Geometric Error
Geometric errors in inertial measurement units arise when individual accelerometers are not located exactly at the center of rotation for the platform. The size-effect error describes the additional acceleration measured by a sensor due to its physical offset from the rotational axis. The unwanted signal is a function of the angular velocity and the distance between the proof mass and the pivot point.
Centripetal Force
Forces act on the offset sensor whenever the platform turns. If the size-effect error is not corrected, the system interprets these forces as linear movement, leading to inaccurate velocity calculations. The magnitude of the error depends on the square of the angular rate and the length of the effective lever arm.
For high precision navigation, these offsets are measured to within a fraction of a millimeter during the assembly of the inertial measurement unit.
Mathematical Correction
Compensation algorithms use the known lever arm distances and the current gyro data to subtract the induced acceleration. The calculation must be performed at high speeds to keep the data synchronized with the raw sensor outputs. The size-effect error correction is particularly important in systems that undergo rapid maneuvering or high frequency vibration.
Moving Center
Shifting the center of rotation during flight, such as in a gimbaled system, requires dynamic updates to the compensation parameters. Ensuring the stability of these corrections is a primary task for the integration team during the qualification phase.
