An apparatus includes an inertial measurement unit (IMU) configured to generate information identifying accelerations and changes in angular orientation associated with an object in motion. The apparatus also includes at least one processor configured to identify a navigation state of the object within an Earth-fixed frame of reference using the information and perform one or more navigation functions based on the navigation state. To identify the navigation state of the object, the at least one processor is configured to use (i) an object body or IMU-to-inertial transformation that is updated based on the changes in angular orientation and (ii) an inertial-to-Earth-fixed transformation. The navigation state of the object may be identified in each of multiple iterations, and the at least one processor may be configured to update the inertial-to-Earth-fixed transformation during the iterations.