Time-dependent Origin-Destination (OD) matrices are an essential input to transportation models. A cost-efficient and widely used approach for estimating OD matrices involves the exploitation of flow counts from stationary traffic detectors. This estimation approach is also referred to as assignment-based OD matrix estimation because, typically, Dynamic Traffic Assignment (DTA) models are used to map the OD matrix to the link flows. The conventional DTA establish a complex non-linear relationship between the demand, and the link flows, adding an inherent complexity to the OD matrix estimation problem. In this paper, attempting to exploit the growing availability of Floating-Car Data (FCD), we suggest a solution approach that is based on a Data-Driven Network Assignment (DDNA) mechanism. The DDNA utilises the FCD from probe vehicles to capture congestion effects, providing a linear mapping of the OD matrix to the link flow observations. We present the results of two synthetic-data experiments that serve as proof of concept, indicating that if FCD are available, the computationally costly DTA may not be necessary for solving the OD matrix estimation problem. Abbreviations APR: average penetration rate; DDNA: data driven network assignment; DDNL: data driven network loading; DODME: dynamic OD matrix estimation; DTA:dynamic traffic assignment; FCD: floating-car data; ITS: intelligent transportationsystems; NNLSQ: non-negative least squares; OD: origin destination; ODME: ODmatrix estimation; PV: probe vehicle; RUM: random utility model