Search Results (182)

To address the nonlinear orbit determination problem under multi-satellite cooperative observation, this paper proposes an orbit determination method integrating a plane-constrained observation model with adaptive robust filtering. Based on angular measurements from multiple observation nodes, a linearized observation model is constructed using spatial geometric constraints. The Maximum Correntropy Criterion is then introduced to adaptively weight each measurement component, and a hybrid kernel function is employed to suppress the effects of non-Gaussian noise and outliers. Meanwhile, an adaptive factor based on the covariance matching principle is designed to adjust the process noise intensity online, thereby improving the robustness of the Cubature Kalman Filter in state prediction and update. Simulation results under severe non-Gaussian noise show that the proposed adaptive robust cubature Kalman filter (ARCKF) reduces the position RMSE from 95.3 m for CKF to 30.8 m, corresponding to an improvement of approximately 67.7%, while increasing the computation time from 6.52 s to 7.35 s. These results indicate that the proposed method can achieve improved accuracy and robustness under uncertain measurement statistics and dynamic disturbances, making it suitable for space-based angles-only orbit determination, although further computational optimization is still required for onboard applications. Full article

Accurate and reliable positioning for urban vehicles remains challenging under urban canyon conditions, where Global Navigation Satellite System (GNSS) observations are frequently degraded by multipath, blockage, intermittent outages, and unstable recovery after signal reacquisition. An Inertial Navigation System (INS) can provide continuous short-term motion estimation, but its solution gradually drifts over time. Therefore, robust INS/GNSS integration is essential for urban vehicle positioning. However, in position-only fusion, contaminated GNSS positions can directly distort the integrated positioning solution. Conventional fixed-covariance filters and covariance-only adaptive filters are often insufficient to handle urban GNSS errors that are simultaneously time-varying, bias-like, and phase-dependent. To address this issue, this paper proposes a dual-adaptive robust cubature Kalman filter (Dual-ACKF) for urban vehicle INS/GNSS integration under degraded GNSS conditions. Unlike conventional adaptive CKF/UKF methods that mainly regulate the measurement-noise covariance, the proposed Dual-ACKF jointly introduces an explicit GNSS positioning bias state, a slave innovation-energy-based measurement-noise estimator, and scenario-aware robust update strategies for canyon, outage, and recovery conditions. The proposed method is validated using a challenging real-world UrbanNav sequence with Real-Time Kinematic (RTK)-derived reference trajectories and quality-defined GNSS degradation segments. Compared with Dual-AUKF, CKF, and UKF, the proposed Dual-ACKF reduces the P95 horizontal error in the outage segment from 521.23 m, 582.72 m, and 591.60 m to 228.21 m, corresponding to reductions of 56.22%, 60.84%, and 61.43%, respectively. It also reduces the maximum outage error from 638.02 m, 707.37 m, and 718.78 m to 246.45 m, demonstrating stronger long-tail error suppression during degraded and recovery-related periods. These results indicate that explicitly coupling GNSS bias absorption, online measurement-confidence regulation, and phase-dependent robust updates improves the reliability of position-only INS/GNSS integration in challenging urban environments. Full article

This article outlines various specialized adaptations of the Kalman Filter designed to address specific estimation challenges across different domains of Physics. The work demonstrates the significant potential of the Kalman filter to enhance the accuracy and reliability of measurements in Physics, providing robust, real-time, and adaptive estimation capabilities. The paper starts with an extensive introduction to the core of the Kalman filter. A clear description of the different filter categories follows, along with the conditions under which each is applied. Various Kalman filter variants address nonlinear, adaptive, continuous-time, large-scale, and uncertain systems. These include the Extended and Unscented Kalman Filters for nonlinear estimation, Adaptive and Kalman–Bucy filters for changing or continuous dynamics, and Ensemble or Schmidt–Kalman filters for large or reduced-order systems. Robust, Cubature, Probabilistic, and Particle Kalman filters further improve performance under outliers, strong nonlinearities, and non-Gaussian uncertainty. To illustrate the practical relevance, detailed applications in Physics are discussed, including thermodynamics, electromagnetism, high-energy physics, quantum physics, and astrophysics, highlighting how Kalman filtering enhances both predictive accuracy and measurement-informed decision-making. Full article

