Optimal and self-tuning information fusion Kalman filter with complex colored noise

For the multisensor systems with complex colored noise, using the modern time series analysis, a steady-state optimal and self-tuning Kalman filter weighted by scalars is presented. State augmentation and measurement transformation methods are applied to transform the colored process noise and colored observation noises into white noises. So these problems are transformed to Kalman prediction problems of normal systems with correlated white noises. A steady-state Kalman predictor with complex colored noises is derived on the basis of linear minimum mean square error estimation and fusion criterion weighted by scalars. Then, the filter for original system with colored noises is derived. The precision of the weighted fusion filter is higher than that of the local Kalman filter for every sensor. When the white noise variances are unknown, a self-tuning information fusion Kalman filter weighted by scalars is obtained. A simulation example proves the effectiveness and feasibility of the filtering fusion algorithm.