Kalman Filter Research Articles

VRDeepSafety: A Scalable VR Simulation Platform with V2X Communication for Enhanced Accident Prediction in Autonomous Vehicles

Safe real-world navigation for autonomous vehicles (AVs) requires robust perception and decision-making, especially in complex, multi-agent scenarios. Existing AV datasets are limited by their inability to capture diverse V2X communication scenarios, lack of synchronized multi-sensor data, and insufficient coverage of critical edge cases in multi-vehicle interactions. This paper introduces VRDeepSafety, a novel and scalable VR simulation platform that overcomes these limitations by integrating Vehicle-to-Everything (V2X) communication, including realistic latency, packet loss, and signal prioritization, to enhance AV accident prediction and mitigation. VRDeepSafety generates comprehensive datasets featuring synchronized multi-vehicle interactions, coordinated V2X scenarios, and diverse sensor data, including visual, LiDAR, radar, and V2X streams. Evaluated with our novel deep-learning model, VRFormer, which uniquely fuses VR sensor data with V2X using a probabilistic Bayesian inference, as well as a hierarchical Kalman and particle filter structure, VRDeepSafety achieved an 85% accident prediction accuracy (APA) at a 2 s horizon, a 17% increase in 3D object detection precision (mAP), and a 0.3 s reduction in response time, outperforming a single-vehicle baseline. Furthermore, V2X integration increased APA by 15%. Extending the prediction horizon to 3–4 s reduced APA to 70%, highlighting the trade-off between prediction time and accuracy. The VRDeepSafety high-fidelity simulation and integrated V2X provide a valuable and rigorous tool for developing safer and more responsive AVs.

Integrated Navigation Algorithm for Autonomous Underwater Vehicle Based on Linear Kalman Filter, Thrust Model, and Propeller Tachometer

For the purpose of reducing the cost, size, and weight of the integrated navigation system of an AUV (autonomous underwater vehicle), and improving the stealth of this system, an integrated navigation algorithm based on a propeller tachometer is proposed. The algorithm consists of five steps: ① establishing the resistance model of AUV, ② establishing the thrust model, ③ utilizing the measured speeds obtained from the AUV’s voyage trials for calibration, ④ discrimination and replacement of outliers from the tachometer measurements, and ⑤ establishing a linear Kalman filter (LKF) with water currents as state variables. This paper provides the modeling procedure, formula derivations, model parameters, and algorithm process, etc. Through research and analysis, the proposed algorithm’s accuracy has been improved. The specific values of the localization error are detailed in the main text. Therefore, the proposed algorithm has high accuracy, a strong anti-interference capability, and good robustness. Moreover, it exhibits certain adaptability to complex environments and value for practical engineering.

Enhanced Data-Driven Framework for Anomaly Detection in Smart Grid IEDs

The incorporation of Information and Communication Technologies (ICT) into traditional power grids has transformed them into smart grids, revolutionizing energy management systems. At the core of this transformation are Intelligent Electronic Devices (IEDs), which provide essential data for key Energy Management System (EMS) applications, such as state estimation and optimal power flow. IEDs are critical for ensuring the stability and security of smart grid operations, but they are also vulnerable to various anomalies, including infrastructure faults, equipment malfunctions, energy theft, and cyberattacks. Detecting these anomalies is vital to maintaining the reliability of smart grid systems and preventing potential threats to national security. This study introduces a statistical data-driven framework designed to detect and explain anomalies in IED-based smart grid systems. The framework includes a preprocessing module for ensuring high-quality input data and an anomaly detection module that prioritizes interpretability and explainability. Using methods like the Gaussian Mixture Model (GMM), Kalman Filter (KF), and ExtraTree Classifier, the framework achieves 99% accuracy in anomaly detection and 88% accuracy in classifying events as either natural occurrences or cyberattacks.