Owing to multi-target tracking in scenarios with nonlinearity, uncertain measurement model and high clutter density, the Poisson multi-Bernoulli mixture (PMBM) recursion is prone to unstable covariance propagation under nonlinear dynamics as well as uncertainty in measurement-to-target association caused by mismatched gate that causes erroneous updates from clutters. In the prediction stage, the singular value decomposition (SVD) is used in place of Cholesky factorization to construct and propagate the square-root covariance factor in the square-root cubature Kalman filter (SCKF), yielding a numerically stable square-root implementation. Then, the resulting SVD-SCKF is incorporated into the PMBM prediction step and used to propagate the Gaussian-mixture components of both the Poisson point process (PPP) intensity and the Bernoulli component in the Multi-Bernoulli mixture (MBM), yielding predicted means and covariances under nonlinear dynamics. An adaptive fading factor is determined from innovation statistics, and covariance inflation is performed to improve robustness under target maneuvers and model mismatch. In the update stage, the unknown measurement function is regressed by Gaussian process (GP) using historical state–measurement samples, yielding an equivalent measurement mapping and state-dependent uncertainty. Furthermore, the predicted measurement distribution is generated from the GP-based conditional measurement distribution with state prior approximated by SVD-SCKF cubature points. An adaptive gate is determined from the GP-based conditional measurement distribution, which is approximated by an equivalent ellipsoidal gate via fitting for screening the current measurements and filtering out clutter. Residual in-gate clutter measurements are handled via Bayesian target discrimination, where the posterior probability of measurement originated from target is employed as a weight and incorporated into association weights and update likelihoods. Simulation results further confirm the effectiveness and stability of the proposed filter in complex scenarios. Full article

This paper proposes a robust navigation method based on a robust square-root cubature Kalman filter (RSRCKF) to address the accuracy divergence of integrated navigation systems caused by drilling-induced slippage and the mismatch between the tail-cable encoder and the robot motion during operations of a seafloor drilling robot in deep-sea soft sedimentary layers. Considering the large-deformation mechanical characteristics of the seabed under drilling conditions, a unified state-space model incorporating a time-varying odometer scale-factor error is first established. To alleviate the numerical instability of the nonlinear system in the presence of non-Gaussian noise, a square-root cubature Kalman filter (SRCKF) framework is employed, in which the positive definiteness of the error covariance matrix is dynamically preserved via QR decomposition. Subsequently, an online fault detection mechanism based on a modified chi-square test is developed. By introducing a two-segment IGG (a classical robust weighting scheme) weighting function, an adaptive variance inflation factor is constructed to enable real-time identification and down-weighting of abnormal observations induced by slippage. Field experiments, including drilling and turning tests conducted on tidal mudflats off the coast of Zhoushan, demonstrate that the proposed method can effectively mitigate the impact of “false displacement” disturbances caused by typical soft clay slippage conditions through enhanced statistical robustness. Taking the conventional SINS/OD integration scheme as the baseline, the proposed method achieves an approximate 82.4% reduction in positioning error. These results verify the robustness and engineering applicability of the proposed algorithm in complex seabed environments. Full article

Real-time performance and adaptability are critical factors influencing the safety and stability of autonomous vehicle trajectory tracking. Therefore, enhancing these aspects is essential for improving driving safety. This paper proposes a trajectory tracking control method for autonomous vehicles based on an adaptive model parameter correction controller (MPACC). First, by integrating the variable universe fuzzy control (VUFC) principle with a model predictive controller (MPC), a variable universe fuzzy model predictive controller (VUFMPC) is designed. This controller enables adaptive adjustment of MPC weighting coefficients, thereby effectively improving the real-time capability and adaptability of the MPC. Second, an adaptive square root cubature Kalman filter (ASRCKF) tire lateral force estimator with adaptive scaling factors is introduced to obtain real-time tire cornering stiffness values as MPC parameters, achieving adaptive correction of the MPC parameters and forming an adaptive model predictive controller (AMPC). Furthermore, an MPACC is designed by integrating VUFMPC and AMPC. This controller allows for real-time adaptive correction of control parameters according to the vehicle’s driving state. Finally, hardware in loop (HIL) tests are conducted for comparative analysis. The results demonstrate that the proposed MPACC exhibits excellent real-time performance and adaptability, while effectively balancing trajectory tracking accuracy and driving stability of autonomous vehicles. Full article

