Kalman Filter Research Articles

A Study on Reducing the Noise Using the Kalman Filter in Digital Holographic Microscopy (DHM)

Digital Holographic Microscopy (DHM) is a technique that uses the phase information of light to generate a three-dimensional (3D) profile of an object. Recently, it has been utilized in various fields such as disease diagnosis and research on microorganisms. In the process in DHM, a narrow region around one of the sidebands from the frequency domain is windowed to avoid noise caused by the direct current (DC) term. However, it may not obtain the high-frequency information about the object. On the other hand, windowing a wide region increases the noise caused by the DC term, and generates the noise in the 3D profile. To solve this trade-off, we propose a noise reduction method using Kalman filter. From the recorded hologram image, we can create the frequency domain. It obtains multiple windowed sidebands centered on multiple pixels at random from the frequency domain. This creates a group of data in which noise is generated randomly. This is regarded as frequency series data, and Kalman filtering is performed. This method can reduce the noise caused by the DC term while acquiring high-frequency information. In addition, this method has the advantage that only one image is needed for frequency series data in the Kalman filter. The effectiveness of the proposed method is verified by comparison with conventional filtering methods and general image processing methods. The validation results prove the usefulness of the proposed method, and the proposed method is expected to have a significant effect on improving the accuracy of disease diagnosis techniques using DHM.

Enhancing Off-Road Topography Estimation by Fusing LIDAR and Stereo Camera Data with Interpolated Ground Plane

Topography estimation is essential for autonomous off-road navigation. Common methods rely on point cloud data from, e.g., Light Detection and Ranging sensors (LIDARs) and stereo cameras. Stereo cameras produce dense point clouds with larger coverage but lower accuracy. LIDARs, on the other hand, have higher accuracy and longer range but much less coverage. LIDARs are also more expensive. The research question examines whether incorporating LIDARs can significantly improve stereo camera accuracy. Current sensor fusion methods use LIDARs’ raw measurements directly; thus, the improvement in estimation accuracy is limited to only LIDAR-scanned locations The main contribution of our new method is to construct a reference ground plane through the interpolation of LIDAR data so that the interpolated maps have similar coverage as the stereo camera’s point cloud. The interpolated maps are fused with the stereo camera point cloud via Kalman filters to improve a larger section of the topography map. The method is tested in three environments: controlled indoor, semi-controlled outdoor, and unstructured terrain. Compared to the existing method without LIDAR interpolation, the proposed approach reduces average error by 40% in the controlled environment and 67% in the semi-controlled environment, while maintaining large coverage. The unstructured environment evaluation confirms its corrective impact.

State of Charge Estimation of Single-Flow Zinc-Nickel Batteries Based on the Improved Unscented Kalman Filter and Extended Kalman Filter Algorithm

Single-flow zinc–nickel batteries are a novel type of flow batteries that feature a simple structure, large-scale energy storage capacity, and low cost. The state of charge (SOC) is a crucial indicator of battery performance, providing essential data for the management and control of the battery management system. However, in the estimation of SOC using a traditional unscented Kalman filter, the covariance matrix P often falls into a non-positive definite state during the decomposition steps, leading to algorithm failure. To address this issue, this paper incorporates the singular-value decomposition method into the unscented Kalman filter, resulting in an improved unscented Kalman filter algorithm. Considering the potential low accuracy of a single filtering method for SOC estimation, the improved unscented Kalman filter algorithm is combined with the extended Kalman filter for joint estimation. Experimental comparisons demonstrate that the improved unscented Kalman filter and extended Kalman filter joint estimation achieve higher estimation accuracy compared to using the improved unscented Kalman filter alone.

Research on Lateral Stability Control of Four-Wheel Independent Drive Electric Vehicle Based on State Estimation

This paper proposes a hierarchical framework-based solution to address the challenges of vehicle state estimation and lateral stability control in four-wheel independent drive electric vehicles. First, based on a three-degrees-of-freedom four-wheel vehicle model combined with the Magic Formula Tire model (MF-T), a hierarchical estimation method is designed. The upper layer employs the Kalman Filter (KF) and Extended Kalman Filter (EKF) to estimate the vertical load of the wheels, while the lower layer utilizes EKF in conjunction with the upper-layer results to further estimate the lateral forces, longitudinal velocity, and lateral velocity, achieving accurate vehicle state estimation. On this basis, a hierarchical lateral stability control system is developed. The upper controller determines stability requirements based on driver inputs and vehicle states, switches between handling assistance mode and stability control mode, and generates yaw moment and speed control torques transmitted to the lower controller. The lower controller optimally distributes these torques to the four wheels. Through closed-loop Double Lane Change (DLC) tests under low-, medium-, and high-road-adhesion conditions, the results demonstrate that the proposed hierarchical estimation method offers high computational efficiency and superior estimation accuracy. The hierarchical control system significantly enhances vehicle handling and stability under low and medium road adhesion conditions.

