Adaptive Filtering (LMS / RLS time-varying system identification) L1-395
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
A desired signal d[n] is modeled as the output of an unknown time-varying linear filter h*[n] applied to a known reference input x[n], plus measurement noise; the adaptive filter iteratively updates an estimate h_hat[n] so that the error e[n] = d[n] - h_hat[n]^T x[n] is minimized in expectation.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- in expectation when x[n] is persistently exciting
- Stability:
- conditional
- κ:
- 500
LMS converges in mean for 0 < mu < 2/lambda_max; RLS converges in one step for stationary deterministic input; tracking error scales with non-stationarity rate.
Solvability C
- Solver class:
- LMS, NLMS, Sign-LMS, Affine-Projection (AP), RLS, Fast-RLS, Kalman-filter-based, learned (Meta-LMS)
- Convergence rate q:
- 1
- Complexity:
- LMS: O(L) per sample; NLMS: O(L); RLS: O(L^2); Fast-RLS: O(L)