Kalman filter with recursive covariance estimation for protection against system uncertainty

Xiao, Xuan; Shen, Kai; Liang, Yuan; Liu, Tingxin

doi:10.1049/iet-cta.2019.1476

Cited by 11 publications

(7 citation statements)

References 39 publications

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“…where the simulation time t is 1000 s. In the simulation, the initial state b x 0 ¼ 200 200 À1:1 1:2 ½ , P 0 ¼ 0:01 Â I 4 , and the nominal initial MNCM is selected as e R 0 ¼ 2I 4 . Additionally, we set the parameters used in algorithm as ρ 0 ¼ 1 À exp À4 ð Þ, N ¼ 10, and l 2 ¼ 8: The KF with true covariance matrices Q and R (KF-trueQR), our algorithm (EAKF), the NVBAKF in Zhao et al [27] and RCEAKF in Xuan et al [21] are constructed for testing. The root mean square error (RMSE) and average RMSE (ARMSE) are chosen to evaluate the performance of different algorithms, which are defined as To determine the estimation accuracy of Q and R, the estimated noise covariance error index λ is utilized.…”

Section: Numerical Simulationmentioning

confidence: 99%

“…In the simulation, the initial state

{\overset{truê}{bold-italicx}}_{0} = ([], \begin{array}{c} 200 & 200 & - 1.1 & 1.2 \end{array})

P_{0} = 0.01 \times I_{4}

, and the nominal initial MNCM is selected as

{\overset{true˜}{bold-italicR}}_{0} = 2 I_{4}

. Additionally, we set the parameters used in algorithm as

ρ_{0} = 1 - \exp ((), - 4), N = 10,

and

l_{2} = 8 .

The KF with true covariance matrices

bold-italicQ

and

bold-italicR

(KF‐trueQR), our algorithm (EAKF), the NVBAKF in Zhao et al [27] and RCEAKF in Xuan et al [21] are constructed for testing. The root mean square error (RMSE) and average RMSE (ARMSE) are chosen to evaluate the performance of different algorithms, which are defined as

({, \begin{array}{l} {RMSE}_{pos} ≜ \sqrt{\frac{1}{M} \sum_{s = 1}^{M} ((), {({bold-italicx}_{k}^{s} - {\overset{x}{true}}_{k}^{s})}^{2} goodbreak+ {({bold-italicy}_{k}^{s} - {\overset{y}{true}}_{k}^{s})}^{2})} \\ {ARMSE}_{pos} ≜ \sqrt{\frac{1}{Mt} \sum_{k = 1}^{t} \sum_{s = 1}^{M} ((), {({bold-italicx}_{k}^{s} - {\overset{x}{true}}_{k}^{s})}^{2} goodbreak+ ({bold-italicy}_{k}^{s} - {\overset{y}{true}}_{k}^{}))} \end{array})

…”

Section: Numerical Simulationmentioning

confidence: 99%

“…Yet the filter has many initial parameters to be determined, and these parameters have serious effect on the performance. Xuan et al [21] designed a measurement sequence‐based AKF (RCEAKF); this method can adaptively estimate the noise covariance based on the information in the measurement sequence. But the algorithm has larger uncertainties in the estimation of the process noise covariance.…”

Section: Introductionmentioning

confidence: 99%

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An enhanced adaptive Kalman filtering for linear systems with inaccurate noise statistics

Chen

2022

Asian Journal of Control

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This paper investigates the simultaneous state and noise covariance estimation for linear systems with inaccurate noise statistics. An enhanced adaptive Kalman filtering (EAKF) based on dynamic recursive nominal covariance estimation (DNRCE) and modified variational Bayesian (VB) inference is presented. The EAKF realizes the concurrently estimation of state and noise covariance matrices by introducing a nominal parameter in the traditional recursive covariance estimation and designing a new adaptive forgotten factor for the dynamic model of the estimated information propagation. The simulation of a target tracking example shows that, compared with the existing filters, the proposed filter has good adaptive performance for inaccurate and time‐varying noise covariance matrices.

show abstract

Section: Numerical Simulationmentioning

confidence: 99%

“…In the simulation, the initial state

{\overset{truê}{bold-italicx}}_{0} = ([], \begin{array}{c} 200 & 200 & - 1.1 & 1.2 \end{array})

P_{0} = 0.01 \times I_{4}

, and the nominal initial MNCM is selected as

{\overset{true˜}{bold-italicR}}_{0} = 2 I_{4}

. Additionally, we set the parameters used in algorithm as

ρ_{0} = 1 - \exp ((), - 4), N = 10,

and

l_{2} = 8 .

