Multiple bridged knife-edge diffraction estimation can be seen as a generalization of the multiple knife-edge diffraction one which can be found in many applications of wireless communications. The considered model is formed by bridging the spaces among knife-edges with reflecting planes. So far, the series-based standard solution for this problem suffers from high computational complexity, thus limiting its use in practice. We, thus, propose a fast recursive algorithm to tackle its computational burden. To illustrate the effectiveness of the proposed algorithm, we compare our results with the state-of-the-art algorithms. Numerical results show that the running time of the proposed algorithm is much faster than that of the standard solution while benefiting from similar accuracy. © 2021 European Signal Processing Conference. All rights reserved.