## 1 Introduction  
Three-dimensional mapping of natural or built environments using high-resolution light detection and ranging (lidar) sensors onboard unoccupied aerial systems (UAS) is now a common practice. Recent advancements in robotics and real-time computing have led to the possibility of autonomous UAS-lidar mapping operations in global navigation satellite system (GNSS)-denied environments (e.g., underground mines) [1]. However, the more common application of autonomous UAS-lidar mapping still occurs in outdoor environments [2]. For observations collected from a moving lidar sensor to produce an accurate digital representation (i.e., point cloud) of the physical environment that is scanned, the time-dependent positions and orientations of the lidar sensor with respect to a fixed reference frame are needed. The most widely used approach to determining these positions and orientations is to collect data with a GNSS-aided inertial navigation system (GNSS/INS) [3]. As a result of advancements in the miniaturization of electronics, GNSS/INS sensors containing high-accuracy GNSS receivers and micro-electro-mechanical system (MEMS)-based inertial measurement units (IMUs) are now commercially available for UAS applications [4; 5]. Using direct georeferencing (DG), lidar observations are fused with GNSS/INS-derived positions and orientations based on a common time reference to produce a georeferenced point cloud [6]. To investigate the positional precision of a point cloud produced by a DG UAS-lidar mapping system, the positioning and navigation aspects of GNSS and INS must be examined. A GNSS receiver can estimate position, velocity, and time (PVT) by observing encoded radio frequency (RF) signals from a constellation of medium Earth-orbit satellites. The encoded RF signal from each satellite allows a GNSS receiver to estimate the signal's travel (transit) time, the satellite's clock error, and the position of the satellite when the signal was transmitted within a global reference frame. The transit time estimates are multiplied by the speed of light to produce range estimates between the GNSS receiver and the satellites. However, the transit time estimates are all biased by a common systematic error known as the receiver's clock offset. By observing encoded RF signals from a minimum of four satellites, a GNSS receiver can simultaneously estimate its clock offset to a precision of less than 30 nanoseconds [7] and its three-dimensional (3D) position within a global reference frame. The encoded RF signals also allow a GNSS receiver to measure the respective Doppler frequency shift for each observed signal. The Doppler frequency shifts of the received signals are produced by the user-satellite relative motion and enable velocity estimates with a precision of a few centimeters per second to be realized [8]. If time-differenced carrier phase (TDCP) methods are used, the precision of the velocity estimates can improve to a few millimeters per second [ibid.]. The GNSS-based PVT estimates have high long-term accuracy, have bounded errors (i.e., no drift), and are independent of previous estimates. An INS consists of triads of orthogonally mounted accelerometers and gyroscopes, collectively called an IMU, in addition to mechanization algorithms, a gravity model, and a computer [9]. The accelerometers are used to measure the specific forces (i.e., non-gravitational accelerations) experienced relative to the orthogonal sensing directions. Integrating the acceleration measurements with respect to time produces velocity estimates and a second integration with respect to time produces position estimates within a local reference frame. The gyroscopes measure the angular rates regarding the orthogonal sensing directions. Integrating the angular rate measurements with respect to time produces angular orientation estimates for the sensing directions within a local frame.