NLMS—Normalized least mean squares method 3 LMS—Least mean squares method
	stimulus signal specifies an array that represents the stimulus signal.
	response signal specifies an array that represents the response signal.
	orders of ARX model specifies the orders and delay of the ARX model. A order specifies the order of the A coefficients of the system model. The value of A order must be greater than or equal to 0. B order specifies the order of the B coefficients of the system model. The value of B order must be greater than or equal to 1. delay specifies the delay k of the system model. The value of delay must be greater than or equal to 0.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	sampling rate (Hz) is the signal sampling rate in hertz. The value of sampling rate must be greater than 0.
	ref value specifies the reference value for the recursive estimation algorithms. When recursive method is KF, ref value is the drift matrix. This method uses the drift matrix to prevent the gradient from approaching zero in the identification process. The gradient indicates the changes of the model coefficients. When recursive method is RLS, this VI uses the value in the first row and the first column of ref value as the forgetting factor. The forgetting factor specifies the percentage of information this VI uses from previous estimation calculations. The range of the forgetting factor is between 0 and 1. For example, if you set the forgetting factor to 0.5, this VI uses 50% of information from previous estimation. If you want to estimate a time-invariant system, you can set the forgetting factor between 0.98 and less than 1. If you want to estimate a time-variant system, you can set a smaller forgetting factor. Then, this VI can have a better ability to track the changes of the system coefficients. When recursive method is NLMS or LMS, this VI uses the value in the first row and the first column of ref value as the step size. The value of the step size is proportional to the convergence rate. The larger the step size, the faster the convergence. However, the algorithm can become unstable if the step size gets too large. An appropriate step size depends on the model type, order, and input signal.
	system model out returns information about the model structure, nominal or estimated parameters, identification result, and so on. Use the Model Management VIs to retrieve the information system model out contains. Note  You can use a customized system model probe to view model information that flows through system model wires when you debug a block diagram created with the System Identification VIs. Right-click a system model wire and select Custom Probe»SI System Model from the shortcut menu to use the system model probe.
	predicted response returns the predicted response output from the current estimated system model. The difference between the values of predicted response and response signal is the measure of the recursive estimation.
	coefficients of ARX model returns the coefficients of the ARX model. A returns the A coefficients of the system model. B returns the B coefficients of the system model.
	error out contains error information. This output provides standard error out functionality.

SI Recursively Estimate ARX Model (MISO Waveform)

	initialize specifies whether to initialize the internal state of the VI. This VI performs calculations that are dependent on all previous data since you last ran the VI or since you set initialize to TRUE. When initialize is TRUE, this VI restarts the calculation dependency. The default is FALSE.
	recursive method specifies the recursive estimation method to use. 0 RLS (default)—Recursive least squares method 1 KF—Kalman filter method 2 NLMS—Normalized least mean squares method 3 LMS—Least mean squares method
	stimulus signals specifies the input waveform array of the stimulus signals. Each element of the array is the waveform of one stimulus signal.
	response signal specifies the input waveform of the response signal.
	orders of ARX model specifies the orders and delays of the ARX model. A order specifies the order of the A coefficients of the system model. The value of A order must be greater than or equal to 0. B orders specifies the orders of the B coefficients of the model. The value of B orders must be greater than or equal to 1. delays specifies the delays k of the model. The value of delays should be greater than 0.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	ref value specifies the reference value for the recursive estimation algorithms. When recursive method is KF, ref value is the drift matrix. This method uses the drift matrix to prevent the gradient from approaching zero in the identification process. The gradient indicates the changes of the model coefficients. When recursive method is RLS, this VI uses the value in the first row and the first column of ref value as the forgetting factor. The forgetting factor specifies the percentage of information this VI uses from previous estimation calculations. The range of the forgetting factor is between 0 and 1. For example, if you set the forgetting factor to 0.5, this VI uses 50% of information from previous estimation. If you want to estimate a time-invariant system, you can set the forgetting factor between 0.98 and less than 1. If you want to estimate a time-variant system, you can set a smaller forgetting factor. Then, this VI can have a better ability to track the changes of the system coefficients. When recursive method is NLMS or LMS, this VI uses the value in the first row and the first column of ref value as the step size. The value of the step size is proportional to the convergence rate. The larger the step size, the faster the convergence. However, the algorithm can become unstable if the step size gets too large. An appropriate step size depends on the model type, order, and input signal.
	system model out returns information about the model structure, nominal or estimated parameters, identification result, and so on. Use the Model Management VIs to retrieve the information system model out contains. Note  You can use a customized system model probe to view model information that flows through system model wires when you debug a block diagram created with the System Identification VIs. Right-click a system model wire and select Custom Probe»SI System Model from the shortcut menu to use the system model probe.
	predicted response returns the predicted response output from the current estimated system model. The difference between the values of predicted response and response signal is the measure of the recursive estimation.
	coefficients of ARX model returns the coefficients of the ARX model. A returns the A coefficients of the system model. B returns the B coefficients of the system model.
	error out contains error information. This output provides standard error out functionality.

