Robust centralized and weighted observation fusion (CAWOF) prediction algorithm is addressed in this article for an uncertain multi-sensor generalized system with linear correlation between observation noises and an input white noise. This uncertainty in the generalized system primarily means that the variances of the aforementioned types of noise, as well as the multiplicative noise variances, are uncertain. Through singular value decomposition and virtual noise compensation, the original generalized system is changed to non-generalized reduced-order subsystems in which only noise variances are uncertain. Utilizing the minimax robustness estimation criterion, robust CAWOF Kalman predictors are put forward on account of the first subsystem with conservative upper bounds of noise variances. Eventually, robust observation fusion Kalman predictors of the original generalized system are proposed. The Lyapunov equation method is applied to verify two fusion predictors' robustness. With regard to all permissible uncertain practical noise variances, CAWOF predictors are robust, namely, the practical prediction error variances of two robust predictors will have minimum upper bounds. This equivalence between CAWOF Kalman predictors is proved by an information filter. In this article, the precision relationship of fusion predictors is given. Meanwhile, robust Kalman predictors for steady-state case are proposed, and the astringency of robust time-variant Kalman predictors is analyzed through the analysis of dynamic error system. The validity and correctness of proposed algorithm are proved by the simulation example of random dynamic input and output system in an economic system.

中文翻译：

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不确定多传感器广义系统的鲁棒CAWOF卡尔曼预测器

本文针对观测噪声和输入白噪声之间具有线性相关性的不确定多传感器广义系统提出了稳健的集中加权观测融合 (CAWOF) 预测算法。广义系统中的这种不确定性主要意味着上述类型噪声的方差以及乘法噪声方差是不确定的。通过奇异值分解和虚拟噪声补偿，将原来的广义系统变为只有噪声方差不确定的非广义降阶子系统。利用最小最大鲁棒性估计准则，考虑到第一子系统具有保守的噪声方差上限，提出了鲁棒的CAWOF卡尔曼预测器。最终，提出了原始广义系统的鲁棒观察融合卡尔曼预测器。应用李雅普诺夫方程方法来验证两个融合预测器的鲁棒性。对于所有允许的不确定实际噪声方差，CAWOF 预测器是稳健的，即两个稳健预测器的实际预测误差方差将具有最小上限。CAWOF 卡尔曼预测器之间的这种等价性由信息过滤器证明。在本文中，给出了融合预测器的精度关系。同时，提出了稳态情况下的鲁棒卡尔曼预测器，并通过动态误差系统的分析，分析了鲁棒时变卡尔曼预测器的收敛性。