Kalman Filter Research Articles

Using the state-space separable cohort model modification for assessment of Pacific cod Gadus macrocephalus (Gadidae) stocks in the Petropavlovsk-Komandorskaya subzone

Results of using a state-space cohort model with smoothing unscented Kalman filter for assessment of Pacific cod stock abundance and the other population parameters in the Petropavlovsk-Komandorskaya Subzone are presented. Series of numerical experiments were carried out with various variants of the recruitment model. The results of the work performed can be used in preparing forecasts of the TAC of marine commercial fish in terms that the observational data allow the use of age-structured models in the state space.

A Novel Non-Line-of-Sight Error Mitigation Algorithm Using Double Extended Kalman Filter for Ultra-Wide Band Ranging Technology

In complex indoor environments, target tracking performance is impacted by non-line-of-sight (NLOS) noises and other measurement errors. In order to fix NLOS errors, a Double Extended Kalman filter (DEKF) algorithm is proposed, which refers to a kind of cascaded structure composed of two Kalman filters. In the proposed algorithm, the first filter is a classic Kalman filter (KF) and the second is an Extended Kalman filter (EKF). The time of arrival (TOA) measurements collected by multiple stationary ultra-wide band (UWB) sensors are used. Residual errors between the measured TOA and the prediction from the first KF are used to adjust the covariance of the first KF accordingly. Then, we use the estimated distance state of the first KF as a measurement vector of the second EKF in order to obtain a smoother observation. One of the advantages of the proposed algorithm is that it is able to perform target tracking with a good accuracy even without or with only one line-of-sight(LOS) TOA measurement for a period of time without prior information of the NLOS noise, which may be difficult to obtain in practical applications. Another advantage is that the accuracy does not significantly decrease when NLOS noises persist for a long period of time. Finally, the proposed DEKF can maintain high-precision positioning characteristics in both the constant velocity (CV) model and the constant acceleration (CA) model for LOS/NLOS environments. In the case of mixed LOS/NLOS environments, the RMSE of the proposed algorithm can be kept within 5 cm, while the RMSEs of other compared algorithms are easily beyond tens of centimeters. At the same time, when the confidence of RMSE is set to 95% for 1000 MC simulations, the confidence interval of the proposed algorithm is the smallest, and the mean value is 3–5 times closer to the true value compared to other algorithms. Simulation and experimental results show that the proposed algorithm performs much better than other state-of-the-art algorithms, particularly in severe mixed LOS/NLOS environments.

Deep-Learning Techniques Applied for State-Variables Estimation of Two-Mass System

The article is focused on the application of neural models for state-variables estimation. The estimators are applied in the control structure (with the state speed controller) of the electric drive with an elastic shaft. The extended amount of feedback is an additional argument for the estimation of the signal. The calculations are performed for three deep neural structures based on the Convolutional Neural Network (CNN) and the long short-term memory (LSTM). The design stages and the overall concept in this case are completely different than with the applications of classical observers (e.g., the Luenberger, the Kalman filter) often used for similar objects. The direct identification of the mechanical part of the drive is not necessary. The parameters and the equations describing the plant are not used. Instead, the signals are used for training the neural networks. The results (performed for the nominal values of the two-mass system and presenting the robustness of the estimators) present the high precision of the signal estimation. The second part of the work deals with the hardware implementation of the neural estimators in the low-cost programmable device with the ARM core. The experimental transients confirm the features of the neural estimators noticed in the simulations.

Experimental Comparative Study on Self-Imputation Methods and Their Quality Assessment for Monthly River Flow Data with Gaps: Case Study to Mures River

Incomplete environmental datasets pose significant challenges in developing accurate predictive models, particularly in hydrological research. This study addresses data missingness by investigating gap imputation methodologies for datasets with 5–20% data absence, focusing on the Mureș River in Romania. Utilizing a novel approach, we applied various imputation techniques, including the ratio method, Kalman filtering, and machine learning algorithms (XGBoost, Gradient Boosting, Random Forest and CatBoost), while developing an innovative self-assessment metric for evaluating imputation performance without relying on external reference data. Through systematic analysis of hydrological station data from four monitoring points, we artificially introduced data gaps to rigorously test method applicability. The research demonstrates the feasibility of constructing a robust self-evaluation framework for selecting optimal imputation techniques, potentially enhancing data reliability and analytical precision in environmental and geospatial research. Our findings contribute a structured methodology for addressing data incompleteness, offering researchers a quantitative approach to improving dataset integrity and predictive modeling in complex environmental systems.

