Adaptive Feedback Cancellation (AFC) methods are used to find an FIR filter to cancel the negative effect of acoustic feedback between the loudspeaker and microphone of the hearing aid. Finding the AFC filter of appropriate order/length directly affects the performance and complexity of the system. In this paper, we use noise injection method to find the AFC filter estimating the feedback path model. We show that the optimum length which guarantees a good compromise between the quality and the complexity of the system may be smaller than the length of the actual feedback path model. However, in order to improve the performance of the system in terms of Misalignment criterion, we propose using multiple short-time noise injections and averaging method to find the best filter estimate of appropriate length.