<p>This paper proposes two novel distributed fusion Koopman optimal filtering algorithms for nonlinear multi-sensor (NMS) systems. The Koopman operator is employed to transform the nonlinear fusion problems into linear ones by transforming the original state space, which enables the application of the linear information fusion methods to NMS systems. Unfortunately, the Koopman operator is infinite-dimensional, and this makes it infeasible in practical applications. To address this issue, a finite-dimensional approximation is constructed using deep learning to learn both the lifting function and the corresponding Koopman operator. By applying the trained Koopman multi-sensor model, a distributed fusion linear Koopman optimal filtering algorithm is proposed by combining the linear optimal filtering method and the information fusion technology. Considering the coupled relationship between the inputs and the states in NMS systems, a distributed fusion bilinear Koopman optimal filtering algorithm is further proposed to improve the accuracy of the fusion estimation. Finally, a numerical example validates the effectiveness of the proposed algorithms. The proposed algorithms outperform the existing methods in tackling nonlinear challenges.</p>