Stability and Super-Resolution of MUSIC and ESPRIT for Multi-Snapshot Spectral Estimation

This paper studies the spectral estimation problem of estimating locations a fixed number point sources given multiple snapshots Fourier measurements collected by uniform array sensors. We prove novel stability bounds for MUSIC and ESPRIT as function noise standard deviation, snapshots, source amplitudes, support. Our most general result is perturbation bound signal space in terms minimum singular value matrices. When are located several separated clumps, we provide an explicit upper noise-space correlation error support Super-Resolution Factor (SRF). The then compared with new Cram\'er-Rao lower clumps model. As result, show that comparable to optimal unbiased estimator(s) dependence on noise, SRF. byproduct our analysis, discover fundamental differences between single-snapshot multi-snapshot problems. theory validated numerical experiments.