Commercial vehicle state estimation based on Interactive Multi-Model Square Root Cubature Kalman Filtering

Abstract Accurate and reliable vehicle state information is essential for ensuring vehicle safety and stability. While Interactive Multiple Model Square Root Cubature Kalman Filtering (IMM-SRCKF) has shown promise in state estimation, this work specifically addresses the unique challenges of achieving high-accuracy and real-time state estimation for commercial vehicles within complex driving scenarios. A nonlinear three-degree-of-freedom vehicle dynamic model, encompassing longitudinal, lateral, and yaw motions, was developed as a foundation. State space and observation equations were then derived. The IMM-SRCKF algorithm was strategically utilized and adapted to enhance the selection of process and measurement noise covariance matrices, effectively integrating multiple model strategies with the inherent advantages of square root Kalman filtering. This approach enables real-time dynamic adjustment of each sub-model's weights. Co-simulation results using TruckSim and MATLAB/Simulink demonstrate that the proposed IMM-SRCKF method offers significant improvements over traditional techniques like the Extended Kalman Filter (EKF), Cubature Kalman Filter (CKF), and Square Root Cubature Kalman Filter (SRCKF), particularly in demanding double lane change and serpentining maneuvers. The notably lower Normalized Root Mean Square Error (NRMSE) values confirm the substantial enhancements in both accuracy and stability for commercial vehicle state estimation.

Low harmonic distortion demodulation scheme for PMDI-TDM structure fiber-optic sensor array

The fiber-optic sensor array based on path-matched differential interferometry (PMDI)-time division multiplexing (TDM) offers the advantages of minimal channel crosstalk and high sensitivity. The 3 × 3 optical fiber coupler demodulation is the commonly employed scheme for PMDI-TDM. However, due to the non-ideal characteristics of the 3 × 3 optical fiber coupler and inconsistencies in multi-channel photodetectors, harmonic distortion occurs during signal demodulation. This paper proposes a low harmonic distortion signal demodulation scheme for PMDI-TDM structure fiber-optic sensor arrays based on multi-channel parameter fitting and tracking. This scheme utilizes the random sample consensus (RANSAC) algorithm to accurately obtain the parameters of the ellipse formed by the interference fringes of each element sensor in the system. Furthermore, the multi-channel parallel extended Kalman filter (MPEKF) is used to realize the real-time tracking of multi-channel demodulation parameters. The RANSAC-MPEKF scheme can suppress the influence of outliers, and effectively eliminate the non-ideal characteristics of 3 × 3 coupler and the non-consistency of photodetector, thereby suppressing harmonic distortion of the demodulation results of each channel. The experimental results demonstrate that the proposed scheme can suppress the influence of outliers, .and achieves a demodulation rate ≥500 kHz with minimal resource consumption, making it particularly suitable for large-scale multiplexing systems with a THD value better than 0.12%.

A Hybrid Approach for Predictive Control of Oil Well Production Using Dynamic System Identification and Real-Time Parameter Estimation

A significant part of modern natural sciences aims to establish a model-based approach to describe the behavior of physical systems and forecast their dynamics in different scenarios. The successful application of model-based analysis of transport phenomena is driven by several components, such as the consistency of a model and the uncertainty associated with its parameters. The unsatisfactory results of simulations can be caused by an improper choice of numerical methods used, but more importantly, it can be a result of wrong assumptions while establishing the model and a poor choice of closure parameters such as physical properties of fluids. This motivated the development of a hybrid approach that combines model identification directly from the data and subsequent real-time parameter estimation, which eventually minimizes the uncertainty of the developed model. This essentially brings a new model-based approach for an optimal simulation of physical phenomena by incorporating stringent interactions between all the stages of the modeling process. The identification of the governing equation from the data is achieved by a regression technique, while the model refinement is performed using the extended Kalman filter algorithm. The obtained in such a way model is then applied for control-oriented analysis. This paper discusses the deployment of such an integrated approach on a step-to-step basis and demonstrates its application to the problem of a single-phase oil inflow to the producing well.

The synergy of assimilating visible and infrared radiances and radar observations

AbstractCloud‐affected satellite observations in the visible and infrared spectrum contain vast and largely complementary information on clouds and atmospheric convection and thereby constitute a promising data source for convective‐scale data assimilation. Preceding studies have demonstrated that the assimilation of either one of these observation types can lead to improved convective‐scale weather forecasts, but research on the combined assimilation of cloud‐affected visible and infrared satellite data as well as radar observations is still very scarce. In this article, we investigate the combined assimilation of multiple infrared and visible satellite channels as well as radar observations, and evaluate their analysis and forecast impact with a primary focus on clouds and precipitation. We assimilate visible (0.6‐) and thermal infrared (6.2‐ and 7.3‐ ) satellite channels in observing‐system simulation experiments (OSSEs) with a perfect‐model forecast for an idealized weather scenario. Observations are simulated synthetically and assimilated by the ensemble adjustment Kalman filter (EAKF). The forecasts used the Weather Research and Forecasting (WRF) model at 2‐km grid resolution. Results show that assimilating satellite channels in addition to radar reflectivity can improve forecasts of cloudiness and precipitation, while improvements in temperature, humidity, and wind fields are about the same as in the radar experiment. The evaluation of the analysis error for different cloud conditions revealed that the combined assimilation can mitigate the ambiguity of individual visible and infrared channels. Assimilating visible reflectance before infrared brightness temperature can remove pre‐existing erroneous water clouds and avoid the introduction of erroneous clouds by the following assimilation of infrared channels. It follows that the combined assimilation of visible and infrared radiances could be crucial to avoid shortcomings of assimilating only visible or infrared radiances in convective‐scale numerical weather prediction.

