Non-coherent over-the-air (OTA) computation has garnered increasing attention for its advantages in facilitating information aggregation among distributed agents in resource-constrained networks without requiring precise channel estimation. A promising application scenario of this method is distributed average consensus in wireless multi-agent systems. However, in such scenario, non-coherent interference from concurrent OTA transmissions can introduce bias in the consensus value. To address this issue, we develop a robust distributed average consensus algorithm by formulating the consensus problem as a distributed optimization problem. Using decentralized projected gradient descent (D-PGD), our proposed algorithm can achieve unbiased mean square average consensus even in the presence of non-coherent interference and noise. Additionally, we implement transmit power control and receive scaling mechanisms to further accelerate convergence. Simulation results demonstrate that our method can significantly enhance the convergence speed of the D-PGD algorithm for OTA average consensus without compromising accuracy.