Discrete Kalman Process Noise Covariance Derivation from Inertial Bench Test Metrics
Bench Allan variance parameters convert to discrete Kalman process noise matrices by integrating state transition matrices over the sampling interval.
Discretization Error
Transformation Loss
Mathematical discrepancies occur when continuous-time models are converted into discrete-time equivalents for processing by digital computers. The magnitude of discretization error represents the difference between the true analytical solution of a differential equation and the numerical approximation produced by the discrete model. This gap is inherent in any system that replaces continuous integrals with finite sums.
Step Influence
Step size determines the magnitude of the approximation loss. When the interval between samples is reduced, the discretization error typically decreases, provided the numerical method is stable. However, extremely small intervals can lead to an accumulation of rounding errors from the processor.
Integration Choice
Integration choices influence how the error scales with the sampling period. Simple first-order methods like the Euler approximation result in a discretization error that is proportional to the time step, while higher-order methods reduce the error at a faster rate. Practitioners must select an integration scheme that balances the need for accuracy against the available computational cycles of the embedded hardware.
This selection is a trade-off between fidelity and speed.
Validation Requirement
Validation requirements necessitate the comparison of discrete outputs against high-fidelity continuous simulations. Accuracy is often quantified by analyzing the residuals between these two representations. If the discretization error exceeds the specified tolerance, the sampling rate or the integration method must be adjusted.