Inertial Navigation Solution Using Gyroscope and Accelerometer Outputs

To obtain the position, velocity, and attitude angles of an aircraft, the outputs from a gyroscope and accelerometer are processed through inertial navigation algorithms. This process typically involves implementing sensor fusion techniques such as Kalman filtering or complementary filtering to combine gyroscopic angular rate measurements with accelerometer-specific force data. The gyroscope outputs (angular velocities in rad/s) are integrated to track orientation changes through quaternion or rotation matrix propagation, while accelerometer readings (specific forces in m/s²) are double-integrated after gravity compensation to derive velocity and position. Key computational steps include coordinate transformations between body and navigation frames, attitude update using Rodriguez parameters or direction cosine matrices, and velocity/position propagation through numerical integration methods like Runge-Kutta. The implementation requires careful handling of sensor biases, noise reduction through digital filtering, and periodic calibration to maintain accuracy during extended navigation periods.