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.
Axis Non Orthogonality
Geometric Deviation
Angular misalignment between the nominal sensing axes of a multi-axis instrument defines the geometric defect of the transducer assembly. This physical imperfection, known as axis non orthogonality, introduces cross-axis sensitivity where acceleration or rotation along one axis registers on another. The error prevents the sensing axes from forming a perfect Cartesian coordinate system.
Measurement Protocol
Laboratory calibration against a known rotation or gravity vector isolates these alignment errors from other sensor biases. During this procedure, the practitioner rotates the sensor through a series of precise positions. The resulting dataset allows the estimation of the off-diagonal terms in the coupling matrix.
This matrix maps the raw, skewed sensor outputs to an idealized, orthogonal frame of reference.
Mathematical Model
Representation of the misalignment typically uses a matrix of small-angle approximations to scale and rotate the raw measurements. Since the error is deterministic, applying the inverse of this calibration matrix removes the cross-coupling mathematically before the data enters downstream navigation algorithms. Without this adjustment, the cross-talk acts as a source of drift that degrades long-term trajectory estimation in inertial navigation.
Performance Impact
Uncorrected coupling generates errors that scale with the magnitude of the applied dynamics. For example, high acceleration along the longitudinal axis yields spurious lateral signals, which corrupts the heading calculation.