Accurate and continuous outdoor pedestrian positioning using smartphones remains challenging in complex environments like urban canyons, where Global Navigation Satellite System (GNSS) signals are frequently degraded or blocked, and Pedestrian Dead Reckoning (PDR) suffers from cumulative errors. To address this, this paper proposes a novel fusion method based on a Robust Adaptive Cubature Kalman Filter (RACKF). The core of our approach is a two-stage filtering architecture: the first stage employs a quaternion-based RACKF to optimally fuse gyroscope and magnetometer data for robust heading estimation; the second stage performs the core fusion of GNSS observations with an enhanced 3D PDR solution. Key innovations include an adaptive noise estimation strategy combining fading and limited memory weighting, a robust M-estimator-based mechanism to suppress outliers, and the integration of differential barometric height measurements. Experimental results demonstrate that the proposed method achieves a horizontal positioning accuracy of 3.28 m (RMSE), outperforming standalone GNSS and improving 3D PDR by 25.97% and 10.39%, respectively. This work provides a practical, infrastructure-free solution for robust smartphone-based outdoor navigation. Full article

Accurate prediction of aquifer water abundance is critical for coal mine safety, yet traditional static models often fail to capture the spatial heterogeneity and non-stationarity of hydrogeological conditions. This study proposes a dynamic evaluation methodology integrating Grey Relational Analysis, the Analytic Hierarchy Process, and a Time-Varying Parameter Cubature Kalman Filter (TVP-CKF). By reconceptualizing spatial borehole data as a dynamic time-series process, the model recursively updates the contribution weights of six controlling factors based on monitoring data from 2012 to 2020. Analysis reveals a structural shift in the groundwater system: the influence of hydrochemical factors (TDS) has diminished, while hydraulic conductivity has become the dominant control over time. The TVP-CKF model significantly outperformed static regression and recursive least squares baselines, demonstrating superior convergence stability and precisely capturing transient inflow fluctuations. Furthermore, its uncertainty quantification effectively bounded extreme low-flow events within 95% confidence intervals. This approach validates the necessity of adaptive modeling in evolving geological environments, providing a robust, risk-quantified tool for precise water inrush prevention. Full article

Orbit determination for non-cooperative targets represents a significant focus of research within the domain of space situational awareness. In contrast to cooperative targets, non-cooperative targets do not provide their orbital parameters, necessitating the use of observation data for accurate orbit determination. The increasing prevalence of low-cost, low-thrust spacecraft has heightened the demand for advancements in real-time orbit determination and parameter estimation for low-thrust maneuvers. This paper presents a novel dual-layer filter approach designed to facilitate real-time acceleration estimation for non-cooperative targets. Initially, the method employs a square-root cubature Kalman filter (SRCKF) to handle the nonlinearity of the system and a Jerk model to address the challenges in acceleration modeling, thereby yielding a preliminary estimation of the acceleration produced by the thruster of the non-cooperative target. Subsequently, a specialized filtering structure is established for the estimated acceleration, and two filtering frameworks are integrated into a dual-layer filter model via the cubature transform, significantly enhancing the estimation accuracy of acceleration parameters. Finally, to adapt to the potential on/off states of the thrusters, the Interacting Multiple Model (IMM) algorithm is employed to bolster the robustness of the proposed solution. Simulation results validate the effectiveness of the proposed method in achieving real-time orbit determination and acceleration estimation. Full article

The Linked Autonomous Interplanetary Satellite Orbit Navigation (LiAISON) technique enables cislunar spacecraft to obtain accurate position and velocity information, allowing full state estimation of two vehicles using only inter-satellite range (ISR) measurements when both their dynamical states are unknown. However, its stand-alone use leads to significantly increased orbit determination errors when the orbital planes of the two spacecraft are nearly coplanar, and is characterized by long initial convergence times and slow recovery following dynamical disturbances. To mitigate these issues, this study introduces an integrated navigation method that augments inter-satellite range measurements with line-of-sight vector angles relative to background stars. Additionally, an enhanced Adaptive Robust Cubature Kalman Filter (ARCKF) incorporating a chi-square test-based adaptive forgetting factor (AFF-ARCKF) is developed. This algorithm performs adaptive estimation of both process and measurement noise covariance matrices, improving convergence speed and accuracy while effectively suppressing the influence of measurement outliers. Numerical simulations involving spacecraft in Earth–Moon L4 planar orbits and distant retrograde orbits (DRO) confirm that the proposed method significantly enhances system observability under near-coplanar conditions. Comparative evaluations demonstrate that AFF-ARCKF achieves faster convergence compared to the standard ARCKF. Further analysis examining the effects of initial state errors and varying initial forgetting factors clarifies the operational boundaries and practical applicability of the proposed algorithm. Full article

