Stabilize Merwe sigma-point scaling for small alpha - #4287
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Closing as duplicate of #4289. The latter is the preferred Merwe sigma-point cancellation fix. |
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Summary
alpha**2 * (n + kappa)n + (alpha**2 * (n + kappa) - n)ValueErrorsalphaBug
MerweScaledSigmaPointsfirst formedFor sufficiently small but representable positive scales, subtracting and re-adding
ncauses catastrophic cancellation. Withn=2,kappa=0, andalpha=1e-9, the mathematically correct scale is2e-18, but the current implementation roundslambda_to-2.0and reconstructsscaleas exactly0.0. Construction then fails with division by zero, and sigma-point generation would collapse the spread.Fix
Compute the positive scale directly and reuse that value for both weights and Cholesky scaling. This preserves the intended formula without the cancellation-prone round trip through
lambda. The implementation also validates that the resulting scale and weights remain finite.Validation
0.0, direct scale2e-18sqrt(2e-18)python -m py_compilepasses for the modified source and regression testmainand zero behind