Kalman filter enhanced active learning sampling for inelastic neutron scattering: The case of CrSBr

Kalman filter enhanced active learning sampling for inelastic neutron scattering: The case of CrSBr

Crankshaft high cycle bending fatigue test method based on the combined extended Kalman filtering algorithm and different failure criterion parameters.

In this paper, an accelerated bending fatigue test method for the crankshaft was proposed based on the combination of the extended Kalman filtering algorithm method (EKF) and different failure criterion parameters. First the intrinsic frequency of the system and the fatigue crack depth were chosen to be the failure criterion parameters based on the test regulation and the theory of fracture mechanics. Then the extended Kalman filtering method was adopted in predicting the remaining high cycle fatigue life of the crankshaft during the experiment process. Finally the predicted fatigue life was selected to replace the actual test results for the key fatigue property parameter analysis. Based on this research, the time duration of the test was reduced obviously without affecting the key analysis parameters obviously. In addition, compared with the intrinsic frequency of the system, the fatigue crack depth is more suitable to be selected as the failure criterion to provide more reasonable enhancing effect. The main conclusions draw from this paper can provide some theoretical guidance for the design and manufacturing process of the part.

Online Cell-by-Cell Calibration Method to Enhance the Kalman-Filter-Based State-of-Charge Estimation

Kalman filter (KF) is an effective way to estimate the state-of-charge (SOC), but its performance is heavily dependent on the state-space model parameters. One of the factors that causes the model parameters to change is battery aging, which is individually and non-uniformly experienced by the cells inside the battery pack. To mitigate this issue, this paper proposes an online calibration method considering the impact of cell aging and cell inconsistency. In this method, the state-of-health (SOH) levels of the individual cells are estimated using the deep learning method, and the historical parameter loop-up table is constructed to update the state-space model. The proposed calibration framework provides enhanced accuracy for cell-by-cell SOC estimation by lightweight computing devices. The SOC estimation errors of the calibrated EKF reduce to 1.81% compared to 12.1% of the uncalibrated algorithms.

Dataset of noise signals generated by smart attackers for disrupting state of health and state of charge estimations of battery energy storage systems.

This dataset is generated from real-time simulations conducted in MATLAB/Simscape, focusing on the impact of smart noise signals on battery energy storage systems (BESS). Using Deep Reinforcement Learning (DRL) agent known as Proximal Policy Optimization (PPO), noise signals in the form of subtle millivolt and milliampere variations are strategically created to represent realistic cases of False Data Injection Attacks (FDIA). These signals are designed to disrupt the State of Charge (SoC) and State of Health (SoH) estimation blocks within Unscented Kalman Filters (UKF). The low-magnitude noise signals are specifically crafted to be stealthy, evading easy detection while still effectively causing malfunctions in the estimation processes. Additionally, we introduce a verification case using a different battery model and estimation algorithm to enhance generalization. This case involves high-noise signals with defined thresholds for current and voltage noise levels, which cause significant disruptions to Kalman Filters. These signals serve as a complementary example of adversarial attacks, demonstrating how such noise can destabilize estimation algorithms and lead to critical control errors. This dataset is valuable for researchers and engineers aiming to understand and mitigate the effects of smart cyber-physical attacks on BESS. These attacks can disrupt real-time BESS controllers by injecting false input data related to SoC and SoH, leading to physical control manipulations, increased energy costs, inefficiencies in demand-side management, and incorrect day-ahead scheduling, thereby destabilizing grid operations. The data is reusable in studies focused on enhancing the resilience of SoC and SoH estimation methods, as well as in developing robust defensive strategies against smart DRL-based adversarial attacks.

JTF-SqueezeNet: A SqueezeNet network based on joint time-frequency data representation for egg-laying detection in individually caged ducks.

