A theoretical method for analyzing the observability of a strapdown inertial navigation system (SDINS) integrated with the global positioning system (GPS) is proposed. The analysis is performed based on two types of maneuvers for a vehicle on a horizontal trajectory: level flight with constant north velocity and level flight with constant east velocity. The observability also is analyzed using the convergence theorem, stationary state observability analysis results, and Kalman filter measurement information to rearrange the SDINS error model equation. The state variables are divided into observable and unobservable parts, and determine which state variables are observable and estimable with some errors from the relationship of observable and unobservable state variables. Our results have shown that the north and east axes accelerometer bias errors were unobservable, and that attitude errors, and east and down axes gyro bias errors were estimable with some unknown bias errors. It has been shown that horizontal maneuvering improves the observability of down axis gyro bias error compared with the stationary state, and the estimation errors of the heading error state and east axis gyro bias error are dependent on the magnitude of north velocity. The results of the theoretical observability analysis are confirmed through computer simulation.