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We consider the problem of resolving overlapping pulses from noisymulti-snapshot measurements, which has been a problem central to variousapplications including medical imaging and array signal processing. ESPRITalgorithm has been used to estimate the pulse locations. However, existingtheoretical analysis is restricted to ideal assumptions on signal andmeasurement models. We present a novel perturbation analysis that overcomes theprevious theoretical limitation, which is derived without a stringentassumption on the signal model. Our unifying analysis applies to varioussub-array designs of the ESPRIT algorithm. We demonstrate the usefulness of theperturbation analysis by specifying the result in two practical scenarios. Inthe first scenario, we quantify how the number of snapshots for stable recoveryscales when the number of Fourier measurements per snapshot is sufficientlylarge. In the second scenario, we propose compressive blind array calibrationby ESPRIT with random sub-arrays and provide the corresponding non-asymptoticerror bound. Furthermore, we demonstrate that the empirical performance ofESPRIT corroborates the theoretical analysis through extensive numericalresults.

Stable estimation of pulses of unknown shape from multiple snapshots via ESPRIT