复杂有色噪声广义系统信息融合Kalman滤波器

Information fusion Kalman filter with complex coloured noise for descriptor systems

针对带复杂有色噪声的线性广义系统,提出了矩阵加权融合稳态Kalman滤波器。应用奇异值分解将原广义系统滤波问题转化为两个正常子系统滤波问题。通过状态增广与量测变换法将有色过程噪声、有色量测噪声化为白噪声,因此问题转化为带相关白噪声正常系统Kalman预报问题。基于线性最小方差意义与矩阵加权融合准则得到了复杂有色噪声作用下的广义系统融合Kalman预报器,进而得到带复杂有色噪声的原广义系统滤波器。该滤波加权融合算法精度高于各单传感器局部滤波器,低于集中式融合滤波器。Monte-Carlo仿真实验证明了该滤波融合算法的有效性与可行性。

Aiming at the descriptor systems with complex coloured noise, a steady-state Kalman filter with fusion weigh- ted by matrix is presented. By using the singular value decomposition, the filtering problem of descriptor system is trans- formed 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 effective- ness and feasibility of the filtering fusion algorithm.