Accurate individual egg-laying detection is crucial for eliminating low-yielding breeder ducks and improving production efficiency. However, existing methods are often expensive and require strict environmental conditions. This study proposes a data processing method based on wearable sensors and joint time-frequency representation (TFR), aimed at accurately identifying egg-laying in ducks. First, the sensors continuously monitor the ducks' activity and collect corresponding X-axis acceleration data. Next, a sliding window combined with Short-Time Fourier Transform (STFT) is applied to convert the continuous data into spectrograms within consecutive windows. SqueezeNet is then used to detect spectrograms containing key features of the egg-laying process, marking these as egg-laying state windows. Finally, Kalman filtering was used to continuously predict the detected egg-laying status, allowing for the precise determination of the egg-laying period. The best detection performance was achieved by applying the 10-fold cross-validation to a dataset of 59,135 spectrograms, using a window size of 50 min and a step size of 3 min. This configuration yielded an accuracy of 95.73 % for detecting egg-laying status, with an inference time of only 2.1511 milliseconds per window. The accuracy for identifying the egg-laying period reached 92.19 %, with a precision of 93.57 % and a recall rate of 91.95 %. Additionally, we explored the scalability of the joint time-frequency representation to reduce the computational complexity of the model.

Development of source term estimation model using Kalman filter technique and its evaluation against reversal method

Development of source term estimation model using Kalman filter technique and its evaluation against reversal method

Utilizing ensemble Kalman filtering in proper orthogonal decomposition Galerkin reduced-order models for turbulent flow prediction

Developing reduced-order models for turbulent flow prediction is essential for engineering applications. This research introduces a reduced-order model based on the ensemble Kalman filter (EnKF) approach, designed to refine the ordinary differential equation constants in proper orthogonal decomposition Galerkin (POD-Galerkin) reduced-order models using time coefficient constraints. The model's predictive capability is validated with two cases: flow around a cylinder and flow around a wall-mounted hemisphere. Notably, the time coefficients of the POD-Galerkin model, updated with EnKF, showed high consistency with the original POD coefficients after several iterations, indicating enhanced prediction accuracy. The results revealed that only 17 iterations were required for the two-dimensional cylinder flow model to reduce the relative prediction error to below 1%. For the three-dimensional hemisphere flow case, the relative error was 2.03%, with the time coefficients' relative errors in various modes decreasing by one to two orders of magnitude compared to the traditional POD-Galerkin method. This approach effectively prevents divergence in low-order models over long time periods and provides a robust method for low-dimensional representation of high-fidelity flow fields.

Enhanced moving-step unscented transformed-dual extended Kalman filter for accurate SOC estimation of lithium-ion batteries considering temperature uncertainties

Enhanced moving-step unscented transformed-dual extended Kalman filter for accurate SOC estimation of lithium-ion batteries considering temperature uncertainties

Variational unscented Kalman filter on matrix Lie groups

In this paper, several estimation algorithms called the variational unscented Kalman filters (UKF-Vs) are proposed for matrix Lie groups. The proposed filters are inspired by the unscented Kalman filter in Euclidean space and they exhibit advantages over conventional methods, as the prediction step and the measurement update step are established on the Lie algebra and its dual space, which therefore avoids direct operations on highly nonlinear Lie group configuration spaces. Correspondingly, the proposed UKF-Vs exhibit significant improvements in terms of the estimation error and mean square error. This also makes it possible to construct a computationally efficient geometric integrator for the filtering dynamics. The obtained formulation is independent of the nonlinear Lie group state-space, and it sheds light on fully predicting and updating on the Lie algebra and its dual which are endowed with vector space structures. In particular, these formulations can avoid singularities or the well-known gimbal lock in the attitude estimation problem. Furthermore, the stochastic stability of the proposed filters is studied. The performances of the proposed filters are demonstrated for the satellite attitude estimation problem, which is an important benchmark from a control perspective. Numerical results show that the proposed UKF-Vs keep less computational complexity and perform significantly high accuracy compared with two unscented Kalman filters on Lie groups.

