This paper describes the reconstruction of postflight trajectories of suborbital free flying units by using logged GPS raw data. We took the reconstruction as a global least squares optimization problem, using both the pseudo-range and Doppler observables, and solved it by using the trust-region-reflective algorithm, which enabled navigational solutions of high accuracy. The code tracking was implemented with a large number of correlators and least squares curve fitting, in order to improve the precision of the code start times, while a more conventional phased lock loop was used for Doppler tracking. We proposed a weighting scheme to account for fast signal strength variation due to free-flier fast rotation, and a penalty for jerk to achieve a smooth solution. We applied these methods to flight data of two suborbital free flying units launched on REXUS 12 sounding rocket, reconstructing the trajectory, receiver clock error and wind up rates. The trajectory exhibits a parabola with the apogee around 80 km, and the velocity profile shows the details of payloadwobbling. The wind up rates obtained match the measurements from onboard angular rate sensors.