Under the multi-sensor discrete system with correlated measurement noises and different unknown measurement functions, the distributed fusion Kalman filtering algorithm is proposed according to the existing fusion algorithms based on Bayes estimation weighted least squares (BYEWLS). The algorithm makes full use of the prior information for the unknown parameters. BYEWLS algorithm gains an advantage over WLS algorithm according to risk function. Meanwhile, the online method is proposed to eliminate the bias emerged with BYEWLS fusion algorithm. The distributed fusion algorithms can reduce the computational burden and improve the fusion accuracy, therefore they are suitable for real time applications. As a result, the simulation example indicates the validity of the theory analysis.