Efficient estimation of initial-condition parameters for partially observable initial conditions

Efficient and numerically well-conditioned scoring algorithms are presented for the maximum-likelihood estimation of initial means and covariances from an ensemble of tests when the initial condition is not observable per test. These algorithms take account also of the possibility that the estimated initial covariance may be singular. A sufficient statistic is used to reduce the computational burden and singular-value-decomposition and square root techniques are used to increase the numerical accuracy of the algorithm.