When the observation equation of system has not been verified or corrected under certain environmental conditions, applying it will yield to unknown system error and filtering error. The unknown system error can be effectively eliminated by introducing the incremental equation. In this article, the local Kalman estimator for the incremental system with correlated noises is first presented. It solves the state estimation problem for the system with unknown measurement error, which does not meet the requirements of classical Kalman filter. Furthermore, under the linear minimum variance optimal fusion criterion, the optimal weighted measurement fusion Kalman estimator is proposed for the multi‐sensor incremental system with correlated noises. It effectively solves the state estimation problem for the multi‐sensor system under poor observation condition. The proposed algorithms are simple in form and small in computational burden so as to be easily applied in engineering practice. A simulation example shows their effectiveness and feasibility.

中文翻译：

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具有相关噪声的增量系统的最优加权融合卡尔曼估计

如果在某些环境条件下尚未对系统的观测方程进行验证或校正，则将其应用到未知的系统误差和滤波误差中。通过引入增量方程可以有效地消除未知的系统误差。在本文中，首先介绍了具有相关噪声的增量系统的局部Kalman估计。它解决了测量误差未知的系统的状态估计问题，不符合经典卡尔曼滤波器的要求。此外，在线性最小方差最优融合准则下，针对具有相关噪声的多传感器增量系统，提出了最优加权测量融合卡尔曼估计器。它有效地解决了在观测条件较差的情况下多传感器系统的状态估计问题。所提出的算法形式简单，计算量小，易于在工程实践中应用。仿真实例表明了其有效性和可行性。