Direction-of-Arrival Estimation (narrowband array processing) L1-387
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
K narrowband plane-wave sources impinge on an L-element uniform linear (or arbitrary) sensor array; the array-manifold matrix A(theta) in C^{L x K} encodes the steering-vector per angle. Each snapshot is y[t] = A(theta) s[t] + n[t] with source vector s in C^K and sensor noise n ~ CN(0, sigma^2 I).
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- up to K < L (identifiability bound)
- Stability:
- conditional
- κ:
- 500
Identifiable when K <= L-1 for ULA; CRLB proportional to 1/(T * SNR * array_aperture); coherent sources require spatial smoothing; sub-wavelength (super-resolution) regimes rely on MUSIC/ESPRIT subspace projection or L1-min.
Solvability C
- Solver class:
- beamforming (conventional, Capon/MVDR), MUSIC, Root-MUSIC, ESPRIT, SPICE, L1-SVD, sparse Bayesian, ML grid-search
- Convergence rate q:
- 2
- Complexity:
- MUSIC: O(L^3 + L^2*T + L*Ngrid); ESPRIT closed-form; L1-min O(Ngrid^3) or O(K^2 * L * Ngrid) with OMP