An acoustic feedback cancellation scheme in digital hearing aids is proposed.In this scheme

a pre-filter is introduced to solve the correlation problem between the receiver signal and the microphone signal

and make sure the unbiased convergence of the adaptive estimation algorithm.Moreover

adaptive projection subgradient method（APSM）is proposed to estimate the feedback path.Compared to the traditional NLMS algorithm

the proposed scheme has achieved better performance including fast speed

accurate precision and robust to noises.Simulations using both white noises and real speech segments show that the proposed scheme always convergent to the correct paths whether the long room feedback path or the short feedback path within the hearing aids is estimated.