Enhancing Localization Accuracy and Reducing Processing Time in Indoor Positioning Systems: A Comparative Analysis of AI Models

This paper presents a comparative study of different AI models for indoor positioning systems, emphasizing improvements in localization accuracy and processing time. This study examines Artificial Neural Networks (ANNs), Long Short-Term Memory (LSTM), Recurrent Neural Networks (RNNs), and the Kalman filter using a real Received Signal Strength Indicator (RSSI) and 9-axis ICM-20948 sensor. An in-depth analysis is provided in this paper for data cleaning and feature selection to reduce errors for all the models. We evaluate these models in terms of localization accuracy and prediction time. The RNN model shows the best performance, achieving a localization error of 0.247 m with a delay of 0.077 s per position location for an area of 12m×9.5m using four anchors. This research highlights the importance of selecting AI models for effective mobile tracking according to test and validation data.

A generalized diffusion model for remaining useful life prediction with uncertainty

Forecasting the remaining useful life (RUL) is a crucial aspect of prognostics and health management (PHM), which has garnered significant attention in academic and industrial domains in recent decades. The accurate prediction of RUL relies on the creation of an appropriate degradation model for the system. In this paper, a general representation of diffusion process models with three sources of uncertainty for RUL estimation is constructed. According to time-space transformation, the analytic equations that approximate the RUL probability distribution function (PDF) are inferred. The results demonstrate that the proposed model is more general, covering several existing simplified cases. The parameters of the model are then calculated utilizing an adaptive technique based on the Kalman filter and expectation maximization with Rauch-Tung-Striebel (KF-EM-RTS). KF-EM-RTS can adaptively estimate and update unknown parameters, overcoming the limits of strong Markovian nature of diffusion model. Linear and nonlinear degradation datasets from real working environments are used to validate the proposed model. The experiments indicate that the proposed model can achieve accurate RUL estimation results.

A Combination of Classification Robust Adaptive Kalman Filter with PPP-RTK to Improve Fault Detection for Integrity Monitoring of Autonomous Vehicles

Real-time integrity monitoring (IM) is essential for autonomous vehicle positioning, requiring high availability and manageable computational load. This research proposes using precise point positioning real-time kinematic (PPP-RTK) as the positioning method, combined with an improved classification adaptive Kalman filter (CAKF) for processing. PPP-RTK enhances IM availability by allowing undifferenced and uncombined observations, enabling individual observation exclusion during fault detection and exclusion (FDE). The CAKF reduces FDE computational load by using a robustness test instead of traditional FDE methods, improving precision and availability in protection level estimation. Epoch-wise weighting adjustments in the robustness test create a more accurate stochastic model, aided by an adaptive unit weight variance (UWV) calculated with a sliding window, achieving a 7–28% UWV reduction. Three test scenarios with up to four simultaneous faults in code and phase observations, ranging from 1 to 200 m and 0.4 to 20 m, respectively, demonstrated successful identification and de-weighting of faults, resulting in maximum positioning errors of 6 mm (horizontal) and 11 mm (vertical). The method reduced FDE computational load by 50–99.999% compared to other approaches.

A State Estimation of Dynamic Parameters of Electric Drive Articulated Vehicles Based on the Forgetting Factor of Unscented Kalman Filter with Singular Value Decomposition

In this paper, a state estimation method of distributed electric drive articulated vehicle dynamics parameters based on the forgetting factor unscented Kalman filter with singular value decomposition (SVD-UKF) is proposed. The 7DOF nonlinear dynamics model of a distributed electric drive articulated vehicle is established. The unscented Kalman filter algorithm is the foundation, with singular value decomposition replacing the Cholesky decomposition. A forgetting factor is introduced to dynamically adapt the observation noise covariance matrix in real time, resulting in a centralized parameter state estimator for the articulated vehicle. The proposed parameter state estimation method based on the forgetting factor SVD-UKF is simulated and compared with the unscented Kalman filter (UKF) estimation method. Key dynamic parameters are estimated, such as the lateral and longitudinal velocities and accelerations, angular velocity, articulated angle, wheel speeds, and longitudinal and lateral tire forces of both the front and rear vehicle bodies. The results show that the proposed forgetting factor SVD-UKF method outperforms the traditional UKF method. Furthermore, a prototype vehicle test is conducted to compare the estimated values of various dynamic parameters with the actual values, demonstrating minimal errors. This verifies the effectiveness of the proposed dynamic parameter estimation method for articulated vehicles.