SI Recursively Estimate ARX Model (MISO Array)

	initialize specifies whether to initialize the internal state of the VI. This VI performs calculations that are dependent on all previous data since you last ran the VI or since you set initialize to TRUE. When initialize is TRUE, this VI restarts the calculation dependency. The default is FALSE.
	recursive method specifies the recursive estimation method to use. 0 RLS (default)—Recursive least squares method 1 KF—Kalman filter method 2 NLMS—Normalized least mean squares method 3 LMS—Least mean squares method
	stimulus signals specifies an array that represents the stimulus signals. Each row in the array is one stimulus signal.
	response signal specifies an array that represents the response signal. Each row in the array is one response signal.
	orders of ARX model specifies the orders and delays of the ARX model. A order specifies the order of the A coefficients of the system model. The value of A order must be greater than or equal to 0. B orders specifies the orders of the B coefficients of the model. The value of B orders must be greater than or equal to 1. delays specifies the delays k of the model. The value of delays should be greater than 0.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	sampling rate (Hz) is the signal sampling rate in hertz. The value of sampling rate must be greater than 0.
	ref value specifies the reference value for the recursive estimation algorithms. When recursive method is KF, ref value is the drift matrix. This method uses the drift matrix to prevent the gradient from approaching zero in the identification process. The gradient indicates the changes of the model coefficients. When recursive method is RLS, this VI uses the value in the first row and the first column of ref value as the forgetting factor. The forgetting factor specifies the percentage of information this VI uses from previous estimation calculations. The range of the forgetting factor is between 0 and 1. For example, if you set the forgetting factor to 0.5, this VI uses 50% of information from previous estimation. If you want to estimate a time-invariant system, you can set the forgetting factor between 0.98 and less than 1. If you want to estimate a time-variant system, you can set a smaller forgetting factor. Then, this VI can have a better ability to track the changes of the system coefficients. When recursive method is NLMS or LMS, this VI uses the value in the first row and the first column of ref value as the step size. The value of the step size is proportional to the convergence rate. The larger the step size, the faster the convergence. However, the algorithm can become unstable if the step size gets too large. An appropriate step size depends on the model type, order, and input signal.
	system model out returns information about the model structure, nominal or estimated parameters, identification result, and so on. Use the Model Management VIs to retrieve the information system model out contains. Note  You can use a customized system model probe to view model information that flows through system model wires when you debug a block diagram created with the System Identification VIs. Right-click a system model wire and select Custom Probe»SI System Model from the shortcut menu to use the system model probe.
	predicted response returns the predicted response output from the current estimated system model. The difference between the values of predicted response and response signal is the measure of the recursive estimation.
	coefficients of ARX model returns the coefficients of the ARX model. A returns the A coefficients of the system model. B returns the B coefficients of the system model.
	error out contains error information. This output provides standard error out functionality.

Example

Refer to the Online Model Estimation VI in the labview\examples\System Identification\Getting Started\Recursive Estimation.llb for an example of using the SI Recursively Estimate ARX Model VI.