We present an alternative technique for estimating the response of a cold atom interferometer (CAI). Using data from a conventional inertial measurement unit (IMU) and common strapdown terminology, the position of the atom wave packet is tracked in a newly introduced sensor frame, enabling hybridization of both systems in terms of acceleration and angular rate measurements. The sensor frame allows for an easier mathematical description of the CAI measurement and integration into higher-level navigation systems. The dynamic terms resulting from the transformation of the IMU frame into the CAI sensor frame are evaluated in simulations. The implementation of the method as a prediction model in an extended Kalman filter is explained and demonstrated in realistic simulations, showing improvements of over two orders of magnitude with respect to the conventional IMU strapdown solution. Finally, the implications of these findings for future hybrid quantum navigation systems are discussed.