Constrained Maximum Likelihood Estimation of Initial Population Statistics from an Ensemble of Kalman Smoother Estimates

A method is presented for constrained maximum likelihood estimation of the initial mean and covariance of an otherwise known linear discrete time dynamical system. An obvious technique to use is to obtain Kalman smoother estimates of the initial conditions for each of a series of tests and then combine them into an estimate of the initial distribution. This may be implemented either as a special case of the Expectation-Maximization (EM) or Scoring methods of statistical parameter identification. It is shown here that constraints can be added which improve convergence and identifiability in practical applications. This is accomplished via a hybrid EM/Scoring algorithm which combines the best features of both approaches.