which pdf should be choose for a System Identification and prediction based on Expectation maximisation?

Hello to everyone!

well, i have read more than 10 papers on expectation maximization and likelihood, such as "System Identification of Nonlinear State-Space Models", by Thomas B. Schön& [...]. And i do understand the Em algorithm. My only problem to be able to implement it, is to know which pdf(probability density function) is to be used for system identification of a nonlinear model. Whitout this information i can't process, since one has to maximize log(P(theta)), in order to approximate the system parameters theta, where P(theta) is the probability density function, that depends of the predicted parameter!. Thanks for your help!

Answer 1

[José Goulart]

Armand,

To model a system using system identification, one approach commonly used is the so called prediction error approach, which consists in minimizing some cost function (usually quadratic) of the prediction errors defined as the difference between the response of the system and the response of the model.

For instance, when the model is linear in the parameters and the sum of the squares of the residuals (prediction errors) is chosen as the cost function, this leads to a least-squares approach, and this means that relatively simple and numerically robust algorithms can be used to estimate the parameters.

I am not completely sure, but it seems to me that the prediction error approach corresponds to a maximum likelihood one. Anyway, a good book on this subject is the one by Ljung called "System Identification: Theory for the user". I am sure you will find the answer there.