Cubature Kalman filters: Derivation and extension

Zhang, Xinchun; Guo, Chengjun

doi:10.1088/1674-1056/22/12/128401

Cited by 30 publications

(10 citation statements)

References 30 publications

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“…Such approximations are extremely easy to apply, which explains the popularity of the filter. However, when dealing with highly nonlinear systems, the EKF estimates suffer serious problems, such as unstable and quickly divergent behaviors, poor linearization and/or erratic behaviors [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

An Improved Extended Kalman Filter for Radar Tracking of Satellite Trajectories

Coelho¹,

Bousson²,

Ahmed³

2021

Designs

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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.

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Section: Introductionmentioning

confidence: 99%

An Improved Extended Kalman Filter for Radar Tracking of Satellite Trajectories

Coelho¹,

Bousson²,

Ahmed³

2021

Designs

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“…However, Bayesian sampling methods are alternatives to the EKF. These methods are divided into random sampling and deterministic sampling [22]. Random sampling methods involve a high computational burden, which makes them inappropriate for practical applications where fast estimation is required.…”

Section: Introductionmentioning

confidence: 99%

“…Random sampling methods involve a high computational burden, which makes them inappropriate for practical applications where fast estimation is required. Among the deterministic sampling methods, cubature Kalman filters (CKFs) have attracted particular interest recently due to their attractive features such as accuracy, lower computational burden, and good numerical stability properties [22]- [24].…”

Section: Introductionmentioning

confidence: 99%

Tracking Control for a DC Microgrid Feeding Uncertain Loads in More Electric Aircraft: Adaptive Backstepping Approach

Yousefizadeh

Bendtsen

Vafamand

et al. 2019

IEEE Trans. Ind. Electron.

100

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More electric aircrafts (MEAs) comprise a vast amount of power electronic loads, which usually behave as constant power loads (CPLs). The incremental negative impedance of CPLs threatens system stability. To ensure an effective control of power flow in MEAs, eliminating the undesired behavior of CPLs is a necessity. This aim requires spontaneous power estimation of the time-varying uncertain loads. In this paper, an adaptive backstepping controller, which is interconnected to a 3 rd degree cubature Kalman filter (CKF), is developed for a DC MG feeding non-ideal CPLs. At first, the load power is considered as an artificial state and augmented into the system states, which enables estimation of not only the DC MG states but also the unknown value of the load power. The estimated load power is then forwarded to a backstepping controller. The systematic approach of this controller allows obtaining the control signal, which is the duty ratio of the switch, to not only system stabilizing but also tracking a desired voltage of the DC bus under the load power variations. The proposed adaptive controller is tested on a DC MG that has one CPL. The conducted experimental results verify the proposed nonlinear control in tracking the desired voltage of the DC bus under slow and fast variations of the load power.Index Terms-More electric aircraft power system, DC microgrid (MG), Constant power load (CPL), Cubature Kalman filter (CKF), Adaptive backstepping controller.

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“…However, the use of EKF results in a poor performance if the process or measurement model is highly nonlinear [5]. In addition, the computation of Jacobian matrices is also a heavy computational burden in practical situations [6]. As a better alternative to EKF, unscented Kalman filter (UKF) has been proposed to solve highly nonlinear state estimation problems [7].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, owing to satisfactory filtering accuracy, cubature Kalman filter (CKF) based on the sphericalradial cubature rule has received much attention in solving nonlinear state estimation problems [6,11,14,15]. However, for nonlinear dynamic systems with large uncertainties such as target tracking and long-term orbit uncertainty propagation [16,17], the performance of CKF may degrade due to the uncertainty of system mode.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear state estimation using neural-cubature Kalman filter

Zhang

Zhao

et al. 2017

Automatika

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The cubature Kalman filter (CKF) has been widely used in solving nonlinear state estimation problems because of many advantages such as satisfactory filtering accuracy and easy implementation compared to extended Kalman filter and unscented Kalman filter. However, the performance of CKF may degrade due to the uncertainty of the nonlinear dynamic system model. To solve this problem, a neural-cubature Kalman filter (NCKF) algorithm containing a multilayer feed-forward neural network (MFNN) in CKF is proposed to further improve the estimation accuracy and enhance the robustness of CKF. In the proposed NCKF algorithm, the MFNN was used to modify the nonlinear state estimation of CKF as the measurements were processed, and the CKF was used as both a state estimator and an online training paradigm simultaneously. The experimental results show that the estimation accuracy and robustness of the proposed method are better than those of the CKF, square-root CKF and particle filter.

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Cubature Kalman filters: Derivation and extension

Cited by 30 publications

References 30 publications

An Improved Extended Kalman Filter for Radar Tracking of Satellite Trajectories

An Improved Extended Kalman Filter for Radar Tracking of Satellite Trajectories

Tracking Control for a DC Microgrid Feeding Uncertain Loads in More Electric Aircraft: Adaptive Backstepping Approach

Nonlinear state estimation using neural-cubature Kalman filter

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