Search Results (161)

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

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

Precise and real-time estimation of vehicle mass and road slope plays a pivotal role in attaining accurate vehicle control. Currently, road slope estimation predominantly emphasizes longitudinal slopes, with limited research on intricate slopes that include both longitudinal roads and continuous turning up-and-down slopes. To address the limitations in existing road slope estimation research, this paper puts forward a novel joint-estimation approach for vehicle mass and road slope. Vehicle mass is initially estimated via M-estimation and recursive least squares with a forgetting factor (FFRLS). A road slope estimate approach, which utilizes interacting multiple models (IMM) and cubature Kalman filtering (CKF), is proposed for complex road slope scenarios. This algorithm integrates kinematic and dynamic vehicle models within the multi-model (MM) ensemble of the IMM filter. The kinematic vehicle model is appropriate for longitudinal road gradients, whereas the dynamic vehicle model is better suited for continuous turning up-and-down slope conditions. The IMM filter employs a stochastic process to weight the appropriate vehicle model according to the driving conditions. Consequently, the weights assigned by the IMM filter enable the algorithm to adaptively select the most suitable vehicle model, leading to more accurate slope estimates under complex conditions compared to single-model-based algorithms. Simulations were carried out using Matlab/Simulink2020-Trucksim2020 to verify the effectiveness of the proposed estimation approach. The results demonstrate that, compared with existing methods, the proposed estimation approach has achieved an improvement in the precision of evaluating vehicle mass and road gradient, thus confirming its superiority. Full article

An adaptive constant acceleration (ACA) model is proposed for the maneuvering target tracking problem. Based on the Taylor series expansion of acceleration, we establish the relationship between the Jerk and the velocity as well as the acceleration so that the maneuvering acceleration variance is approximated by the components in the state error covariance matrix. Then, the latter one is connected with the process noise, and the adaptive adjustment of the ACA model is realized. Combining with the strong tracking square-root cubature filter (ST-SCKF) in our previous work, an ACA-ST-SCKF is developed. The simulation results show that the proposed filter possesses better adaptability, tracking accuracy and lower computational complexity compared with the adaptive current statistical (ACS) model-based ST-SCKF, the modified CS (MCS) model-based ST-SCKF, and the IMM-based STF-SCKF. Full article

In order to improve the driving stability of distributed-drive intelligent electric vehicles under different roadway attachment conditions, this paper proposes a multi-parameter control algorithm based on the estimation of road adhesion coefficients. First, a seven-degree-of-freedom (7-DOF) vehicle dynamics model is established and optimized with a layered control strategy. The upper-level control module calculates the desired yaw rate and sideslip angle using the two-degree-of-freedom (2-DOF) vehicle model and estimates the road adhesion coefficient by using the singular-value optimized cubature Kalman filtering (CKF) algorithm; the middle-level utilizes the second-order sliding mode controller (SOSMC) as a direct yaw moment controller in order to track the desired yaw rate and sideslip angle while also employing a joint distribution algorithm to control the torque distribution based on vehicle stability parameters, thereby enhancing system robustness; and the lower-level controller performs optimal torque allocation based on the optimal tire loading rate as the objective. A Speedgoat-CarSim hardware-in-the-loop simulation platform was established, and typical driving scenarios were simulated to assess the stability and accuracy of the proposed control algorithm. The results demonstrate that the proposed algorithm significantly enhances vehicle-handling stability across both high- and low-adhesion road conditions. Full article

The field of autonomous vehicle technology has experienced remarkable growth. A pivotal trend in this development is the enhancement of tracking performance and stability under high-speed conditions. Model predictive control (MPC), as a prevalent motion control method, necessitates an extended prediction horizon as vehicle speed increases and will lead to heightened online computational demands. To address this, a path preview strategy is integrated into the MPC framework that temporarily freezes the vehicle state within the prediction horizon. This approach assumes that the vehicle state will remain consistent for a specified preview distance and duration, effectively extending the prediction horizon for the MPC controller. In addition, a stability controller is designed to maintain handling stability under high-speed conditions, in which a square-root cubature Kalman filter (SRCKF) estimator is employed to predict tire forces to facilitate the cornering stiffness estimation of vehicle tires. The double lane change maneuver under high-speed conditions is conducted through the Carsim/Simulink co-simulation. The outcomes demonstrate that the SRCKF estimator could provide a reasonably accurate estimation of lateral tire forces throughout the whole traveling process and facilitates the stability controller to guarantee the handling stability. On the premise of ensuring handling stability, integrating the preview strategy could nearly double the prediction horizon for MPC, resulting in the limited increase of online computation burden brought while maintaining path tracking accuracy. Full article

The accurate estimation of flow angles is crucial for enhancing flight performance and aircraft safety. Flow angles of fixed-wing small unmanned aerial vehicles (SUAVs) are more vulnerable due to their low airspeed. Current flow angle measurement devices have not been widely implemented in SUAVs due to their substantial cost and size constraints. Moreover, there are no general estimation methods suitable for SUAVs based on their rudimentary sensor suite. This study presents a generalized optimization-assisted filter estimation (OAFE) method for estimating the relative velocity and flow angles of fixed-wing SUAVs based on a standard sensor suite. This OAFE method mainly consists of a cubature Kalman filter and an optimizer. The filter serves as the main loop with which to generate flow angles in real time by fusing the acceleration, angular rate, attitude, and airspeed. Without flow angle measurements, the optimizer generates approximate aerodynamic derivatives, which serve as pseudo-measurements with which to refine the performance of the filter. The results demonstrate that the estimated angle of attack and side slip angle displayed root mean square errors of around 0.11° and 0.24° in the simulation. The feasibility was also verified in field tests. The OAFE method does not require flow angle measurements, the prior acquisition of aerodynamic parameters, or model training, making it suitable for quick deployment on different SUAVs. Full article

