Cyclic seesaw optimization with applications to state-space model identification

In cyclic (or alternating) method, the full parameter vector is divided into two or more subvectors and the process proceeds by sequentially optimizing each of the subvectors while holding the remaining parameters at their most recent values. One example of the advantage of the scheme is the preservation of large investments in software while allowing for an extension of capability to include new parameters for estimation. A specific case involves cross-sectional data represented in state-space form, where there is interest in estimating the mean vector and covariance matrix of the initial state vector as well as parameters associated with the dynamics of the underlying differential equations (e.g., power spectral density parameters). This paper shows that under reasonable conditions the cyclic scheme will converge to the joint estimate for the full vector of unknown parameters. Convergence conditions here differ from others in the literature.