Acoustic rake filters perform coherent summation of the early room reflections using beamforming, with the aim of improving beamforming performance. This concept has been investigated for speech enhancement applications, improving noise reduction and late reverberation attenuation. Current studies typically assume that the parameters of the early reflections, such as the direction-of-arrival, delay and amplitude, are known in advance in the rake filter design. This work presents a novel investigation of the acoustic rake filter in a more practical context, focusing on the minimum variance distortionless response (MVDR) formulation. First, the sensitivity of the filter performance to perturbations in the reflection parameters is derived analytically, and investigated numerically using Monte Carlo simulations with a spherical microphone array. Then, an end-to-end example of rake filtering in a blind scenario is presented, where the reflection parameters are estimated from speech signals without any prior information. This example demonstrates for the first time the use of rake filtering in a realistic scenario.