A GLRT and bootstrap approach to detection in magnetic resonance force microscopy

Magnetic resonance force microscopy (MRFM) is a technology that will potentially enable microscopy of molecules and proteins at atomic-scale detail. Physicists are pursuing MRFM and single electron spin microscopy (SESM). Many technological challenges exist for MRFM and SESM to deliver on the promise of "visualizing" a single electron spin. The forces of interest are in the subattoneNewton and attoneNewton range (10^-18 N). In this paper we consider the problem in MRFM and SESM of detecting extremely weak signals buried in noise with SNR in the range of -15 dB to -40 dB. We describe a model that, although simplistic, captures the features of the problem. We present a GLRT and bootstrap approach that incorporates a bank of Viterbi algorithms, and show by simulations that, with physically realistic parameter values, the detector can achieve probability of detection β = 0.9 with false alarm rate α = 0.05, at SNR= -20 dB.