In order to improve the estimation precision of nonlinear systems

based on Gauss-Hermite approximation and weighted least square method

a weighted measurement fusion cubature Kalman filter（WMF-CKF） for nonlinear systems with correlated noises is proposed.Decorrelation method is used to remove the correlation between the correlated noises

then transforms the original system into a non-linear system with independent noises.And then the Gauss-Hermite（G-H） approximation method is used to compress the multi-sensor measurement data.In order to reduce the computational burden

the weighting coefficient matrix is calculated in an offline manner

and finally the weighted measurement fusion of multi-sensor nonlinear system is realized.Compared with the traditional optimal centralized fusion（CMF） algorithm

the proposed fusion algorithm is slightly lower in precision

but can significantly reduce the computational burden.The fusion algorithm provides an effective solution to the nonlinear multi-sensor fusion estimation problem.A simulation example of a non-linear system with 4-sensor noise correlation shows the correctness of the algorithm.