OKID¶

OKID function. (Book: Applied System Identification, Jer-Nan Juang, 1994)

modred.okid.OKID(inputs, outputs, num_Markovs)[source]¶

Approximates Markov paramters using arbitrary input and output data.

Args:

inputs: Array of input signals. Each row corresponds to a different input, each each column to a different time.

outputs: Array of output signals. Each row corresponds to a different output, each each column to a different time.

num_Markovs: Number of Markov parameters to estimate.

Returns:

Markovs_est: Array of Markov paramemters. Array dimensions correspond to times, outputs, and inputs, respectively. Thus Markovs_est[ti] is the Markov parameter at time index ti.

OKID can be sensitive to the choice of parameters. A few tips:

Use a tail (input=0) for your input/output data, otherwise the Markov parameters might grow rather than decay at large times.
If necessary, artificially append your data with zero input and exponentially decaying output.
Set num_Markovs less than or equal to half of the number of samples ( $num_Markovs <= num_samples / 2$ ). Estimating too many Markov parameters can produce spurious oscillations.
Data with more than one input tends to be harder to work with.