AbstractInference problems in dynamically data-driven application systems use physical measurements along with a physical model to estimate the parameters or state of a physical system. Errors in measurements and uncertainties in the model lead to inaccurate inference results. This work develops a methodology to estimate the impact of various errors on the variational solution of a DDDAS inference problem. The methodology is based on models described by ordinary differential equations, and use first-order and second-order adjoint methodologies. Numerical experiments with the heat equation illustrate the use of the proposed error estimation machin- ery.