Originally the Accumulated State Density (ASD) has been proposed to provide an exact solution to the out-of-sequence measurement problem. To this end, the posterior of the joint density of all states accumulated over time was derived for a single sensor scenario. An exact solution for T2TF has been published as the Distributed Kalman Filter (DKF). However, the DKF is exact only if global knowledge in terms of the measurement models for all sensors are available at a local processor. This paper demonstrates that an exact solution for T2TF can also be achieved as a convex combination of local ASDs generated at each node in a distributed sensor system. This method crucially differs from the DKF, in that an exact solution is achieved without each processing platform being required to have knowledge of the global information. Therefore, this theoretical development has significant potential for achieving exact T2TF in practical problems. The resulting algorithm is called the Distributed Accumulated State Density (DASD) filter.