## 1 Introduction
Starting with a gravity model and the initial values for position, velocity, and orientation, the computer operates on the IMU's outputs to furnish the current position, velocity, and orientation [9]; thus, an INS is a sophisticated implementation of dead reckoning [10]. The INS-based position, velocity, and orientation estimates have high short-term accuracy, have unbounded errors (i.e., drift due to accumulation of errors), and are dependent on previous estimates. Capitalizing on the complementary characteristics of GNSS and INS, their synergistic integration overcomes their individual drawbacks and provides a more accurate and robust navigation solution than either could achieve on its own [9]. Estimation techniques, predominantly based on Kalman filtering, are employed to optimally fuse the GNSS and IMU observations to yield a reliable navigation solution [ibid]. The optimization techniques are classified as either loosely coupled, tightly coupled, or ultra-tightly coupled, and indicate how and what information from each system is used to improve the accuracy, precision, and robustness of the fused navigation solution. Each technique has an associated level of complexity, achievable accuracy and precision, and application suitability. Table 1 summarizes the important and complimentary characteristics of GNSS and INS. The navigation solution--commonly referred to as a trajectory--contains the time-tagged position estimates (e.g., latitude, longitude, and ellipsoidal height), angular orientation estimates (e.g., roll, pitch, and heading), and velocity estimates for the GNSS/INS sensor. These estimates are commonly reported at rates of 200 Hz or higher. The highest accuracy position estimates are achieved when differential GNSS techniques based on the carrier phase observable are used, provided the carrier phase ambiguity terms are resolved to their correct integer values. High accuracy roll and pitch orientation estimates are achieved when the direction of gravity is precisely determined by the accelerometers, which is improved when GNSS measurements are used to account for the impact of dynamic motion on the accelerometer readings [11]. Unlike the roll and pitch estimates, which are measured with respect to the direction of gravity, the heading orientation estimate is measured with respect to the geographic (true) north direction. Common approaches used by GNSS/INS sensors for determining the true north direction include using additional hardware sensors (e.g., a magnetometer or a GNSS compass) and data-driven methods (e.g., GNSS course over ground, gyro-compassing, and dynamic alignment) [11; 12; 13]. For single-antenna GNSS/INS sensors, a combination of a triaxial magnetometer and dynamic alignment is widely employed for heading determination. This type of GNSS/INS sensor loses the observability of heading during low-dynamic or static situations in which dynamic alignment becomes impossible and commonly falls back on the lower accuracy magnetometers' observations to continue stabilizing heading [11]. For dual-antenna GNSS/INS sensors, a combination of a GNSS compass and dynamic alignment are commonly used for heading determination. A GNSS compass can determine the relative displacement (i.e., vector) between two GNSS antennas to millimeter-level precision in real-time using carrier phase measurements and does not require sensor motion as is the case for dynamic alignment [11]. However, the fixed distance between the GNSS antennas--referred to as the compass baseline length--affects the achievable precision of the heading estimate. As the distance between GNSS compass antennas is decreased, with short distances often unavoidable onboard a UAS (<1 m typical), the heading precision improvement provided by the GNSS compass will diminish. In practice, dual-antenna GNSS/INS sensors rely on dynamic alignment when available but during periods of low-dynamics, the GNSS compass solution is used instead [11].