An Extended Kalman Filter with Remainder Terms and Correlation Compensation for Nonlinear State Monitoring and Soft Sensing

In networked sensing systems, nonlinear state monitoring and soft sensing are widely used to reconstruct key variables that cannot be directly measured in real time. For such nonlinear estimation tasks, the Extended Kalman Filter (EKF) is a commonly used recursive method. However, the conventional EKF neglects higher-order truncation terms during first-order Taylor linearization. As the nonlinearity increases, these neglected terms may accumulate and degrade filtering accuracy, and even lead to divergence in some cases. In addition, the statistical influence of the remainder terms and the correlation between prediction and measurement errors are usually ignored. To address these issues, this paper proposes an Extended Kalman Filter with remainder terms considering correlations (REKF). The proposed method replaces the higher-order terms in the Taylor expansion with remainder terms and identifies them incrementally by using least squares, thereby improving the EKF update process. A higher-order filtering framework is then constructed to jointly estimate the system state and the remainder-related random variables while accounting for the induced error correlation. Numerical simulations on typical nonlinear models demonstrate that the proposed REKF achieves better estimation performance than the conventional EKF. In this work, the proposed REKF is mainly developed for nonlinear estimation problems in which the dominant challenge arises from strong nonlinearity in the state evolution, while the measurement update is treated in a locally linearized EKF form. The results show that incorporating higher-order remainder information can effectively improve nonlinear state estimation for state monitoring and soft sensing tasks.