  Parameter estimation in ordinary differential equations, although applied and
refined in various fields of the quantitative sciences, is still confronted
with a variety of difficulties. One major challenge is finding the global
optimum of a log-likelihood function that has several local optima, e.g. in
oscillatory systems. In this publication, we introduce a formulation based on
continuation of the log-likelihood function that allows to restate the
parameter estimation problem as a boundary value problem. By construction, the
ordinary differential equations are solved and the parameters are estimated
both in one step. The formulation as a boundary value problem enables an
optimal transfer of information given by the measurement time courses to the
solution of the estimation problem, thus favoring convergence to the global
optimum. This is demonstrated explicitly for the fully as well as the partially
observed Lotka-Volterra system.
