Search Results (214)

To address the issue of output anomalies that frequently occur in position sensors of permanent magnet synchronous motors within electromechanical actuation systems operating in harsh environments and can lead to degradation in system performance or operational interruptions, this paper proposes an integrated method for fault diagnosis and fault-tolerant control based on the Cubature Kalman Filter (CKF). This approach effectively combines state reconstruction, fault diagnosis, and fault-tolerant control functions. It employs a CKF observer that utilizes innovation and residual sequences to achieve high-precision reconstruction of rotor position and speed, with convergence assured through Lyapunov stability analysis. Furthermore, a diagnostic mechanism that employs dual-parameter thresholds for position residuals and abnormal duration is introduced, facilitating accurate identification of various fault modes, including signal disconnection, stalling, drift, intermittent disconnection, and their coupled complex faults, while autonomously triggering fault-tolerant strategies. Simulation results indicate that the proposed method maintains excellent accuracy in state reconstruction and fault tolerance under disturbances such as parameter perturbations, sudden load changes, and noise interference, significantly enhancing the system’s operational reliability and robustness in challenging conditions. Full article

The degradation of nonlinear filtering in INS/GNSS integrated navigation due to missing GNSS observations and system noise uncertainty is addressed in this paper. An improved cubature Kalman filter (ICKF) is proposed, leveraging a modified cubature point update framework (MUF) and the maximum likelihood (ML) principle. In the ICKF, the ML principle is employed to estimate the process noise covariance, which is then integrated into the MUF to construct the posterior cubature points directly, bypassing the need for resampling. As the process noise covariance is updated in real time, and the prediction cubature points’ error is directly transferred to the posterior cubature points, the proposed algorithm demonstrates reduced sensitivity to missing observations and system noise uncertainty. The effectiveness of the proposed algorithm has been validated through both simulation and practical experiments. Full article

In the operation of high-speed trains, the effective transmission of traction force heavily relies on the adhesion between the wheel and the rail. Excessive traction or braking force may exceed the adhesion limit, causing wheel creep or slide, which threatens both equipment and safety. To address this, a state estimation method based on the SVD-ACKF (singular value decomposition adaptive cubature Kalman filter) is proposed for high-precision estimation of train speed. Combined with an extremum-seeking algorithm, a closed-loop adhesion control strategy is developed to maintain train operations near the maximum adhesion point. Simulation results show that the method ensures accurate tracking under varying rail conditions and noise, while the control algorithm maintains adhesion utilization above 90%, thereby meeting operational demands and enhancing railway safety. Full article

Target tracking in typical radar applications faces critical challenges in complex environments, including nonlinear dynamics, non-Gaussian noise, and sensor outliers. Current robustness-enhanced approaches remain constrained by empirical kernel tuning and computational trade-offs, failing to achieve balanced noise suppression and real-time efficiency. To address these limitations, this paper proposes the variational Bayesian-based maximum correntropy criterion cubature Kalman filter (VBMCC-CKF), which integrates variational Bayesian inference with CKF to establish a fully adaptive robust filtering framework for nonlinear systems. The core innovation lies in constructing a joint estimation framework of state and kernel size, where the kernel size is modeled as an inverse-gamma distributed random variable. Leveraging the conjugate properties of Gaussian-inverse gamma distributions, the method synchronously optimizes the state posterior distribution and kernel size parameters via variational Bayesian inference, eliminating reliance on manual empirical adjustments inherent to conventional correntropy-based filters. Simulation confirms the robust performance of the VBMCC-CKF framework in both single and multi-target tracking under non-Gaussian noise conditions. For the single-target case, it achieves a reduction in trajectory average root mean square error (Avg-RMSE) by at least 14.33% compared to benchmark methods while maintaining real-time computational efficiency. Integrated with multi-Bernoulli filtering, the method achieves a 40% lower optimal subpattern assignment (OSPA) distance even under 10-fold covariance mutations, accompanied by superior hit rates (HRs) and minimal trajectory position RMSEs in cluttered environments. These results substantiate its precision and adaptability for dynamic tracking scenarios. Full article

To address the issue of poor yaw stability in distributed-drive electric pickup trucks at medium-to-high speeds, particularly under the influence of continuously varying tire forces and road adhesion coefficients, a novel Kalman filter-based method for estimating the road adhesion coefficient, combined with a Tube-based Model Predictive Control (Tube-MPC) algorithm, is proposed. This integrated approach enables real-time estimation of the dynamically changing road adhesion coefficient while simultaneously ensuring vehicle yaw stability is maintained under rapid response requirements. The developed hierarchical yaw stability control architecture for distributed-drive electric pickup trucks employs a square root cubature Kalman filter (SRCKF) in its upper layer for accurate road adhesion coefficient estimation; this estimated coefficient is subsequently fed into the intermediate layer’s corrective yaw moment solver where Tube-based Model Predictive Control (Tube-MPC) tracks desired sideslip angle and yaw rate trajectories to derive the stability-critical corrective yaw moment, while the lower layer utilizes a quadratic programming (QP) algorithm for precise four-wheel torque distribution. The proposed control strategy was verified through co-simulation using Simulink and Carsim, with results demonstrating that, compared to conventional MPC and PID algorithms, it significantly improves both the driving stability and control responsiveness of distributed-drive electric pickup trucks under medium- to high-speed conditions. Full article

