Prediction and Simulation

This page summarizes the functions used after a model has been estimated.

Both functions accept the model dictionary returned by any pysib estimator.

pysib.predict

yp = pysib.predict(u, y, model)

Computes the one-step-ahead predicted output.

Conceptually:

yp(t) = y(t) + H(z)^(-1) (G(z) u(t) - y(t))

Parameters:

• u: input signal.
• y: measured output signal.
• model: model dictionary with keys A, B, C, D, and F.

Returns:

• yp: predicted output array.

Use predict to evaluate one-step-ahead prediction performance using the measured output history.

pysib.simulate

ys = pysib.simulate(u, model)

Computes the noise-free simulated output.

Conceptually:

ys(t) = G(z) u(t)

Parameters:

• u: input signal.
• model: model dictionary with keys A, B, C, D, and F.

Returns:

• ys: simulated output array.

Use simulate to evaluate the deterministic input/output response of an estimated model.

Example

theta, model = pysib.arx(u, y, na=1, nb=1, nz=1)

yp = pysib.predict(u, y, model)
ys = pysib.simulate(u, model)

predict uses y; simulate does not.