A system is provided for tracking and maintaining an inventory of location of containers that are stored on cargo ships or in a container yard. The system includes one or more sensors, such as GPS and INS sensors for obtaining real-time position information, as well as a processor configured to automatically provide post processing to recover lost data and to correct erroneous data, such as when real-time position signals are blocked or distorted, the post processing performed by estimating trajectories and correcting the location errors. Post-processed positioning techniques are continuously applied to the stored position data to iteratively determine calibrated position locations to provide calibrated second trajectory segments in a real-time fashion. The calibrated second trajectories are then used to identify the errors in the past real-time position data as soon as a segment of the second calibrated trajectory becomes statistically trustworthy. Corrections can be automatically made in inventory locations stored in a database to correct position errors for the containers.