Robust adaptive extended target filtering based on multiplicative noise model

Abstract This study proposes two novel methods for tracking extended target with elliptical shape under non-Gaussian noise conditions.To achieve this, an explicit nonlinear measurement equation is formulated by incorporating a multiplicative noise term that connects the target's kinematic and shape parameters with the measurements.This measurement equation is employed to derive a closed-form solution for the Student's t extended Kalman filter based on multiplicative noise model (St-EKF-MNM)}with recursive measurement updates.To further optimize the target tracking performance, the Hessian matrix was used to deal with the nonlinearity in the measurement equation, further derive the Student's t second-order extended Kalman filter based on multiplicative noise model (St-SOEKF-MNM).The effectiveness and robustness of the proposed methods are demonstrated with simulation.

Modelling of the gas purification system for flue gas acid production

AbstractEstablishing a gas pressure model of the purification system to accurately estimate the system output pressure is a powerful guarantee to ensure the stable and efficient operation of the acid production process. This paper presents a study on the establishment of gas pressure models for three facilities in the purification system at the Guixi Smelter in China, including a pulse jet fabric filter, an electrostatic precipitator, and a drying tower. Through analysis of the operating mechanisms of these facilities, pressure mechanism models are established for the gas flows. Considering the nonlinearity and time‐varying nature of the model, an improved extended Kalman filter (EKF) algorithm is proposed to perform online identification of the unknown parameters within the model. Compared to the first‐order EKF, the improved algorithm achieves significantly better performance without incurring additional computational overhead. Field experiments on pressure estimation at the acid production site validate the reasonableness of the established models, as well as the efficacy of the proposed identification algorithm.

Research on a Hybrid Correction Method for SINS/DVL Kalman Filter Integrated Navigation Based on Convergence Factor Judgment

Abstract The strapdown inertial navigation system (SINS)/doppler velocity log (DVL) integrated navigation is one of the primary methods for underwater navigation, providing autonomous underwater vehicles with precise information on position, velocity, and attitude. The core idea of the SINS/DVL integrated navigation using the Kalman filter is to establish the state and observation equations to estimate the SINS navigation error using DVL velocity. The optimal state estimation and correction strategies are critical to the accuracy of integrated navigation. To address this, this paper proposes a hybrid correction method for SINS/DVL Kalman filter integrated navigation based on a convergence factor judgment (HCKF-CFJ). First, the convergence factor for the Kalman filter is constructed using the diagonal elements of the estimated error covariance matrix corresponding to the velocity error state. Then, the filter's stability is assessed based on this convergence factor. When stability is confirmed, direct feedback correction is applied to the SINS velocity, and indirect feedback correction is applied to the SINS position. SINS velocity and position undergo feedforward correction if the stability condition is not met. Finally, ship experiments validate the effectiveness of the proposed method.

Precision Quaternion Estimation with Partially Norm-Constrained Unscented Kalman Filtering

Abstract Accurate orientation estimation is a key challenge in dynamics and control, particularly for rigid body motion. Quaternions are commonly used to represent rotations due to their computational efficiency, but they must always maintain a unit norm to function correctly. If this constraint is not enforced properly, it can lead to significant errors in orientation estimation. This paper proposes an unscented Kalman filter that ensures the quaternion parameters, a subvector within the state vector, adhere to the unit norm constraint. The proposed method provides a closed-form solution without dividing the state vector into constrained and unconstrained vectors. In simulation studies under high noise conditions, the filter demonstrates significantly improved performance compared to standard unscented and pseudo-unscented Kalman filters, enhancing accuracy during both transient and steady-state phases. These results highlight the importance of enforcing quaternion constraints to reduce mean square error and improve convergence.

STOCK PRICE PREDICTION AND SIMULATION USING GEOMETRIC BROWNIAN MOTION-KALMAN FILTER: A COMPARISON BETWEEN KALMAN FILTER ALGORITHMS

Stocks have high-profit potential but also have high risk. Many people have ways to forecast stock prices. The Geometric Brownian Motion (GBM) method forecasts stock prices. The data used in this study are closing stock price data from July 1, 2021 to August 31, 2021 taken from Yahoo! Finance. The stocks used in this research are Bank Rakyat Indonesia (BBRI), Indofood Sukses Makmur (INDF), and Telkom Indonesia (TLKM). A strategy is carried out to improve prediction accuracy by utilising the Kalman Filter (KF). This research will compare the mean absolute percentage error (MAPE) value between GBM-KF, which was manually computed and computed using the Python library. As an example of this research, for BBRI stock, the high GBM MAPE value of 9.02% can be reduced to 3.52% with manually computed GBM-KF and 3.68% with Python library computed GBM-KF. Similarly, INDF and TLKM stocks are showing a significant reduction in MAPE values to deficient levels in some cases. The GBM-KF method employing manual computing may enhance the overall precision of stock price forecasting. Future research may enhance this study by using the GBM-KF model on alternative financial instruments, integrating supplementary market data, or evaluating its efficacy under extreme market conditions.

