State Variance
Quantifying uncertainty in state prediction requires an explicit covariance matrix known technically as Kalman filter process noise, which models how unmodeled dynamics and external disturbances corrupt the system model between measurement updates. Dynamic systems undergo continuous physical shifts that defy perfect mathematical representation, introducing discrepancies that accumulate unless properly bounded by the covariance parameter. Selecting an appropriate spectral density value for this matrix determines how heavily the algorithm weights incoming sensor measurements against prior state predictions.
Low values force the estimator to trust the internal model excessively, leading to sluggish response times and persistent lag during rapid maneuvers. High values instruct the filter to discard the prediction model in favor of raw sensor data, leaving the output vulnerable to high-frequency measurement jitter.
Sensor Calibration
Hardware degradation introduces systematic biases that interact unpredictably with state estimation algorithms, necessitating careful tuning of error parameters during bench testing. Thermal drift in gyroscopes and accelerometers alters zero-bias offsets over operating temperature ranges, creating residuals that standard covariance matrices cannot absorb without adjustment. Technicians verify sensor performance against optical references on vibration tables, measuring noise spectral density profiles under controlled laboratory conditions to establish baseline parameters.
Uncompensated scale factor errors generate state estimation divergence during high-acceleration transients, forcing engineers to inflate the covariance bounds manually to maintain tracking stability.
Filter Divergence
Unmatched covariance settings cause the estimation error covariance to drop below the actual statistical variance of the system, leading to catastrophic filter divergence. Underestimated dynamics create overconfident state estimates that ignore genuine trajectory changes, effectively blinding the tracking loop to sudden maneuvers. Conversely, massive overestimation degrades the estimator into a simple low-pass filter, neutralizing the mathematical advantage of optimal recursive state reconstruction.
Analytical checks on the normalized innovation squared statistic reveal whether the chosen matrix accurately reflects unmodeled physical accelerations during field deployment.
Update Frequency
Sampling rates dictate the temporal granularity of state updates, directly influencing how system disturbances accumulate within the discrete-time covariance integration step. High-frequency loops reduce the magnitude of unmodeled acceleration occurring between consecutive epochs, allowing smaller covariance values to maintain stable tracking performance. Processing bottlenecks in embedded hardware often force lower update rates, expanding the time horizon over which unknown disturbances accumulate and demanding larger covariance bounds.
Computational latency introduces time-skew between sensor acquisition and filter execution, adding unmodeled phase error that degrades the nominal state trajectory.
