New GNSS applications demand resilience against radio interference and high position accuracy. Separately, these demands can be fulfilled by multi-antenna systems using spatial filtering and carrier phase positioning algorithms like Real Time Kinematics (RTK), respectively. However, combining these approaches encounters a severe issue: The spatial filtering induces a phase offset into the measured carrier phase leading to a loss of position accuracy. This paper presents a new approach to compensate the phase offset in a blind manner, i.e., without knowing the antenna array radiation pattern or the direction of arrival of the signals. The proposed approach is experimentally validated in two jamming scenarios. One includes a jammer with increasing power and the other includes a moving jammer. The results demonstrate that the approach successfully compensates for the phase offset and, hence, allows the combined use of RTK positioning and spatial filtering even under jamming.