Include accumulated IMU error in prediction uncertainty
Receiver position error alone cannot describe an inertial prediction. Noise in an IMU (inertial measurement unit) accumulates as velocity, orientation and position error. This software component adds that contribution under explicit linearized assumptions, without fitting aircraft observations.
Scope
Use a nine-coordinate error state: position, velocity and small orientation error, each with three axes. Acceleration noise enters velocity; gyro noise enters orientation. A supplied constant three-by-three coupling maps orientation error into acceleration error. Supply full cross-axis noise spectral matrices; do not insert manufacturer performance numbers as raw-noise measurements.
Integrate this linear stochastic system analytically. Preserve the specified origin even when the first position observation is later, and preserve correlation across training and future times. Add the existing declared receiver covariance before any conditioning. Return the complete small-problem covariance in epoch-major three-coordinate order; cap the diagnostic at 512 epochs. Existing frozen error-model and streaming implementations remain unchanged.
Qualification
Focused deterministic tests compare the analytic transition and process covariance with a separate matrix-exponential and numerical-quadrature reference. Test irregular sampling, cross-axis signs, zero coupling, zero noise, three candidate coupling examples, a four-minute horizon, interval subdivision, time-origin preservation, positive definiteness with receiver error, coordinate transforms and invalid inputs. These small tests use one numerical thread, reserving one for the active growth screen. No optimizer or aircraft read runs.
Limits
This is a supplied Gaussian, linearized, white-driving-noise model, not an empirically established law for a recording. It does not establish that actual IMU quantization errors are independent, cover unknown onboard corrections, bound nonlinear stochastic propagation, or qualify an uncertain integration clock. Initial state uncertainty and constant calibration belong to the separate shared-calibration treatment; the component starts from zero stochastic error at the declared origin. Dependence between receiver and inertial noise is assumed absent, not demonstrated. Recording-length usefulness and whole-program numerical bounds remain separate requirements of V01.
Success here qualifies the component mathematics only. It does not open V02, change the 53-stretch findings or permit protected ESA outcome inspection.