EM algorithm for linear state-space models

Computes the MLE parameter estimate for linear state-space models with the EM algorithm.

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Computes the maximum-likelihood estimate of A,B,R,E,F and Q in
Y(:,t) = A + B*X(:,t) + e(:,t), e(:,t)~N(0,R)
X(:,t) = E + F*X(:,t-1) + u(:,t), u(:,t)~N(0,Q)
where Y is a N by T vector of observables and X is a K by T unobserved state vector.
A structural parameter-expanded EM algorithm is used for computing one element of the parameter set estimate which is mapped to the unique point estimate in a normalized parameter space. Many popular normalizations (parameterizations) are supported. The algorithm implements a square-root Kalman filter. Overall, the SPX-EM algorithm is more robust and converges much faster than a standard EM algorithm. This first release has few bells and whistles: Please let me know of any additional features that might be useful to you. Report bugs or unexpected behavior as well...

Cite As

Sebastien Blais (2026). EM algorithm for linear state-space models (https://se.mathworks.com/matlabcentral/fileexchange/64585-em-algorithm-for-linear-state-space-models), MATLAB Central File Exchange. Retrieved .

General Information

MATLAB Release Compatibility

  • Compatible with any release

Platform Compatibility

  • Windows
  • macOS
  • Linux
Version Published Release Notes Action
1.0