An offline methodology is presented: it simultaneously estimates dynamic origin-destination (O-D) matrices, without using assignment matrices that incorporate within-day transition equations. The proposed formulation and solution approach extends a calibration method recently developed that directly uses the output of any network loading model (such as a dynamic traffic assignment or simulation model) so that the complex relationships between O-D flows and model outputs are accurately captured (as opposed to the more common method of approximate linear relationships based on the assignment matrix). The study extends the original formulation by incorporating spatial and temporal relationships among various O-D flows (transition equations). These transition equations link O-D flow variables across time intervals in such a way that known structural demand patterns can be preserved in the new estimates. Such transition equations, although common in the context of real-time O-D flows, complicate the offline simultaneous estimation of O-D flows and have not been used to their full potential in the past. The approach is demonstrated through a case study.