ar_to_state_space

hcipy.util.ar_to_state_space(ar_coefficients, noise_variance, dt)

Convert a discrete-time AR(p) model to continuous-time state space.

Converts a discrete-time autoregressive model:

\[x_k = a_1 x_{k-1} + a_2 x_{k-2} + \cdots + a_p x_{k-p} + w_k\]

to an equivalent continuous-time state space model.

Parameters:

ar_coefficientsarray_like

AR coefficients \([a_1, a_2, ..., a_p]\) for the discrete-time model.

noise_variancefloat

Variance of the discrete-time driving noise.

dtfloat

Sampling time of the discrete-time AR model.

Returns:

transition_matrixndarray

Continuous-time state transition matrix (\(p\) x \(p\)).

noise_matrixndarray

Continuous-time noise matrix (\(p\) x 1).

observation_matrixndarray

Observation matrix (1 x \(p\)), selects the first state.