Simultaneous state and parameter estimation is essential for control system design and dynamic modeling of physical systems. This capability provides critical real-time insight into system behavior, supports the discovery of underlying mechanisms, and facilitates adaptive control strategies. Surveyed in this review paper are two classes of state and parameter estimation methods: Kalman Filters and Luenberger Observers. The Kalman Filter framework, including its major variants such as the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Cubature Kalman Filter (CKF), and Ensemble Kalman Filter (EnKF), has been widely applied for joint and dual estimation in linear and nonlinear systems under uncertainty. In parallel, Luenberger observers, typically used in deterministic settings, offer alternative approaches through high-gain, sliding mode, and adaptive observer structures. This review focuses on the theoretical foundations, algorithmic developments, and application domains of these methods and provides a comparative analysis of their advantages, limitations, and practical relevance across diverse engineering scenarios. Full article

To achieve accurate estimates of a lithium-ion battery’s charge level (SOC) and health condition (SOH), this paper tackles key issues in battery management by introducing a framework built around an adaptive square root cubature Kalman filter (ASRCKF) that tracks parameters in real time for better performance in changing environments. It uses ASRCKF to gauge SOC, while an extended Kalman filter (EKF) identifies battery traits online and monitors capacity loss, with a two-way feedback system that feeds SOH updates directly into the SOC calculations. Testing in high-speed driving, the New European Driving Cycle, and urban stop–start conditions showed the method keeps average SOC errors to 0.16% at most and peak errors to 0.33%, beating out standard EKF and SRCKF approaches in accuracy; SOH errors averaged 0.42%. Overall, this setup proves reliable for combined SOC-SOH tracking in diverse real-world situations, helping to ensure safer battery operations. Full article

Hypersonic glide targets (HGTs) pose significant challenges for radar tracking due to complex maneuver strategies and time-varying statistics of measurement noise. Conventional single-model tracking methods are generally insufficient to fully capture maneuver modes, while existing multiple-model methods face trade-offs between model set completeness and computational efficiency. In addition, existing tracking methods struggle to cope with the non-Gaussian noise during hypersonic flight. To overcome these limitations, a Hierarchical Adaptive Moment Matching (HAMM) multiple-model method is proposed in this paper. Firstly, a comprehensive model set is constructed to cover characteristic maneuver modes. Subsequently, a hierarchical multiple-model framework is developed where: (1) a coarse model set is dynamically adapted by multi-frame posterior probability evolution and Rényi divergence criteria; (2) a fine model set is generated based on the moment matching method. Furthermore, the minimum error entropy cubature Kalman filter (MEECKF) is proposed to suppress the non-Gaussian measurement noise with high stability. Monte Carlo simulations demonstrate that the proposed method achieves improved positioning accuracy and faster convergence. Full article

Small unmanned aerial vehicles are now commonly equipped with integrated navigation systems to obtain high-precision navigation parameters. However, affected by the dual impacts of multipath effects and dynamic environmental changes, their state estimation process is vulnerable to interference from measurement outliers, which in turn leads to the degradation of navigation accuracy and poses a threat to flight safety. To address this issue, this research presents an adaptive minimum error entropy cubature Kalman filter. Firstly, the cubature Kalman filter is introduced to solve the problem of model nonlinear errors; secondly, the cubature Kalman filter based on minimum error entropy is derived to effectively curb the interference that measurement outliers impose on filtering results; finally, a kernel bandwidth adjustment factor is designed, and the kernel bandwidth is estimated adaptively to further improve navigation accuracy. Through numerical simulation experiments, the robustness of the proposed method with respect to measurement outliers is validated; further flight experiment results show that compared with existing related filters, this proposed filter can achieve more accurate navigation and positioning. Full article

Nonlinear filtering algorithms have significant implications in the optimal estimation of navigation states and in improving the accuracy, reliability, and robustness of navigation systems. This manuscript surveys the developments of the nonlinear filtering algorithms (extended Kalman filtering (EKF), unscented Kalman filtering (UKF), Cubature Kalman filtering (CKF), particle filtering (PF), neural network filtering (NNF)) and adaptive/robust KF in integrated navigation systems. The principle, application, and existing problems of these nonlinear filtering algorithms are mainly studied, and the comparative analysis and prospect are carried out. Full article