In order to solve the problem that intelligent vehicle active collision avoidance systems have different decision-making results under different road conditions, the square-root cubature Kalman filtering algorithm is used to estimate the road adhesion coefficients, which are introduced into the safety distance model and combined with the fireworks algorithm for braking and steering weight coefficient allocation to ensure that the vehicle can safely avoid collision. The simulation results show that the square-root cubature Kalman filter has higher estimation accuracy and robustness compared with the cubature Kalman filter, and a more reasonable collision avoidance control can be adopted in the subsequent collision avoidance control. Therefore, the proposed new estimation method of road adhesion coefficients proves effective in mitigating vehicle collision risks. Full article

Space-based radar systems offer significant advantages for air surveillance, including wide-area coverage and extended early-warning capabilities. The integrated design of detection and imaging in space-based wideband radar further enhances its accuracy. However, in the wideband tracking mode, large aircraft targets exhibit extended characteristics. Measurements from the same target cross multiple range resolution cells. Additionally, the nonlinear observation model and uncertain measurement noise characteristics under space-based long-distance observation substantially increase the tracking complexity. To address these challenges, we propose a robust aerial target tracking method for space-based wideband radar applications. First, we extend the observation model of the gamma Gaussian inverse Wishart probability hypothesis density filter to three-dimensional space by incorporating a spherical–radial cubature rule for improved nonlinear filtering. Second, variational Bayesian processing is integrated to enable the joint estimation of the target state and measurement noise parameters, and a recursive process is derived for both Gaussian and Student’s t-distributed measurement noise, enhancing the method’s robustness against noise uncertainty. Comprehensive simulations evaluating varying target extension parameters and noise conditions demonstrate that the proposed method achieves superior tracking accuracy and robustness. Full article

The optimization of computational algorithms is one of the main problems of computational mathematics. This optimization is well demonstrated by the example of the theory of quadrature and cubature formulas. It is known that the numerical integration of definite integrals is of great importance in basic and applied sciences. In this paper we consider the optimization problem of weighted quadrature formulas with derivatives in Sobolev space. Using the extremal function, the square of the norm of the error functional of the considered quadrature formula is calculated. Then, minimizing this norm by coefficients, we obtain a system to find the optimal coefficients of this quadrature formula. The uniqueness of solutions of this system is proved, and an algorithm for solving this system is given. The proposed algorithm is used to obtain the optimal coefficients of the derivative weight quadrature formulas. It should be noted that the optimal weighted quadrature formulas constructed in this work are optimal for the approximate calculation of regular, singular, fractional and strongly oscillating integrals. The constructed optimal quadrature formulas are applied to the approximate solution of linear Fredholm integral equations of the second kind. Finally, the numerical results are compared with the known results of other authors. Full article

Accurate dynamic estimation is of vital importance for the real-time monitoring of the operating status of power systems. To address issues such as non-Gaussian noise and outlier interference, a cubature Kalman filter state estimation method based on robust functions (RF-CKF) is proposed. Firstly, based on the exponential absolute value, an estimator is established, which is represented by the exponential absolute value and quadratic functions. Secondly, the regression form of batch processing mode is established, and the estimator based on the exponential absolute value is integrated into the cubature Kalman filter framework. Finally, an example of a standard IEEE 39-bus system is used to verify the effectiveness of the proposed method. Compared with the unscented Kalman filter, cubature Kalman filter and H-infinity CKF, the proposed method has better estimation accuracy and stronger robustness in an anomaly environment. Full article

In the complex underwater environment, it is hard to obtain accurate system noise prior information. If uncertainty system noise model is used in state determination, the precision will decrease. To address the problem, this paper proposes a novel inverse-Wishart (IW) based variational Bayesian adaptive cubature Kalman filter (IW-VACKF), and the inverse-Wishart distribution is employed as the conjugate prior distribution of system noise covariance matrices. To improve the modeling accuracy, a mixing probability vector is introduced based on the inverse-Wishart distribution to better characterize the uncertainty and dynamic of state noise in underwater environments. Then, the state transition and the measurement process are derived as hierarchical Gaussian models. Subsequently, the posterior information of the system is jointly calculated by employing the variational Bayesian method. Simulations and real trials illustrate that the proposed IW-VACKF can improve the state estimation precision efficiently in the complex underwater environment. Full article

Gravity matching is a key technology in gravity-aided inertial navigation. The traditional Sandia inertial matching algorithm introduces linearization errors using the linear error model, which can diminish navigation accuracy. To address this issue, we propose a novel gravity-matching algorithm based on modified adaptive transformed cubature quaternion estimation (MA-TCQUE), designed for a nonlinear error model to enhance accuracy in gravity-aided navigation. Additionally, the proposed algorithm can estimate the measurement noise matrix demonstrating improved filtering stability in complex and dynamic environments. Finally, simulation and experimental results validate the advantages of the proposed matching algorithm compared to existing state-of-the-art methods. Full article

