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Weak measurement is a novel technique for parameter estimation with higherprecision. In this paper we develop a general theory for the parameterestimation based on weak measurement technique with arbitrary postselection.The previous weak value amplification model and the joint weak measurementmodel are two special cases in our theory. Applying the developed theory, thetime-delay estimation is investigated in both theory and experiment.Experimental results shows that when the time-delay is ultra small, the jointweak measurement scheme outperforms the weak value amplification scheme, and isrobust against not only the misalignment errors but also thewavelength-dependence of the optical components. These results are consistentwith the theoretical predictions that has not been verified by any experimentbefore.

Ultra-small phase estimation via weak measurement technique with postselection