For the multi-sensor  descriptor system with correlated measurement noises,the new fused measurement can be obtained by  least square method based on  all measurements. The state equation of the descriptor system can be decomposed into two normal mutual coupling sub-systems by using
  singular value decomposition.  And  the fused  measurement equation  is changed to the measurement of one state component.  Then,   the problem is the state estimation of one-sensor normal system. For the new reduced-order sub-systems,  the weighted measurement fusion  Kalman predictor is presented, by applying   Kalman filtering.    The prediction error variances of the weighted measurement fusion Kalman  predictor for the descriptor system is obtained. This method avoids to compute the cross-variance of  all local predictors, and the accuracy   of fused predictor is higher than that of  local predictors and  state     fusion Kalman predictor. A simulation example of 4-sensor descriptor  system verifies the effectiveness of the method.