A laser tracking attitude dynamic measurement method based on real-time calibration and AEKF with a multi-factor influence analysis model

Abstract To address the limitations of six-degree-of-freedom (6-DOF) visual tracking systems in terms of low dynamic performance and the inability to perform measurements under light occlusion, this paper proposes a novel laser tracking attitude dynamic measurement method integrating vision and inertial measurement unit (IMU). A tailored real-time calibration model is developed to enable precise alignment of the vision and IMU coordinate systems during dynamic operations. To overcome the limitations of extended Kalman filter (EKF) that rely on static noise assumptions in complex dynamic measurement scenarios, this study proposes an adaptive mechanism based on multi-factor influence analysis. Through dynamic monitoring of visual observation noise, an adaptive EKF algorithm is designed to enhance performance under varying conditions. When integrated into a vision/IMU fusion system, the algorithm significantly enhances the system’s sensitivity to variations in visual sensor observation noise caused by changes in lighting and motion states. This capability allows rapid adjustment of filtering parameters, leading to substantial improvements in filtering accuracy and stability. Simulation results demonstrate that the proposed algorithm outperforms traditional EKF in fusion measurement accuracy when tested in simulated noise environments featuring sinusoidal and random jump signals. Furthermore, the fusion measurement accuracy is mainly influenced by the data density of the visual sensor and the measurement distance. Finally, the proposed method was validated on a precision turntable. Experimental results reveal that at a 3 m measurement distance and within a 0°–25° angular range, when the turntable rotates at a constant speed of 5°/s along a single axis, the maximum absolute deviation in repeatability of the fused attitude measurements was below 0.11°, and the system is capable of achieving a high measurement frequency of 100 Hz.

IMU Sensor-Based Worker Behavior Recognition and Construction of a Cyber–Physical System Environment

According to South Korea’s Ministry of Employment and Labor, approximately 25,000 construction workers suffered from various injuries between 2015 and 2019. Additionally, about 500 fatalities occur annually, and multiple studies are being conducted to prevent these accidents and quickly identify their occurrence to secure the golden time for the injured. Recently, AI-based video analysis systems for detecting safety accidents have been introduced. However, these systems are limited to areas where CCTV is installed, and in locations like construction sites, numerous blind spots exist due to the limitations of CCTV coverage. To address this issue, there is active research on the use of MEMS (micro-electromechanical systems) sensors to detect abnormal conditions in workers. In particular, methods such as using accelerometers and gyroscopes within MEMS sensors to acquire data based on workers’ angles, utilizing three-axis accelerometers and barometric pressure sensors to improve the accuracy of fall detection systems, and measuring the wearer’s gait using the x-, y-, and z-axis data from accelerometers and gyroscopes are being studied. However, most methods involve use of MEMS sensors embedded in smartphones, typically attaching the sensors to one or two specific body parts. Therefore, in this study, we developed a novel miniaturized IMU (inertial measurement unit) sensor that can be simultaneously attached to multiple body parts of construction workers (head, body, hands, and legs). The sensor integrates accelerometers, gyroscopes, and barometric pressure sensors to measure various worker movements in real time (e.g., walking, jumping, standing, and working at heights). Additionally, incorporating PPG (photoplethysmography), body temperature, and acoustic sensors, enables the comprehensive observation of both physiological signals and environmental changes. The collected sensor data are preprocessed using Kalman and extended Kalman filters, among others, and an algorithm was proposed to evaluate workers’ safety status and update health-related data in real time. Experimental results demonstrated that the proposed IMU sensor can classify work activities with over 90% accuracy even at a low sampling rate of 15 Hz. Furthermore, by integrating internal filtering, communication modules, and server connectivity within an application, we established a cyber–physical system (CPS), enabling real-time monitoring and immediate alert transmission to safety managers. Through this approach, we verified improved performance in terms of miniaturization, measurement accuracy, and server integration compared to existing commercial sensors.

Stability Study of Distributed Drive Vehicles Based on Estimation of Road Adhesion Coefficient and Multi-Parameter Control

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.

