Inertial Navigation System Lever Arm Effect Algorithm

In inertial navigation systems, particularly during strapdown inertial navigation system (SINS) processing, the lever arm effect represents a significant error source that cannot be overlooked. The lever arm effect occurs when the inertial measurement unit (IMU) installation position doesn't coincide with the vehicle's rotation center, causing the IMU to experience different linear acceleration from that at the rotation center due to the vehicle's angular motion. This phenomenon directly impacts navigation accuracy, especially in high-dynamic environments.

The compensation algorithm for lever arm effects typically involves several critical steps: First, precise measurement of the lever arm vector between the IMU installation position and the vehicle's rotation center is required. Second, during attitude calculation, the additional acceleration caused by the lever arm effect is computed using the vehicle's angular velocity information. Finally, this additional acceleration component is subtracted from the original acceleration measurements to obtain the true acceleration at the rotation center. Implementation-wise, this requires vector cross product operations between angular velocity and lever arm vectors, typically handled through matrix transformations in the navigation algorithm.

For strapdown inertial navigation systems, lever arm effect compensation is typically synchronized with the attitude update algorithm. Algorithm implementation requires consideration of coordinate system transformations, usually involving the conversion of the lever arm vector from the IMU coordinate system to the navigation coordinate system. This transformation is commonly achieved through direction cosine matrices or quaternion operations. Additionally, under high-dynamic conditions, second-order small quantity effects must be considered to ensure compensation accuracy, which may involve Taylor series expansion or higher-order integration methods in the numerical implementation.

In practical applications, the effectiveness of lever arm effect compensation is closely related to the calibration accuracy of the lever arm vector. Therefore, the initial calibration of the lever arm during system installation represents a critical phase, typically requiring specialized calibration equipment or calibration algorithms. Modern inertial navigation systems, with advancements in navigation algorithms, can now achieve real-time, efficient lever arm effect compensation, significantly enhancing navigation accuracy in high-dynamic environments through optimized computational methods and efficient matrix operations.