This work aims to propose an iterative method for approximating solutions of two-dimensional weakly singular Fredholm integral Equation (2D-WSFIE) by incorporating the product integration technique, an appropriate cubature formula, and the Picard algorithm. This iterative approach is utilized to approximate the solution of the 2D-WSFIE that arises in some contact problems in linear elasticity. Under some sufficient conditions, the existence and uniqueness of the solution are established, an error bound for the approximate solution is estimated, and the order of convergence of the proposed algorithm is discussed. The effectiveness of the proposed method is illustrated through its application to some contact problems involving weakly singular kernels. Full article

Under large azimuth misalignment conditions, the initial alignment of strapdown inertial navigation systems (SINS) is challenged by the nonlinear characteristics of the error model. Traditional particle filter (PF) algorithms suffer from the inappropriate selection of importance density functions and severe particle degeneration, which limit their applicability in high-precision navigation. To address these limitations, this paper proposes an adaptive mixed-order spherical simplex-radial cubature particle filter (MLG-AMSSRCPF) algorithm based on matrix Lie group representation. In this approach, attitude errors are represented on the matrix Lie group SO(3), while velocity errors and inertial sensor biases are retained in Euclidean space. Efficient bidirectional conversion between Euclidean and manifold spaces is achieved through exponential and logarithmic maps, enabling accurate attitude estimation without the need for Jacobian matrices. A hybrid-order cubature transformation is introduced to reduce model linearization errors, thereby enhancing the estimation accuracy. To improve the algorithm’s adaptability in dynamic noise environments, an adaptive noise covariance update mechanism is integrated. Meanwhile, the particle similarity is evaluated using Euclidean distance, allowing the dynamic adjustment of particle numbers to balance the filtering accuracy and computational load. Furthermore, a multivariate Huber loss function is employed to adaptively adjust particle weights, effectively suppressing the influence of outliers and significantly improving the robustness of the filter. Simulation and the experimental results validate the superior performance of the proposed algorithm under moving-base alignment conditions. Compared with the conventional cubature particle filter (CPF), the heading accuracy of the MLG-AMSSRCPF algorithm was improved by 31.29% under measurement outlier interference and by 39.79% under system noise mutation scenarios. In comparison with the unscented Kalman filter (UKF), it yields improvements of 58.51% and 58.82%, respectively. These results demonstrate that the proposed method substantially enhances the filtering accuracy, robustness, and computational efficiency of SINS, confirming its practical value for initial alignment in high-noise, complex dynamic, and nonlinear navigation systems. Full article

For manoeuvring surface target tracking in the presence of glint noise, Huber-based Kalman filters have been widely regarded as effective. However, when the proportion of outlier measurements is high, their numerical stability and estimation accuracy can deteriorate significantly. To address this issue, we propose a Robust Cubature Kalman Filter with the Current Statistical (RCKF_CS) model. Inspired by the Huber equivalent weight function, an adaptive factor incorporating a penalty strategy based on a smoothing approximation function is introduced to suppress the adverse effects of glint noise. The proposed method is then integrated into the Cubature Kalman Filter framework combined with the Current Statistical model. Unlike conventional Huber-based approaches, which process measurement residuals independently in each dimension, the proposed method evaluates the residuals jointly to improve robustness. Numerical stability analysis and extensive simulation experiments confirm that the proposed RCKF_CS achieves improved numerical robustness and filtering performance, even under strong glint noise conditions. Compared with existing Huber-based filters, the proposed method enhances filtering performance by 2.66% to 10.18% in manoeuvring surface target tracking tasks affected by glint noise. Full article

In ground-based bearing-only tracking of multiple maneuvering targets, there are difficulties in data association due to the reliance solely on azimuth information, making it challenging to distinguish and identify multiple targets. This problem is particularly pronounced when targets are close or overlapping, leading to disassociation or target loss. Moreover, bearing-only information struggles to accurately capture the dynamic changes in maneuvering targets, significantly affecting tracking accuracy. To address these issues, this paper proposes an Improved Maneuver Detection-Based Multiple Hypothesis Bearing-Only Target Tracking (IMD-MHRPCKF) algorithm. To begin with, the observation range is segmented into multiple sub-intervals through a distance parameterization technique, and within each sub-interval, a Cubature Kalman Filter (CKF) is applied. The Multiple Hypothesis Tracking (MHT) algorithm is then used for data association, solving the measurement ambiguity problem. To detect target maneuvers, the sliding window average of the innovation sequence is calculated. When a target maneuver is detected, the sub-filter parameters are reinitialized to ensure filter stability. In contrast, if no maneuver is detected, the filter parameters remain unchanged. Finally, simulations are used to compare this algorithm with various other algorithms. The results show that the proposed algorithm significantly improves system robustness, reduces tracking errors, and effectively tracks bearing-only multiple maneuvering targets. Full article