Conventional Cubature Kalman Filter Research Articles

Robust Cubature Kalman Filter for Moving-Target Tracking with Missing Measurements.

Handling the challenge of missing measurements in nonlinear systems is a difficult problem in various scientific and engineering fields. Missing measurements, which can arise from technical faults during observation, diffusion channel shrinking, or the loss of specific metrics, can bring many challenges when estimating the state of nonlinear systems. To tackle this issue, this paper proposes a technique that utilizes a robust cubature Kalman filter (RCKF) by integrating Huber's M-estimation theory with the standard conventional cubature Kalman filter (CKF). Although a CKF is often used for solving nonlinear filtering problems, its effectiveness might be limited due to a lack of knowledge regarding the nonlinear model of the state and noise-related statistical information. In contrast, the RCKF demonstrates an ability to mitigate performance degradation and discretization issues related to track curves by leveraging covariance matrix predictions for state estimation and output control amidst dynamic disruption errors-even when noise statistics deviate from prior assumptions. The performance of extended Kalman filters (EKFs), unscented Kalman filters (UKFs), CKFs, and RCKFs was compared and evaluated using two numerical examples involving the Univariate Non-stationary Growth Model (UNGM) and bearing-only tracking (BOT). The numerical experiments demonstrated that the RCKF outperformed the EKF, EnKF, and CKF in effectively handling anomaly errors. Specifically, in the UNGM example, the RCKF achieved a significantly lower ARMSE (4.83) and ANCI (3.27)-similar outcomes were observed in the BOT example.

Adaptive control for stochastic nonlinear systems with time‐varying delays via multidimensional Taylor network

AbstractControl of stochastic nonlinear systems turns out to be notoriously difficult when stochastic uncertainties and time‐varying delays occur simultaneously. This article presents a tractable adaptive control scheme for the stochastic nonlinear system with time‐varying delays. To mitigate the effects of stochastic uncertainties, an adaptive embedded cubature Kalman filter is developed to realize the robust estimation of the state. Unlike the conventional cubature Kalman filter with fixed construction, a semi‐definite programming is designed to adjust the weights of cubature points dynamically. Such programming guarantees the positive definiteness of the error covariance matrix, which enhances the reliability of the filtering procedure. Based on more accurate state estimations, the multidimensional Taylor network (MTN) is utilized to evaluate the dynamic performance under time‐varying delays and approximate the optimal policy in the deterministic policy gradient framework. Adaptive tracking control with high computational efficiency is achieved due to the concise topological structure of MTN. The exponential convergence of the state estimation error and the semi‐globally uniform ultimate boundness of the tracking error are verified theoretically. The effectiveness of the proposed method is confirmed by a numerical simulation based on a practical electric industrial system.

Robust Cubature Kalman Filter for SINS/GPS Integrated Navigation Systems With Unknown Noise Statistics

to the vehicle’s severe maneuver and abnormal measurements of GPS in practical applications, the statistic of process noise in SINS/GPS integrated navigation system may be unknown and the measurement noise may not follow the Gaussian distribution, which results in a deteriorated performance for the conventional cubature Kalman filter. To address this issue, we propose in this paper a new robust cubature Kalman filter based on the adaptive information entropy theory. In the proposed filter, the process uncertainty and non-Gaussian measurement noise are simultaneously suppressed based on a new constructed cost function using the maximum correntropy and residual orthogonal principle based weighted least squares technology, which is independent of noise distribution and more insensitive to the non-Gaussian noise. Moreover, a multiple-channel adaptive strategy for the better process uncertainty suppression is given. Furthermore, some improvements are proposed to avoid the numerical problem and implement the proposed robust filter effectively. Extensive simulation and car-mounted experiment demonstrate that the proposed filter can achieve higher estimation accuracy and better robustness as compared with the related state-of-the-art methods.

Continuous Stirred Tank Reactor Fault Detection Using Higher Degree Cubature Kalman Filter

Continuous Stirred Tank Reactor (CSTR) plays a major role in chemical industries, it ensures the process of mixing reactants according to the attended specification to produce a specific output. It is a complex process that usually represent with nonlinear model for benchmarking. Any abnormality, disturbance and unusual condition can easily interrupt the operations, especially fault. And this problem need to detect and rectify as soon as possible. A good knowledge based fault detection using available model require a good error residual between the measurement and the estimated state. Kalman filter is an example of a good estimator, and has been exploited in many researches to detect fault. In this paper, Higher degree Cubature Kalman Filter (HDCKF) is proposed as a method for fault detection by estimation the current state. Cubature Kalman filter (CKF) is an extension of the Kalman filter with the main purpose is to estimate process and measurement state with high nonlinearities. It is based on spherical radial integration to estimate current state by generating cubature points with specific value. Conventional CKF use 3rd degree spherical and 3rd degree radial, here we implement Higher Degree CKF (HDCKF) to have better accuracy as compared to conventional CKF. High accuracy is required to ensure no false alarm is detected and furthermore good computational cost will improve its detection. Finally, a numerical example of CSTR fault detection using HDCKF is presented. Implementation of HDCKF for fault detection is compared with other filter to show effective results.

