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

The paper solves the robust weighted fusion Kalman filtering problem for systems with linearly correlated noise and mixed uncertainties of noise variances, multiplicative noises, and multiple networked inducements including missing measurements, packets dropouts, and two‐step random measurement delays. It is assumed that system noise variances are uncertain but bounded above, and the other four uncertainties are compensated to fictitious white noise by the proposed model‐transformation method. For the transformed local multimodel system with correlated fictitious noise, the robust local time‐varying recursive Kalman filters are presented by decorrelation technique and minimax robust filtering principle. Then the six weighted fusion robust Kalman filters are presented in a unified form. The robustness of local and fused robust Kalman filters is proved by the extended Lyapunov equation approach, matrix factorization, and elementary transformation. Further, the local and fused steady‐state robust Kalman filters are designed. Finally, a simulation study applied to F404 aircraft engine system is provided to examine effectiveness and applicability of the proposed algorithm.

Section: Introductionmentioning

confidence: 99%

Robust weighted fusion Kalman filters under linearly correlated noise and mixed uncertainties of noise variances, multiplicative noises, and multiple networked inducements

Yang,

Zhao,

Liu

2023

Weighted information entropy‐based Kalman filter for outliers and structural noise

Ma,

Yao,

Huang

et al. 2024

Structural noise and outliers are widely present in real‐world state estimate scenarios, and they significantly degrade the performance of most filtering algorithms based on minimum mean square error (MMSE) criterion. To address this problem, this paper first models structural noise and outliers as independent and piecewise identical distribution (IPID). Then, a minimum error weighted entropy‐based Kalman filter (MEWE‐KF) is proposed, where a new cost function is constructed by introducing a weight function related to error location distances in an original information space into the minimum error entropy (MEE) criterion. Further, the iterative formulations of the proposed filter are derived, and the computational complexity and the convergence are also analyzed. Simulation results show that the proposed filter with adaptive weights has the superior performance for suppressing structural noise and outliers.

Maximum weighted correntropy filters for nonlinear non‐Gaussian systems

Liu,

Zhang,

Song

2024

In this paper, we focus on the filtering issue for nonlinear non‐Gaussian systems. Considering the limitations of the Gaussian function with a single kernel bandwidth, we design a novel extended version called weighted Gaussian function, which consists of a weighting coefficient and two distinct kernel bandwidths. The additional coefficient can directly balance two kernel bandwidths, which improves the flexibility and performance of the correntropy. We develop a cost function utilizing the suggested weighted Gaussian function and statistical linearization method, followed by deriving a maximum weighted correntropy filter based on the maximum correntropy criterion. The proposed algorithm is demonstrated to converge to a Gaussian filter as the kernel bandwidths approach infinity. In addition, we derive the corresponding information filter, which takes the form of information matrix and information vector. It is computationally efficient and easier to generalize to multisensor systems. The performance of the proposed algorithms is compared with other filters based on the third‐order spherical cubature rule and the fixed point iteration technique in a target tracking system. Simulation results confirm the effectiveness of the new approaches.