Stochastic encryption against stealthy attacks in CPSs: A zero-sum game approach

The zero-sum game-based stochastic encryption problem for cyber–physical systems (CPSs) under stealthy attacks is investigated in this paper. Firstly, a deterministic encryption strategy is presented to achieve the same estimation performance as the standard Kalman filter in the absence of attacks. Since a deterministic procedure may be deciphered, the encryption/attack strategy will be randomly employed to counter potential adversaries. The impact of stochastic strategies on the estimation performance is evaluated by calculating the expected error covariance. Based on the trade-off among the energy levels of encryption parameters, attackers, and defenders, the Nash equilibrium for the attacker-defender game is derived offline, providing guidance on when to implement encryption and attack strategies. In particular, we also provide a criterion for selecting encryption parameters to restrict the attacker’s payoff. The theoretical results are validated through simulations.

Research on data assimilation approach of wind turbine airfoils in stall conditions

This study aims to analyze the applicability of the turbulence model constants obtained through data assimilation on various airfoils in stall conditions, thereby offering the potential for computational resource savings. Through the wind tunnel experiments and published test data at Reynolds numbers ranging from the order of 105 to 106, the ensemble Kalman filter method was proposed to optimize the constants of the SA (Spalart-Allmaras) model, and its efficacy was validated. The assimilated constants obtained from YA-21 and S809 airfoils were applied separately to other airfoils with similar separation degrees for comparative analysis of their assimilation effects. Based on this, the influence of each model constant on numerical simulation was explored, and the pressure distributions were compared before and after assimilation as well as on other airfoils. Additionally, the impact of variations in airfoil thickness and Reynolds number on assimilated results was investigated. The results suggest that the constants that impact assimilation outcomes appreciably under stall conditions pertain to production and diffusion terms. When the Reynolds numbers are on the order of 105, assimilated constants derived from the 21% thickness airfoil exhibited optimization effects on the NACA4415 and S809 airfoil, providing a more accurate depiction of separated flow over an airfoil than the original constants conditions. The optimization effect persisted when the Reynolds number reached the order of 106. As the primary factor in the production term, Cb1 became sensitive to changes in Reynolds number exceeding other constants. However, the applicability of thick airfoils is slightly degenerated. Thicker airfoils are more susceptible to changes in the constants of the production and diffusion terms, which makes the assimilated constants need to be applied with caution. These findings demonstrate the feasibility of the mentioned approach, suggesting that assimilated constants from a medium-thickness airfoil can be partially used to replace the self-assimilated constants of other airfoils.

Robust EKF based on the framework of dynamic data reconciliation for state estimation of chemical processes with gaussian/non-gaussian measurement noise

State estimation plays a critical role in modern industry. The extended Kalman filter (EKF) is effective for nonlinear chemical processes with Gaussian noise, but it struggles when gross errors are present. This paper addresses this limitation by reformulating the EKF within the dynamic data reconciliation (DDR) framework, resulting in a robust DDR-based EKF tailored for state estimation in chemical processes with non-Gaussian measurement noise. The combination of random and gross errors is modeled using a contaminated Gaussian distribution. Model predictions are incorporated as prior knowledge, and a fixed-point iterative strategy is employed to update the posterior probability. Additionally, a first-order linearization technique is applied for convergence analysis. The robustness and effectiveness of the DDR-based EKF are demonstrated through both a classic mathematical example and a styrene polymerization reaction. Simulation results show that the DDR-based EKF effectively mitigates gross errors, achieving reliable state estimation.

Adaptive unscented Kalman filter based on sequential state difference for spacecraft autonomous navigation during the approach phase

Accurate spacecraft position and velocity is crucial for autonomous navigation technique for deep space mission. For the deep space spacecraft approaching a target planet, the rapid increase in the gravitational pull of the celestial body results in a swift rise in the error of the spacecraft’s state integral, thereby making it challenging to accurately estimate the process noise covariance in real-time, which degrades the autonomous navigation system performance. Thus, state estimation for deep space spacecraft during the approach phase under unknown process noise is an important research topic. The traditional adaptive unscented Kalman filter (AUKF) algorithm, relying on measurement innovation, faces challenges in directly capturing abrupt variations in process noise, potentially leading to navigation system divergence. To address the issue of divergence in spacecraft navigation systems and enhance navigation accuracy, this paper proposes an adaptive unscented Kalman filter based on sequential state difference (AUKF-SSD). Additionally, a state-based chi-square test is employed for real-time detection of abrupt variations in process noise. Based on the dynamics model, the AUKF-SSD method is applied to state estimation of Mars spacecraft. Compared with the traditional unscented Kalman filter, the AUKF based on measurement innovation, and the AUKF based on variational Bayesian, the proposed method can effectively restrain estimation errors and solve the divergence problem, in the case of sudden changes in the system process noise.