Simultaneous localization and mapping (SLAM) faces significant challenges due to high computational costs, low accuracy, and instability, which are particularly problematic because SLAM systems often operate in real-time environments where timely and precise state estimation is crucial. High computational costs can lead to delays, low accuracy can result in incorrect mapping and localization, and instability can make the entire system unreliable, especially in dynamic or complex environments. As the state-space dimension increases, the filtering error of the standard cubature Kalman filter (CKF) grows, leading to difficulties in multiplicative noise propagation and instability in state estimation results. To address these issues, this paper proposes an extended-dimensional embedded CKF based on truncated singular-value decomposition (TSVD-AECKF). Firstly, singular-value decomposition (SVD) is employed instead of the Cholesky decomposition in the standard CKF to mitigate the non-positive definiteness of the state covariance matrix. Considering the effect of small singular values on the stability of state estimation, a method is provided to truncate singular values by determining the truncation threshold using the Akaike information criterion (AIC). Furthermore, the system noise is embedded into the state variables, and an embedding volume criterion is used to improve the conventional CKF while extending the dimensionality. Finally, the proposed algorithm was validated and analyzed through both simulations and real-world experiments. The results indicate that the proposed method effectively mitigates the increase in localization error as the state-space dimension grows, enhancing time efficiency by 55.54%, and improving accuracy by 35.13% compared to the standard CKF algorithm, thereby enhancing the robustness and stability of mapping. Full article

Aiming at the uncertainty of target motion and observation models in multi-maneuvering target tracking (MMTT), this study presents an innovative data-driven approach based on a Gaussian process (GP). Traditional multi-model (MM) methods rely on a predefined set of motion models to describe target maneuvering. However, these methods are limited by the finite number of available models, making them unsuitable for handling highly complex and dynamic real-world scenarios, which, in turn, restricts the adaptability and flexibility of the filter. In addition, traditional methods often assume that observation models follow ideal linear or simple nonlinear relationships. However, these assumptions may be biased in actual application and so lead to degradation in tracking performance. To overcome these limitations, this study presents a learning-based algorithm-leveraging GP. This non-parametric GP approach enables learning an unlimited range of target motion and observation models, effectively mitigating the problems of model overload and mismatch. This improves the algorithm’s adaptability in complex environments. When the motion and observation models of multiple targets are unknown, the learned models are incorporated into the cubature Kalman probability hypothesis density (PHD) filter to achieve an accurate MMTT estimate. Our simulation results show that the presented approach delivers high-precision tracking of complex multi-maneuvering target scenarios, validating its effectiveness in addressing model uncertainty. Full article

This paper considers the problem of tracking a three-dimensional target under the condition that only a single two-dimensional radar is available. Since a two-dimensional radar can only measure the slant range and azimuth information relative to the target, an unobservability issue arises in this tracking application. Therefore, we first investigate the observability issue of tracking a three-dimensional target with a single two-dimensional radar from two perspectives, including intuitive illustration and quantitative analysis. From the perspective of intuitive illustration, we demonstrate “What is the unobservability issue” and “How does the relative target-radar geometry influence the observability of the tracking system”. From the perspective of quantitative analysis, we construct a novel observability metric for this special tracking problem. Second, aiming at improving tracking performance under the unobservability of target height, we propose an observability-based Gaussian sum cubature Kalman filter. Built within the Gaussian sum framework and based on the height-parameterized strategy, this novel algorithm uses a set of independent fifth-degree cubature Kalman filters, each of which can detect the system observability variation and enhance the tracking accuracy by using a Gaussian splitting scheme under low-degree observability. Finally, the effectiveness of the presented filtering algorithm is validated through lots of simulation experiments. Full article

Road roughness significantly impacts vehicle safety and dynamic responses. For nonlinear suspension systems, the nonlinear characteristics often make it challenging for estimators to identify the actual road roughness accurately. This paper proposes a hybrid road roughness identification algorithm based on nonlinear auto-regressive with exogenous inputs (NARX) and a process noise adaptive square root cubature Kalman filter (PASCKF) to address this issue. Driven by vehicle acceleration data, an NARX-based road roughness identification system is constructed to mitigate the model uncertainties. Furthermore, a hybrid strategy is proposed. On the one hand, the accurate road roughness estimated by the NARX is converted into process noise covariance, enhancing the estimator’s accuracy and convergence rate. Another switching strategy is proposed to optimize the non-convergence issues of the PASCKF. Finally, simulation and actual vehicle experiment data demonstrate that this approach offers superior identification accuracy and adaptability compared to the standalone SCKF algorithm. Full article

Estimating the state of a system by fusing sensor data is a major prerequisite in many applications. When the state is time-variant, derivatives of the Kalman filter are a popular choice for solving that task. Two variants are the square-root unscented Kalman filter (SRUKF) and the square-root cubature Kalman filter (SCKF). In contrast to the unscented Kalman filter (UKF) and the cubature Kalman filter (CKF), they do not operate on the covariance matrix but on its square root. In this work, we modify the SRUKF and the SCKF for use on manifolds. This is particularly relevant for many state estimation problems when, for example, an orientation is part of a state or a measurement. In contrast to other approaches, our solution is both generic and mathematically coherent. It has the same theoretical complexity as the UKF and CKF on manifolds, but we show that the practical implementation can be faster. Furthermore, it gains the improved numerical properties of the classical SRUKF and SCKF. We compare the SRUKF and the SCKF on manifolds to the UKF and the CKF on manifolds, using the example of odometry estimation for an autonomous car. It is demonstrated that all algorithms have the same localization performance, but our SRUKF and SCKF have lower computational demands. Full article