Information fusion Kalman filter with complex coloured noise for descriptor systems

Aiming at the descriptor systems with complex coloured noise, a steady-state Kalman filter with fusion weighted by matrix is presented. By using the singular value decomposition, the filtering problem of descriptor system is transformed into the filtering problems of two normal subsystems. State augmentation and measurement transformation method are applied to transform the coloured process noise and coloured observation noise into white noises. So these problems are transformed to Kalman prediction problems of normal systems with correlated white noise. A steady-state descriptor Kalman predictor with complex coloured noise is derived on the basis of linear minimum mean square error estimation and fusion criterion weighted by matrices. Then, the filter for original descriptor system with coloured noise is derived. The precision of the filtering weighted fusion algorithm is higher than that of the local Kalman filter for every sensor and is lower than that of optimal centralized Kalman fusion filter. Monte-Carlo simulation experiment proves the effectiveness and feasibility of the filtering fusion algorithm.