Because a modular motor drive is composed of multiple identical pole drive units and controllers, it can be considered as a multi-agent system. This makes modular motor drives particularly interesting during faults, when the remaining healthy agents assure the continuity of operation. Nevertheless, for some crucial information such as the rotor position, these drives still rely on a single sensor which introduces a single point of failure. In this work, this single high-resolution position sensor is replaced by multiple binary, low-resolution position sensors. A vector tracking observer algorithm, implemented in the different controllers, processes this low-resolution sensor data into a position estimate. Subsequently, these position estimates of the different agents are exchanged with other agents using a distributed averaging algorithm. For this latter approach, it is shown in this work that it improves the position estimation under healthy conditions as well as during agent malfunctions. The concept is demonstrated on a modular axial-flux permanent magnet synchronous machine with fifteen pole drive units, each equipped with a low-resolution position sensor, that are assigned to five agents.