Analytical Error Bounds in Static Leveling and Gyrocompassing Systems
Analytical error bounds combine accelerometer bias tilt projection and latitude secant gyrocompassing equations to establish deterministic spatial uncertainty limits.
Gravity Projection
Vector Resolution
Resolution of the local gravitational acceleration vector onto the sensing axes of an accelerometer defines the static orientation of an instrument. This components of acceleration, representing the gravity projection, provides the primary reference for determining pitch and roll angles. It acts as an absolute tilt sensor when the device is otherwise stationary.
Tilt Sensitivity
Measurement accuracy of the inclination depends heavily on the angle of the sensor relative to the gravity vector. When a sensing axis is parallel to the ground, the projection is highly sensitive to small angular changes. Conversely, when the axis aligns directly with the gravity vector, the cosine response makes it insensitive to small tilts.
Inertial Compensation
Distinguishing between actual linear acceleration and the gravitational component requires advanced filtering or secondary sensor inputs. In a moving vehicle, horizontal acceleration registers on the sensor in the same manner as tilt, which causes a measurement ambiguity. Integrating gyroscopes allows the system to track rotation and subtract the gravity vector from the total measured acceleration.
Reference Frame
Standard calibration routines establish the zero-tilt output by rotating the sensor through a full circle in the gravity field. This procedure determines both the scale factor and bias of the accelerometer.