TSA Stochastic State-Space Modeling VI

Owning Palette: Modeling and Prediction VIs

Requires: Advanced Signal Processing Toolkit

Estimates the stochastic state-space model of a multivariate (vector) time series. Wire data to the Xt input to determine the polymorphic instance to use or manually select the instance.

Details  

TSA Vector Stochastic State-Space Modeling (Waveform)

	Xt specifies the multivariate (vector) time series. The number of samples must be greater than two times model order.
	model order specifies the model order of the state-space model. The value of model order must be at least twice the number of frequency components that you want to estimate. The default is 4.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	noise subspace specifies the percentage of the noise subspace in the whole space, which is the combination of the signal subspace and the noise subspace. The default is 10.
	A returns the estimated state transition matrix of the stochastic state-space model.
	C returns the estimated measurement matrix of the stochastic state-space model.
	frequency components returns information about the estimated frequency components. frequency returns the estimated frequency of the frequency component. damping factor returns the estimated damping factor of the frequency component. magnitude returns the estimated magnitude of the frequency component. Each element of the array represents one channel series in Xt. phase returns the estimated phase of the frequency component. Each element of the array represents one channel series in Xt.
	error out contains error information. This output provides standard error out functionality.

TSA Vector Stochastic State-Space Modeling (Array)

	Xt specifies the multivariate (vector) time series. Each column of the 2D array represents a vector at certain time.
	model order specifies the model order of the state-space model. The value of model order must be at least twice the number of frequency components that you want to estimate. The default is 4.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	noise subspace specifies the percentage of the noise subspace in the whole space, which is the combination of the signal subspace and the noise subspace. The default is 10.
	A returns the estimated state transition matrix of the stochastic state-space model.
	C returns the estimated measurement matrix of the stochastic state-space model.
	frequency components returns information about the estimated frequency components. frequency returns the estimated frequency of the frequency component. damping factor returns the estimated damping factor of the frequency component. magnitude returns the estimated magnitude of the frequency component. Each element of the array represents one channel series in Xt. phase returns the estimated phase of the frequency component. Each element of the array represents one channel series in Xt.
	error out contains error information. This output provides standard error out functionality.

TSA Stochastic State-Space Modeling Details

This VI estimates the stochastic state-space model of a multivariate (vector) time series according to the following equations:

S_k+1 = AS_k + w_k

x_k = CS_k+v_k

x_k is the m×1 vector time series with m variables, S_k is the state vector with n state variables, n is model order, A is the state transition matrix with the size n × n, C is the measurement matrix with the size m × n, and w_k and v_k are n × 1 and m × 1 noise vectors, respectively, with a mean of zero.

You can use the estimated stochastic state-space model to describe the signal subspace. The noise subspace parameter specifies the amount of noise subspace as a percentage in the whole space, which is the combination of the signal subspace and the noise subspace.

You can characterize the dynamic behavior of a system by converting the matrix A and matrix C into the frequency, damping factor, magnitude and phase parameters that the modal parametric model contains. Refer to the TSA Modal Parametric Modeling VI for the definition of modal parameters.