The KF with true covariance matrices

bold-italicQ

and

bold-italicR

({, \begin{array}{l} {RMSE}_{pos} ≜ \sqrt{\frac{1}{M} \sum_{s = 1}^{M} ((), {({bold-italicx}_{k}^{s} - {\overset{x}{true}}_{k}^{s})}^{2} goodbreak+ {({bold-italicy}_{k}^{s} - {\overset{y}{true}}_{k}^{s})}^{2})} \\ {ARMSE}_{pos} ≜ \sqrt{\frac{1}{Mt} \sum_{k = 1}^{t} \sum_{s = 1}^{M} ((), {({bold-italicx}_{k}^{s} - {\overset{x}{true}}_{k}^{s})}^{2} goodbreak+ ({bold-italicy}_{k}^{s} - {\overset{y}{true}}_{k}^{}))} \end{array})

…”

Section: Numerical Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An enhanced adaptive Kalman filtering for linear systems with inaccurate noise statistics

Chen

2022

Asian Journal of Control

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“…According to the assumption of noise, state-estimation methods are mainly divided into two categories. One is the state estimation method based on the assumption of random noise, that is, it is assumed that the noise is random and satisfies a certain probability distribution, such as in the Kalman filtering method [3,4]. The second is the state estimation method based on the assumption of UBB noise, namely, the set-membership estimation method [5].…”

Section: Introductionmentioning

confidence: 99%

Zonotope and Gaussian Kalman filters based state estimation algorithm for linear system with dual noise term

Zhan

Wang

et al. 2022

IET Control Theory & Appl

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To solve the problem of state estimation for systems with dual noise terms, a zonotope and Gaussian Kalman filters based state estimation algorithm is proposed. A state estimator is designed to obtain the estimation interval of the true state in the presence of both stochastic and unknown but bounded (UBB) uncertainties. A novel coefficient that weighs the relative influence of stochastic and UBB uncertainties is introduced, and the optimal weight solution is introduced by minimizing the polyhedron space and mean square error. Finally, two simulation examples are presented to demonstrate the accuracy and effectiveness of the proposed algorithm.

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“…In addition, there is also an AKF with maximum likelihood principle (MLP) [5,15,23,24]. The MLP can estimate the unknown parameters by making sure that the likelihood function between the unknown parameters and the given measurement values is maximized.…”

Section: Introductionmentioning

confidence: 99%

A novel maximum likelihood and moving weighted average based adaptive Kalman filter

Chen

2022

J. Inst.

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For the state estimation with inaccurate noise statistics, the existing adaptive Kalman filters (AKFs) usually have substantial computational complexity or are not easy to estimate online. Inspired by the fact, a new computationally efficient AKF based on maximum likelihood and moving weighted average (MMAKF) is proposed. Firstly, to reduce computational complexity, instead of estimating the noise covariance matrixes, the maximum likelihood principle is introduced to directly estimate the prediction error covariance matrix and innovation covariance matrix. Subsequently, a new moving weighted average algorithm is designed to optimize the estimated results. Then, a computationally efficient AKF is derived, and its convergence performance and application are discussed. Simulation results for the target tracking example illustrate that the proposed AKF can effectively reduce error caused by inaccurate noise statistics and basically keep simplicity and elegance of the classical KF.

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Kalman filter with recursive covariance estimation for protection against system uncertainty

Cited by 11 publications

References 39 publications

An enhanced adaptive Kalman filtering for linear systems with inaccurate noise statistics

An enhanced adaptive Kalman filtering for linear systems with inaccurate noise statistics

Zonotope and Gaussian Kalman filters based state estimation algorithm for linear system with dual noise term

A novel maximum likelihood and moving weighted average based adaptive Kalman filter

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