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A partitioned recursive algorithm for the estimation of dynamical and initial-condition parameters from cross-sectional data

Many practical applications require the simultaneous estimation of unknown dynamical parameters and unknown initial means and covariances from an ensemble of tests. A recursive algorithm which asymptotically obtains the maximum likelihood estimate of both sets of unknown parameters is presented. The computational requirements of the algorithm are greatly reduced by partitioning the parameter vector into initial and dynamical parameters and making use of a sufficient statistic as an intermediate variable for the estimation of initial condition parameters. This partitioning leads to a two-tier filter for calculating some of the required parameter sensitivities. The results are illustrated by an application to a simplified robotic system.