Abstract
Nonlinear state estimation problem is an important and complex topic, especially for real-time applications with a highly nonlinear environment. This scenario concerns most aerospace applications, including satellite trajectories, whose high standards demand methods with matching performances. A very well-known framework to deal with state estimation is the Kalman Filters algorithms, whose success in engineering applications is mostly due to the Extended Kalman Filter (EKF). Despite its popularity, the EKF presents several limitations, such as exhibiting poor convergence, erratic behaviors or even inadequate linearization when applied to highly nonlinear systems. To address those limitations, this paper suggests an improved Extended Kalman Filter (iEKF), where a new Jacobian matrix expansion point is recommended and a Frobenius norm of the cross-covariance matrix is suggested as a correction factor for the a priori estimates. The core idea is to maintain the EKF structure and simplicity but improve its accuracy. In this paper, two case studies are presented to endorse the proposed iEKF. In both case studies, the classic EKF and iEKF are implemented, and the obtained results are compared to show the performance improvement of the state estimation by the iEKF.
Highlights
Nonlinear state estimation is a desirable and required tool in several engineering applications, especially in aerospace, where it is crucial for tasks such as surveillance, guidance, navigation, attitude control, obstacle avoidance and target tracking [1,2,3,4,5,6]
Acknowledging that EKF is one of the most popular algorithms to deal with radar tracking and to address its limitations, this paper proposes an improved Extended Kalman Filter with an adaptive structure
By observing the graphics spikes (Figures 7 and 9), it is possible to verify that the EKF holds an unstable behavior, that is, the error oscillations are higher than the improved Extended Kalman Filter (iEKF)
Summary
Nonlinear state estimation is a desirable and required tool in several engineering applications, especially in aerospace, where it is crucial for tasks such as surveillance, guidance, navigation, attitude control, obstacle avoidance and target tracking [1,2,3,4,5,6]. The concern for optimal filtering methods began in the early 1940s, with Wiener and Kolmogorov [8,9] They solved the estimation problem for stochastic processes based on the linear least square. The key problem with these nonlinear filtering methods is to balance the computational complexity with the desired estimation accuracy Most of those methods require intensive calculations, which means more computational time, and a significant limitation for crucial time applications. Some methods (e.g., infinity norm filter) require more tuning to get acceptable performance, and this is not ideal for nonlinear systems performing in time-critical environments This is one of the reasons why this filter is not as popular as the Kalman Filter.
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