Unscented Kalman Filter (UKF) L1-429
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.
Forward model E
Sigma points X_i = {x_hat, x_hat ± \sqrt{(n+kappa)\cdot P)}; Y_i = h(X_i); y_hat = sum w_i Y_iUnscented Kalman Filter (UKF): UKF: deterministic sigma-point approximation propagates Gaussian through nonlinear system to 3rd order accuracy. The forward operator produces the measurement through a 3-node primitive DAG (S.ukf.sigma_points_UT…); recovery is posed as a nonlinear_inverse problem. Difficulty tier delta=3 with effective condition number kappa_eff~50; heavy_tail_distribution, rank_deficient_covariance set the accuracy floor at the Omega boundary. See the forward_model field for the closed-form equation.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 1000
Existence of the recovered nonlinear_state_estimate is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 50); heavy_tail_distribution dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.
Solvability C
- Solver class:
- sequential-filter [UKF_Wan_Merwe or SRUKF_square_root]
- Convergence rate q:
- 2
- Complexity:
- O(n ** 3) per step (2n+1 sigma points each requiring f evaluation) per iteration