For many airborne sensor applications, knowledge of the aerial platform's position and velocity assists in construction of the target image and mapping the resultant model onto a surveyed map. Since sensor data is processed during post-processing, emphasis is placed on an accurate trajectory estimate as opposed to a real-time navigation. In this paper we present a smoothing approach for integration of Inertial Measurement Unit (IMU) and Global Positioning System (GPS) pseudorange measurements in a tightly coupled UAV system. We combine all available sensor information in a probabilistic graph connected by a motion model that relates each state to its predecessor states. We then solve for a Maximum a Posteriori (MAP) estimate by finding the parameters that maximize the joint probability model derived from the probabilistic graph. An Iterative Least Squares (ILS) algorithm is used to solve for the parameters of the MAP estimate. In order to validate our algorithms, we set up an experimental test bed using an Asctec Pelican Quadrotor equipped a u-blox LEA-6T receiver. Implementing our algorithm on collected GPS Pseudorange and accelerometer flight data, we show that we can combine GPS code measurements and noisy IMU sensor data for smoother, more precise state estimates of a UAV's trajectory.