INS Error Model

The Schuler period (84 minutes) is a natural resonance in a horizontal INS embedded in a gravity field. A horizontal position error causes a pendulum-like oscillation of velocity and heading. The error-state Kalman filter models this oscillation explicitly and can damp it through external updates (e.g., GNSS corrections). Tuning the filter gain correctly ensures the oscillation is damped, not excited.

A constant bias (bias) is a fixed offset in sensor output; it causes position error to grow quadratically. Bias instability (often called random walk) is a time-varying bias driven by white noise; it causes heading error to grow over time. The error model treats these differently: constant bias is a state to be estimated, while random-walk bias appears as a white-noise driving term.

Process noise (Q) models unmodeled dynamics and sensor noise accumulation; measurement noise (R) models external reference uncertainty. Start with manufacturer specs (IMU noise density, GNSS accuracy) and adjust via Monte-Carlo simulation or empirical data fitting. Too large Q causes filter to trust INS too much; too large R causes filter to over-correct to external data.

Yes, for simple applications. A complementary filter is faster to implement and tune but is suboptimal (does not minimize mean-squared error). The INS error model justifies using a Kalman filter when performance guarantees, certification, or operation near limits is required.