Use covariance weights in hyperspherical arbitrary-noise prediction

[FlorianPfaff]

Summary

• use Merwe covariance weights (Wc) when computing covariance in HypersphericalUKF.predict_nonlinear_arbitrary_noise()
• keep the probability-normalized Wm product weights for the predicted mean
• add a focused regression that compares against the explicit unscented-transform covariance

Root cause

The arbitrary-noise path constructed one Cartesian-product weight vector from points.Wm and reused it for both the mean and covariance. Merwe sigma points define separate mean and covariance weights; the central covariance weight includes the 1 - alpha^2 + beta correction. Reusing Wm therefore ignored beta entirely and could produce a negative diagonal covariance entry for a valid positive-definite prior.

Impact

Arbitrary-noise hyperspherical predictions now preserve the intended scaled-unscented-transform covariance. The reproduced two-dimensional identity case changes the first predicted variance from approximately -9.48e-4 to the correct positive value 4.26e-3.

Validation

• added tests/filters/test_hyperspherical_ukf_covariance_weights.py
• ran the regression against a main-equivalent method: failed with the incorrect negative variance
• ran the same regression against the patched method: 1 passed
• compiled the patched module and regression with python -m py_compile
• ran ruff check --select F821,F822,F823 on both changed Python files: passed
• GitHub Actions matrix is queued for the draft PR

[github-actions]

✅MegaLinter analysis: Success

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