Fix IMU covariance whitening with nonzero Coriolis

[dellaert]

With nonzero omegaCoriolis, IMU prediction already converts transported velocity back to physical velocity, but the residual covariance omitted the corresponding conversion into the body-frame error coordinates. This PR applies that conversion to ordinary and Combined IMU-factor whitening across all four preintegration backends.

Provenance and behavior

This omission was found while auditing the rotating-Earth covariance/NEES path following #2774. The rotating predictor uses v_bar = v + omega × p, then projects back to physical v. Covariance previously stopped before that projection. The missing Jacobian block is H(v,p) = -Rᵀ[omega]×R: it both expresses the navigation-frame rotation rate in the endpoint body frame and carries position uncertainty into physical velocity uncertainty. This is more than a rotation of the covariance axes.

Apply H P Hᵀ after the existing backend-chart conversion, retaining the Combined factor's bias-sign convention and navigation–bias cross-covariances. Raw preintegration covariance, mean prediction, and nonlinear residuals are unchanged. When omegaCoriolis is unset or zero, the additional conversion is identity.

The new residualCovarianceAt(predictedAttitude) accessor and factor constructor overloads let callers freeze whitening at their nominal endpoint attitude. With nonzero omegaCoriolis, the recommended argument is pim.predict(nominalState_i, nominalBias_i).attitude(). Existing constructors remain available and use prediction from identity at biasHat(); this fallback can give different whitening for a differently oriented initial state. Whitening stays fixed during optimization. The shared interface exposes the accessor and constructors in Python and MATLAB, and the NEES helper calls the wrapped C++ accessor directly.

Evidence

RotatingMeasurementSensitivity independently differentiates the complete integrate/predict/Logmap path with respect to each accelerometer and gyroscope sample, then propagates the sample-noise covariance through those numerical derivatives. Its reference does not use the covariance conversion or its analytic Jacobian. It covers all four backends, zero/Earth/exaggerated frame rates, and identity/rotated initial states, and explicitly checks that the former covariance fails the same nonzero-rate comparison.

An additional before/after probe uses only the existing residualCovariance() API. The same source was compiled against the original headers at d56360ce6 and the fixed headers, holding integration and prediction code constant. Relative Frobenius covariance error against the numerical reference was:

Backend	Before: Earth rate	Before: stress rate	After: maximum over all three rates
Manifold	1.389e-5	8.148e-2	5.220e-10
Tangent	1.388e-5	8.146e-2	7.490e-10
Lie group	1.389e-5	8.148e-2	5.220e-10
Galilean	1.131e-5	7.151e-2	9.851e-10

The rates have norms 0, 7.295e-5, and 0.539 rad/s; the last deliberately amplifies the defect. Zero-rate results are identical before and after. These are deterministic covariance discrepancies, not Monte Carlo NEES improvements. They establish the omitted first-order transformation directly.

The Galilean regression additionally checks the inverse-lift Jacobian numerically, full 15D cross-covariances, covariance symmetry/positive semidefiniteness, fixed whitening, and factor Jacobians at finite residuals.

Experiment context: NEES notebook and Logmap results report.

Validation

• testGalileanImuFactor, testImuFactorCovariance, testImuFactor, and testCombinedImuFactor pass on the updated develop base.
• Python source-tree suite against the rebuilt wrapper: 553 passed, 20 skipped; focused IMU wrapper tests: 12 passed, 33 subtests passed. The build-directory python-test target encountered one stale, deleted-source MatrixWeightedLocalizationExample test referring to an absent dataset; running the current source tests passes.
• MATLAB wrapper rebuilt; testRotatingImuCovariance passes actual accessor and constructor/whitening calls, including unset, zero, and nonzero omegaCoriolis.
• Reexecuted the 3,000-trial rotating-Earth notebook section and refreshed its table/plot and Markdown report. Physical RMS errors are unchanged; specified-rate mean NEES rounds from 14.012 to 14.011 for Manifold/Tangent/Lie group, while Galilean remains 9.090. Other experiments were not rerun.
• git diff --check passes.