Ground Alignment Mechanics for Stationary Inertial Navigation Systems
Stationary alignment extracts gravity and Earth rate vectors to initialize pitch, roll, and true north azimuth prior to unguided motion tracking.
State Covariance
Mathematical Coupling
Estimation error quantification characterizes the joint distribution of uncertainty within a dynamic filter. State covariance represents the second moment of this estimation error, providing the weight given to individual sensor measurements during correction steps. Large values indicate low confidence in the current prediction while small values suggest reliance on internal model dynamics.
Matrix Structure
Temporal propagation governs how this uncertainty develops between observation intervals. Transition dynamics transform the error distribution forward in time by applying the Jacobian of the motion model to the previous variance. External process noise adds diagonal entries that grow the uncertainty over time because physical systems never behave with absolute predictability.
Measurement Sensitivity
Sensor noise characteristics define the limits of this predictive accuracy during the update cycle. Residuals between the actual measurement and the predicted observation adjust the internal belief based on the relative strength of the two information sources. Proper tuning of these weights prevents the filter from diverging when sensor performance degrades due to environmental interference or hardware aging.
Validation Method
Observational consistency checks verify the actual performance of the estimator against the theoretical bounds provided by the variance diagonal. Discrepancies between expected error and observed deviation highlight unmodeled dynamics or calibration errors in the hardware chain. Calibration cycles identify these offsets and reset the error model to align with reality.
Stationary bias remains the primary challenge to the validity of the computed uncertainty bounds.