In this work, two new formulations for the extended (MW-EKF) and robust extended Kalman filter with moving window estimation (MW-REKF) are proposed. The MW-EKF and MW-REKF are formulated using an elegant quadratic programming problem that facilitates its implementation and decreases its computational cost. Besides that, the constrained extended Kalman filter (CEKF), constrained extended Kalman filter and smoother (CEKFS) and the moving horizon estimation (MHE) are compared in terms of computational cost and fit to the real data. The comparison is performed over a spherical-quadruple-tank model with different settings aiming to raise each approach's advantages and disadvantages. For both state and parameter estimation the MW-REKF has shown the smoothest and most robust behavior among all methodologies. This technique minimized the effect of the outliers, physical limitations, structural discrepancies, among others. The computational cost of the proposed techniques is only four times higher than CEKF and nine times smaller than the MHE.

在这项工作中，提出了两种新的扩展公式（MW-EKF）和带有移动窗口估计的鲁棒扩展卡尔曼滤波器（MW-REKF）。MW-EKF和MW-REKF是使用优雅的二次规划问题制定的，该问题易于实现并降低了计算成本。除此之外，在计算成本方面比较了约束扩展卡尔曼滤波器（CEKF），约束扩展卡尔曼滤波器和平滑器（CEKFS）和移动视域估计（MHE），并适合实际数据。比较是在具有不同设置的球形四重罐模型上进行的，旨在提高每种方法的优缺点。对于状态和参数估计，MW-REKF在所有方法中均表现出最平滑，最鲁棒的行为。此技术将异常值，物理限制，结构差异等的影响降至最低。所提出技术的计算成本仅比CEKF高四倍，而比MHE小九倍。