Parameter estimation via weak measurement with machine learning

Abstract

Weak measurement technique can provide high sensitivity for parameter estimation tasks. However in practice, time-varying errors induced by noises significantly compromise its advantages. While prolonging the measurement time can reduce the effect of short-term correlated noises (e.g. white noise), it will on the other hand increase the estimation errors in the presence of long-term correlated noises(e.g. 1/f and 1/f2 noises). The main obstacle of compensating these kind of errors is to precisely predict the time-varying trend of error, where the disturbances that causing error are highly unpredictable. In this work, we propose a weak measurement scheme with assistance of machine learning algorithm, which can ‘learn’ the time-varying trend of errors from data without an explicit model. In order to verify the feasibility of this scheme, we carry out a time-delay measurement experiment and achieve the noise compensation via machine learning algorithm. Experimental results demonstrate a 6 dB reduction of mean-square error comparing to the setup without machine learning, which suggest that our scheme can effectively improve the performance of weak measurement in the presence of long-time correlated noises.