Robust Onboard Orbit Determination Through Error Kalman Filtering

Accurate and robust on-board orbit determination is essential for enabling autonomous spacecraft operations, particularly in scenarios where ground control is limited or unavailable. This paper presents a novel method for achieving robust on-board orbit determination by integrating a loosely coupled GNSS/INS architecture with an on-board orbit propagator through error Kalman filtering. This method is designed to continuously estimate and propagate a spacecraft’s orbital state, leveraging real-time sensor measurements from a global navigation satellite system (GNSS) receiver and an inertial navigation system (INS). The key advantage of the proposed approach lies in its ability to maintain orbit determination integrity even during GNSS signal outages or sensor failures. During such events, the on-board orbit propagator seamlessly continues to predict the spacecraft’s trajectory using the last known state information and the error estimates from the Kalman filter, which were adapted here to handle synthetic propagated measurements. The effectiveness and robustness of the method are demonstrated through comprehensive simulation studies under various operational scenarios, including simulated GNSS signal interruptions and sensor anomalies.

Research on the Adaptive Fusion Timing Algorithm for BeiDou and LORAN Based on the EKF

This paper addresses the issue of limited timing accuracy in complex environments for both the BeiDou system (BD) and the long-range navigation system (LORAN). We delve into the correction algorithm for LORAN timing signals and an adaptive fusion timing algorithm based on the extended Kalman filter (EKF). First, we introduce the advantages and limitations of the BD and LORAN systems in timing applications, as well as the principles of the EKF algorithm and its application in multisource information fusion. Next, we propose a correction algorithm signal to address the significant fluctuations in LORAN timing signals. Building on this, we continue to study an adaptive BD and LORAN fusion timing algorithm based on the EKF. This involves optimising system noise covariance through adaptive adjustments and establishing a fusion timing algorithm model based on the EKF. Finally, we construct a test platform to verify the effectiveness of the proposed algorithms. The experimental results demonstrate that, compared to a single navigation system, the adaptive BD and LORAN fusion timing algorithm based on the EKF significantly improves the accuracy and stability of system timing. Additionally, correcting the LORAN timing results before fusion further enhances system fusion timing performance metrics. The algorithm still maintains high performance in complex environments, showing great application prospects.

Optimization of Covariance Matrices of Kalman Filter with Unknown Input Using Modified Directional Bat Algorithm

The proper selection of the model error covariance matrix and the measurement noise covariance matrix of Kalman filter is an optimization problem. Some scholars have studied this, but there is relatively little research on the selection of the two covariance matrices for Kalman filters with an unknown input. Recently, the authors proposed a modified directed bat algorithm (MDBA) which introduces the best historical location of individuals and the elimination strategy to effectively prevent falling into local optimal solution. So, two methods are proposed in this paper to optimize the model error covariance matrix and measurement noise covariance matrix of Kalman filter with unknown inputs (KF-UI) and extended Kalman filter with unknown inputs (EKF-UI) by MDBA, respectively. The objective functions are constructed using the measurement vectors and the corresponding estimated values, and MDBA is adopted to optimize the two covariance matrices of KF-UI and EKF-UI. To validate the effectiveness of proposed methods, two simple structure examples and a benchmark example are adopted. The influence of structural parameter uncertainties on KF-UI is also considered. The result shows that the MDBA-optimized KF-UI has a strong convergence and can take into account the effect of parameter uncertainties. Then, the effectiveness of the proposed MDBA-optimized EKF-UI method is validated by comparing it with EKF-UI with empirically selected covariance values through trial-and-error. The identification results showed that the proposed methods achieved better identification accuracy and enhanced convergence compared to KF-UI and EKF-UI with empirical covariance values.

Human autonomy with AI in the loop

ABSTRACT In the wake of recent advancements in the field of AI, this paper investigates the impact of recommender systems and generative models on human decisional and creative autonomy. For this purpose, we adopt Dennett’s conception of autonomy as self-control. We show that recommender systems can play a double role in relation to decisional autonomy: as information filter, they can augment self-control in decision-making, but also act as mechanisms of remote control that clamp degrees of freedom. As for generative models in AI, we show that they can be seen as a powerful system of selection and suggestion (similar to standard recommender systems) but also as an instrument for information production. We suggest that the latter perspective opens new possibilities in terms of creative autonomy. Additionally, for both systems we propose a distinction between “extrinsic” and “intrinsic” mechanisms and effects. Through Dennett’s theory of self-control, this paper offers new insights into the relation between AI and human autonomy by framing it in terms of remote or self-control and by addressing the impact of generative models on creative autonomy.