Adaptive Robust Cubature Kalman Filter for Power System Dynamic State Estimation Against Outliers

This paper develops an adaptive robust cubature Kalman filter (ARCKF) that is able to mitigate the adverse effects of the innovation and observation outliers while filtering out the system and measurement noises. To develop the ARCKF dynamic state estimator, a batch-mode regression form in the framework of cubature Kalman filter is first established by processing the predicted state and measurement data information simultaneously. Subsequently, based on the regression form, the outliers can be detected and downweighted by the robust projection statistics approach. Then, the adverse effects of innovation and observation outliers can be effectively suppressed by the generalized maximum likelihood (GM)-type estimator utilizing the iteratively reweighted least squares approach. Finally, an adaptive strategy is developed to adjust the state estimation error covariance matrix under different conditions. Extensive simulation results obtained from the IEEE New England 10-machine 39-bus test system under various operating conditions demonstrate the effectiveness and robustness of the proposed method, which is able to track the transients of power system in a more reliable way than the conventional cubature Kalman filter (CKF) and the unscented Kalman filter (UKF).

State of Charge Estimation for Lithium Battery Based on Adaptively Weighting Cubature Particle Filter

Accurate estimation of lithium battery state of charge is very important for ensuring the operation of battery management system, realizing the energy management strategy of electric vehicles, reducing mileage anxiety and promoting the sustainable development of electric vehicles. In this paper, several studies are carried out for state of charge estimation of lithium-ion battery: (1) Aiming at the problem of parameter identification of battery model, an optimal identification method of model parameters based on ant lion optimization algorithm is proposed. (2) An adaptive weighting Cubature particle filter (AWCPF) method is proposed for SOC estimation. The proposed AWCPF method is based on particle filter (PF) algorithm, while the Cubature Kalman filter (CKF) algorithm is utilized to generate the proposal distribution for PF algorithm, which can retrain the particles degradation problem in PF algorithm. To solve the problem that the CKF algorithm is sensitive to noise, comparing with fixed sigma point weights of the conventional CKF, the weights of sigma points are adaptively adjusted based on state and measurement residual vectors. Furthermore, the process noise and measurement noise are estimated iterative. In this paper, experimental verification of different initial values of SOC under various working conditions is carried out. The results show that the proposed AWCPF algorithm based SOC estimation method has high estimation accuracy, strong robustness, fast convergence speed, with the maximum SOC estimation error is less than 1%.

Laplace ℓ1 Huber based cubature Kalman filter for attitude estimation of small satellite

This paper offers a solution to the attitude estimation of small satellite with the existence of model error and heavy-tailed noise, which is referred as to the Laplace ℓ1 Huber Based Kalman filter (ℓ1-HBKF). It employs the Laplace distribution and Huber based method to update the measurement covariance to deal with different types of model error or heavy-tailed noise for robust design. Then, the majorization minimization approach is discussed to improve the estimation accuracy by an iterative algorithm. In addition, the proposed ℓ1-HBKF is implemented in the Kalman filtering framework and is further extended by the strategy of fifth-degree cubature rule for high accuracy. Finally, the attitude estimation of small satellite is simulated and compared with conventional cubature Kalman filter (CKF), which can prove the accuracy and robustness of the proposed methods for the attitude estimation with low precision sensors.

Time-Varying Noise Statistic Estimator Based Adaptive Simplex Cubature Kalman Filter

To address the problem that filtering accuracy is reduced with the inaccurate time-varying noise statistic in conventional cubature Kalman filter, a noise statistic estimator based adaptive simplex cubature Kalman filter is put forward in this paper. First, the simplex cubature rule is adopted to approximate the intractable nonlinear Gaussian weighted integral in the filter. Secondly, a suboptimal unbiased constant noise statistic estimator is derived based on the maximum a posteriori estimation criterion. For the time-varying noise, the above estimator is modified using an exponential weighted attenuation method to realize the oblivion of stale data which results in a fading memory estimator, which has the ability to estimate the time-varying noise statistic to revise the filter online. The simulation results indicate that the proposed filter can achieve higher accuracy than conventional filters with inaccurate noise statistic.

Adaptive cubature Kalman filter with directional uncertainties [Correspondence

In this paper, an adaptive cubature Kalman filter (ACKF) is proposed to improve the performance of the conventional cubature Kalman filter. The ACKF uses a new cubature rule that combines a third-degree spherical rule with an adaptive higher degree radial rule along the directions of larger uncertainty. More accurate and robust results can be obtained with slightly more cubature points than the conventional third-degree cubature Kalman filter (CKF). Compared with other high-degree Gaussian filters, ACKF uses much fewer points but maintains very close performance. A target tracking problem is used to demonstrate the effectiveness of the proposed filter.

Derivative‐free square‐root cubature Kalman filter for non‐linear brushless DC motors

This paper presents a non-linear square-root estimation scheme for brushless DC (BLDC) motors. The cubature Kalman filter (CKF) is the main estimation tool for the presented approach. The CKF is a recently proposed estimator for highly non-linear systems and its efficacy has been verified on several applications. The square-root version of the CKF is preferred over the conventional CKF for real-time applications. Despite of having several advantages over other non-linear filters, the CKF has not yet been explored for state estimation of electric drives in the electric drives community. In this study, the authors present a square-root CKF for the speed and rotor position estimation of a highly non-linear and high fidelity BLDC motor, these estimated speed and rotor position are then fed back to control the speed of the BLDC motor. The efficacy of the presented approach for low and high reference speeds, and in the presence of parametric uncertainties, is demonstrated by real-time experiments.