Euler Error Analysis According to Sensor Error Factors for Accelerometer- and Magnetometer- Based Arbitrary Stationary Alignment

In attitude and heading reference systems that rely on inertial measurement units, stationary alignments are performed to determine the initial orientation of the sensor frame relative to the navigation frame. The accuracy of stationary alignment is influenced by sensor error factors, but there have been few studies on describing and analyzing Euler angle errors across various sensor orientations. This study presents a method for analyzing Euler errors according to the sensor error factors during arbitrary stationary alignments using accelerometer and magnetometer signals. We employed three-axis attitude determination (TRIAD) algorithm for stationary alignment and considered three primary error factors: scale error, installation error, and offset error, including noise and bias. This study conducted sensor-aligned and sensor-misaligned simulations, where the Euler angles were 0° and arbitrary, respectively. In the sensor-aligned simulations, the difference between the analytical and numerical methods was less than 0.001°, indicating that the inaccuracy introduced by the linearization in the analytical method is negligible. The sensor-misaligned simulations demonstrated that the proposed method is effective for analyzing Euler angle errors across different sensor orientations.