Take the Levenberg-Marquardt step from the Jacobian, not the normal matrix - #536
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Forming B^T W B squares the condition number of the least-squares problem.
For a six-parameter orbit that is survivable, but adding a non-gravitational
amplitude is not: A2 is of order 1e-14 au/day^2 and shares an unscaled matrix
with positions of order 1 au, so on (6489) Golevka cond(sqrt(W) B) = 2.6e10
becomes cond(B^T W B) = 9.2e19 -- four orders past what double precision
resolves. The solve then rank-truncates without complaint: the three position
components of the step come back as exactly zero and the non-grav amplitude
never leaves its seed.
Solve the equivalent damped least-squares problem
min || [ sqrt(W) B ; sqrt(lambda) I ] dX - [ -sqrt(W) r ; 0 ] ||
by Householder QR instead. The step is the same one; the condition number is
merely no longer squared. A sequential-update prior (issue #419) enters
exactly, as Cholesky rows.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
This was referenced Sep 3, 2026
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Closes #535.
Replaces the normal-equation solve with a Householder QR of the augmented weighted Jacobian,
which is the same damped step with the condition number no longer squared. A sequential-update prior (#419) enters exactly, as Cholesky rows. BᵀWB is still formed for the covariance and the conditioning check.
Full suite green (549 passed). Cross-check: solving the normal equations after Jacobi equilibration gives bit-identical A2 on all seven test fits, so both routes reach the same least-squares solution.
Two follow-ups this exposes are filed separately: the weak-constraint guard tests the whole correlation matrix rather than the non-grav direction, and the 1e-15 A2 placeholder is not dynamically negligible.
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