Kalman Filter Research Articles

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.

Speed-sensorless model predictive thrust control of linear induction motor based on improved extended Kalman filter observer

Speed-sensorless model predictive thrust control of linear induction motor based on improved extended Kalman filter observer

System identification and fault reconstruction in solar plants via extended Kalman filter-based training of recurrent neural networks.

This article proposes using the extended Kalman filter (EKF) for recurrent neural network (RNN) training and fault estimation within a parabolic-trough solar plant. The initial step involves employing an RNN to model the system. Given the challenge of fault discernibility in the collectors, parallel EKFs are employed to reconstruct the parameters of the faults. The parameters are used independently to estimate the system output, and the type of fault is isolated based on the estimation errors using another feedforward neural network. To evaluate the effectiveness of the methodology, simulations are conducted on a loop of the ACUREX plant with irradiances from sunny and cloudy days. The results reveal a fault classification accuracy of approximately 90% and a fault reconstruction error below 3%, with even better accuracies in the cloudy dataset than in the sunny dataset.

Validation and Analysis of Recreational Runners’ Kinematics Obtained from a Sacral IMU

Our aim was to validate a sacral-mounted inertial measurement unit (IMU) for reconstructing running kinematics and comparing movement patterns within and between runners. IMU data were processed using Kalman and complementary filters separately. RMSE and Bland–Altman analysis assessed the validity of each filtering method against a motion capture system. Running data from 24 recreational runners were analyzed using Fourier transform coefficients, PCA, and k-means clustering. High agreement was found for Kalman-filtered data in the frontal, sagittal, and transverse planes, with a Bland–Altman bias of ~2 mm on average, compared to a bias of ~10.5 mm for complementary-filtered data. Pelvic angles calculated from Kalman-filtered data had superior agreement, with systematic biases of ~0.3 versus 3.4 degrees for complementary-filtered data. Our findings suggest that inertial sensors are viable alternatives to motion capture for reconstructing pelvic running kinematics and movement patterns. In the second part of our study, negligible intra-individual differences were observed with changes in speed, while inter-individual differences were large. Two clusters of runners were identified, each showing distinct movement patterns and ranges of motion. These observations highlight the potential usefulness of inertial sensors for performance analysis and rehabilitation as they may permit the use of individual-specific and cluster-specific practice programs.

Experimental Validation of Virtual Torque Sensing for Wind Turbine Gearboxes Based on Strain Measurements

ABSTRACTIn efforts to reduce the operation and maintenance cost of wind turbines, there is an increasing interest to monitor key turbine quantities such as the torque load on the gearbox. Monitoring the torque paves the way for the calculation of remaining useful lifetime, leading to cost reductions through improved reliability and maintenance planning. In order to avoid expensive direct torque sensors, this paper investigates the potential of virtual torque sensing, a technique based on 3 basic components: first, a set of non‐intrusive sensors installed on the gearbox. Three groups of strain gauges on the gearbox as well an angular encoder are considered in this paper. Second is a physics‐based model, capable of predicting the response of aforementioned sensors. These models are constructed with a purposeful balance between accuracy and computational cost. Model validation and updating are performed to ensure efficient and accurate prediction of the sensor output. Finally, an augmented extended Kalman filter (AEKF) is used to combine the measured response with predictions from the model to infer the gearbox input torque. Since a key factor determining the performance of the AEKF is the tuning of the AEKF covariance matrices, multiple methods are introduced to systematically tune the covariance matrices. Experimental validation results show that the virtual torque sensor can detect the load torque with a normalized mean absolute error (NMAE) between 3.41% and 7.47%, depending on the sensor set. The influence of the amount of sensors used and the tuning method are also investigated.

Noninteracting optimal and adaptive torque control using an online parameter estimation with help of polynomials in EKF for a PMSM.

This paper addresses a non-interacting torque control strategy to decouple the d- and q-axis dynamics of a permanent magnet synchronous machine (PMSM). The maximum torque per ampere (MTPA) method is used to determine the reference currents for the desired torque. To realize the noninteracting control, knowledge concerning the inductances Ld and Lq of the electrical machine is necessary. These two inductances are estimated by two extended Kalman filters (EKFs), which use a univariate polynomial as a model to describe the saturation effects of the PMSM. The Kalman filters (KF) are realized within a noninteracting control system to improve the observability of the inductance. Despite the non-perfect decoupling, thanks to the structural stochastic nature of the KFs, noninteracting cancellation errors are represented with its process noise and the inductances are estimated sufficiently well. In this sense, we can speak about KFs for and within noninteracting control. Estimating inductances is fundamental for optimal torque control, which is a viable approach to reducing mechanical vibration and disturbance. Moreover, the control strategy of model-based techniques must be adaptively tuned to work properly. Starting from the existing literature, a viable control structure is proposed in which the stability of the control loop using a Proportional Integral (PI) controller is shown for the resulting time-varying system. In fact, the model is represented as a time-varying system because of the presence of the variable inductances Ld and Lq and because of the presence of the velocity of the rotor which is not considered as a state. In this paper, a forward Euler discretization is used to realize the observer in the discrete experimental setup. Measures realized with hardware in the loop (HIL) show interesting results in the context of inductance estimation, due to the advantage of the reduction of the dimensions of the two decoupled EKFs resulting from the noninteraction control. Using the HIL simulator, the proposed torque control strategy is investigated, showing promising results in terms of increasing observability due to decoupling. This and the usage of univariate polynomials in EKF calculations lead to significant reduction of measurement points, reduction of oscillations and ripples, deviation between desired and achieved torque and reduction of disturbances. Moreover, the proposed control strategy using a very limited calculation load, at the same time, maintains the ripples inside the technical limits of the obtained torque. Both effects are due to the decoupled EKFs with simplified and reduced order of the models using univariate polynomials, which require significantly fewer measuring points in the run-up to the creation of the model of the inductances Ld and Lq.

A Neural-Metaheuristic Kalman Filter for Moving Microburst Wind Shear Identification

Microburst wind shears (MB) are powerful localized three dimensional (3D) columns of wind that occur when cooled air drops from the base of thunderstorms at high speeds. They eventually hit the ground and spread out in all directions. As such MBs are considered a major atmospheric hazard for aircrafts (ACs), especially in terminal flight phases. Though pilots train regularly to survive it, yet the most recommended practice within the aviation community is to avoid its encounter upon detection. Some modern aircrafts have predictive wind shear warning systems, but they have limited short range capability and do not provide quantitative data for engineering application. In this sense, accurate onboard detection and identification of MBs and its characteristics is of importance for flight safety, whose success can lead to design of automatic flight control systems (FCSs) that reduce the risk of aircraft crash landings and accidents. Even though there are some studies on FCS designs for MB encounter, research on MB identification is rare but ongoing. To this aim, the present study is among the firsts that focuses on online identification of multiple and moving MB parameters using onboard aircraft air data and inertial sensors. The identification task is initially performed using the aircraft six degrees of freedom (6DoF) equations of motion (EOM) integrated with a 3D MB model via the utility of nonlinear Kalman filtering (KF) algorithms. Subsequently, an enhanced neural metaheuristic Kalman filter (NMKF) is proposed that improves the estimation accuracy of the MB model parameters. The results demonstrate the efficacy of the proposed NMKF in comparison with previous studies.

Online identification method of power grid load sensitivity based on adaptive Kalman filter

Online identification method of power grid load sensitivity based on adaptive Kalman filter

The use of Kalman filters in human gait analysis using depth sensors

The use of Kalman filters in human gait analysis using depth sensors