On designing consistent extended Kalman filter

Jiang, Yanguang; Huang, Yi; Xue, Wenchao; Fang, Haitao

doi:10.1007/s11424-017-5151-7

Cited by 21 publications

(4 citation statements)

References 13 publications

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“…For general nonlinear systems, it is suggested to design ΔQ k and ΔR k+1 by considering the physical limitation and the magnitudes of variables. Such examples can be referred to the simulation examples in [7,22,23].…”

Section: Remarkmentioning

confidence: 99%

“…However, the MSE of the filters for nonlinear systems (e.g., extended Kalman filter (EKF) [4]) or the distributed filters for linear systems [5] is usually infeasible due to the influence of nonlinearity and unknown correlation between state estimates of sensors. In recent years, the consistency of estimation is studied in the design of both centralized nonlinear filters [6,7] and linear distributed filters [8][9][10][11], which enables estimation precision evaluation at each time using the upper bounds of the MSE. However, the consistency of filters for nonlinear systems with model uncertainties has not been well studied.…”

Section: Introductionmentioning

confidence: 99%

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Consistent Kalman filters for nonlinear uncertain systems over sensor networks

Xue

Fang

et al. 2020

Control Theory Technol.

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In this paper, we study how to design filters for nonlinear uncertain systems over sensor networks. We introduce two Kalmantype nonlinear filters in centralized and distributed frameworks. Moreover, the tuning method for the parameters of the filters is established to ensure the consistency, i.e., the mean square error is upper bounded by a known parameter matrix at each time. We apply the consistent filters to the track-to-track association analysis of multi-targets with uncertain dynamics. A novel track-to-track association algorithm is proposed to identify whether two tracks are from the same target. It is proven that the resulting probability of mis-association is lower than the desired threshold. Numerical simulations on track-to-track association are given to show the effectiveness of the methods.

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Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Consistent Kalman filters for nonlinear uncertain systems over sensor networks

Xue

Fang

et al. 2020

Control Theory Technol.

Self Cite

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“…The EKF uses a Taylor expansion of the nonlinear part of the model at the estimates, and linearization is achieved by a first-order approximation, which transforms the nonlinear problem into a linear KF problem [9]. However, when the linearization error is large and the model is uncertain, the performance of the EKF will be greatly reduced, and even divergence phenomena can be observed [10,11]. This paper proposes a method to utilize the rounding error to solve the EKF problem.…”

Section: Introductionmentioning

confidence: 99%

High-Order Extended Kalman Filter for State Estimation of Nonlinear Systems

Ding,

Wen

2024

Symmetry

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In general, the extended Kalman filter (EKF) has a wide range of applications, aiming to minimize symmetric loss function (mean square error) and improve the accuracy and efficiency of state estimation. As the nonlinear model complexity increases, rounding errors gradually amplify, leading to performance degradation. After multiple iterations, divergence may occur. The traditional extended Kalman filter cannot accurately estimate the nonlinear model, and these errors still have an impact on the accuracy. To improve the filtering performance of the extended Kalman filter (EKF), this paper proposes a new extended Kalman filter (REKF) method that utilizes the statistical properties of the rounding error to enhance the estimation accuracy. After establishing the state model and measurement model, the residual term is used to replace the higher-order term in the Taylor expansion, and the least squares method is applied to identify the residual term step by step. Then, the iterative process of updating the extended Kalman filter is carried out. Within the Kalman filter framework, a higher-order rounding error-based extended Kalman filter (REKF) is designed for the joint estimation of rounding error and random variables, and the solution method for the rounding error is considered for the multilevel approximation of the original function. Through numerical simulations on a general nonlinear model, the higher-order rounding error-based extended Kalman filter (REKF) achieves better estimation results than the extended Kalman filter (EKF) and improves the filtering accuracy by utilizing the higher-order rounding error information, which also proves the effectiveness of the proposed method.

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“…A Kalman filter (KF) is a fundamental tool in many practical systems, such as position estimation, attitude determination, and parameter identification [1][2][3]. For nonlinear stochastic systems, the most widely used state estimation algorithm is the extended Kalman filter (EKF), where the nonlinear models are linearized at the current state estimate, such that the KF equations can be implemented approximately [2,[4][5][6]. It is well known that the process and measurement noise covariance matrices play important roles in the EKF.…”

Section: Introductionmentioning

confidence: 99%

Q‐learning for noise covariance adaptation in extended KALMAN filter

Xiong¹,

Wei²,

Zhang³

2020

Asian Journal of Control

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The extended Kalman filter (EKF) is a widely used method in navigation applications. The EKF suffers from noise covariance uncertainty, potentially causing it to perform poorly in practice. This paper attempts to suppress the unfavorable effect of the noise covariance uncertainty to the EKF in the framework of reinforcement learning. The proposed state estimation algorithm combines the EKF and a Q-learning method, where a covariance adaptation strategy is designed based on the Q-values, leading to a gradual improvement in the estimation performance. The resultant algorithm is called the Q-learning extended Kalman filter (QLEKF), which is less sensitive to the noise covariance uncertainty. To evaluate the estimation error behavior in nonlinear uncertain systems, the stability of the filtering algorithm is investigated. A numerical simulation for spacecraft autonomous navigation is implemented to demonstrate the efficiency of the QLEKF. It is shown that the presented algorithm outperforms a traditional EKF and an adaptive extended Kalman filter (AEKF) in estimation accuracy.

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On designing consistent extended Kalman filter

Cited by 21 publications

References 13 publications

Consistent Kalman filters for nonlinear uncertain systems over sensor networks

Consistent Kalman filters for nonlinear uncertain systems over sensor networks

High-Order Extended Kalman Filter for State Estimation of Nonlinear Systems

Q‐learning for noise covariance adaptation in extended KALMAN filter

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