A Hybrid Architecture for Safe Human–Robot Industrial Tasks

In the context of Industry 5.0, human–robot collaboration (HRC) is increasingly crucial for enabling safe and efficient operations in shared industrial workspaces. This study aims to implement a hybrid robotic architecture based on the Speed and Separation Monitoring (SSM) collaborative scenario defined in ISO/TS 15066. The system calculates the minimum protective separation distance between the robot and the operators and slows down or stops the robot according to the risk assessment computed in real time. Compared to existing solutions, the approach prevents collisions and maximizes workcell production by reducing the robot speed only when the calculated safety index indicates an imminent risk of collision. The proposed distributed software architecture utilizes the ROS2 framework, integrating three modules: (1) a fast and reliable human tracking module based on the OptiTrack system that considerably reduces latency times or false positives, (2) an intention estimation (IE) module, employing a linear Kalman filter (LKF) to predict the operator’s next position and velocity, thus considering the current scenario and not the worst case, and (3) a robot control module that computes the protective separation distance and assesses the safety index by measuring the Euclidean distance between operators and the robot. This module dynamically adjusts robot speed to maintain safety while minimizing unnecessary slowdowns, ensuring the efficiency of collaborative tasks. Experimental results demonstrate that the proposed system effectively balances safety and speed, optimizing overall performance in human–robot collaborative industrial environments, with significant improvements in productivity and reduced risk of accidents.

Designing Stress Scenarios

ABSTRACTWe study the optimal design of stress scenarios. A principal manages the unknown risk exposures of agents by asking them to report losses under hypothetical scenarios before taking remedial actions. We apply a Kalman filter to solve the learning problem, and we relate the optimal design to the risk environment, the principal's preferences, and available interventions. In a banking context, optimal capital requirements cover losses under an adverse scenario, while targeted interventions depend on covariances among residual exposures and systematic risks. Our calibration reveals that information is particularly valuable for targeted interventions as opposed to broad capital requirements.

UltraTimTrack: a Kalman-filter-based algorithm to track muscle fascicles in ultrasound image sequences

Background Brightness-mode (B-mode) ultrasound is a valuable tool to non-invasively image skeletal muscle architectural changes during movement, but automatically tracking muscle fascicles remains a major challenge. Existing fascicle tracking algorithms either require time-consuming drift corrections or yield noisy estimates that require post-processing. We therefore aimed to develop an algorithm that tracks fascicles without drift and with low noise across a range of experimental conditions and image acquisition settings. Methods We applied a Kalman filter to combine fascicle length and fascicle angle estimates from existing and openly-available UltraTrack and TimTrack algorithms into a hybrid algorithm called UltraTimTrack. We applied the hybrid algorithm to ultrasound image sequences collected from the human medial gastrocnemius of healthy individuals (N = 8, four women), who performed cyclical submaximal plantar flexion contractions or remained at rest during passive ankle joint rotations at given frequencies and amplitudes whilst seated in a dynamometer chair. We quantified the algorithm’s tracking accuracy, noise, and drift as the respective mean, cycle-to-cycle variability, and accumulated between-contraction variability in fascicle length and fascicle angle. We expected UltraTimTrack’s estimates to be less noisy than TimTrack’s estimates and to drift less than UltraTrack’s estimates across a range of conditions and image acquisition settings. Results The proposed algorithm yielded low-noise estimates like UltraTrack and was drift-free like TimTrack across the broad range of conditions we tested. Over 120 cyclical contractions, fascicle length and fascicle angle deviations of UltraTimTrack accumulated to 2.1 ± 1.3 mm (mean ± sd) and 0.8 ± 0.7 deg, respectively. This was considerably less than UltraTrack (67.0 ± 59.3 mm, 9.3 ± 8.6 deg) and similar to TimTrack (1.9 ± 2.2 mm, 0.9 ± 1.0 deg). Average cycle-to-cycle variability of UltraTimTrack was 1.4 ± 0.4 mm and 0.6 ± 0.3 deg, which was similar to UltraTrack (1.1 ± 0.3 mm, 0.5 ± 0.1 deg) and less than TimTrack (3.5 ± 1.0 mm, 1.4 ± 0.5 deg). UltraTimTrack was less affected by experimental conditions and image acquisition settings than its parent algorithms. It also yielded similar or lower root-mean-square deviations from manual tracking for previously published image sequences (fascicle length: 2.3–2.6 mm, fascicle angle: 0.8–0.9 deg) compared with a recently-proposed hybrid algorithm (4.7 mm, 0.9 deg), and the recently-proposed DL_Track algorithm (3.8 mm, 3.9 deg). Furthermore, UltraTimTrack’s processing time (0.2 s per image) was at least five times shorter than that of these recently-proposed algorithms. Conclusion We developed a Kalman-filter-based algorithm to improve fascicle tracking from B-mode ultrasound image sequences. The proposed algorithm provides low-noise, drift-free estimates of muscle architectural changes that may better inform muscle function interpretations.

Multi-frequency and multi-system GNSS positioning data fusion algorithm based on Kalman filter

With the widespread application of Global Navigation Satellite System (GNSS) in the fields of positioning and navigation, traditional single frequency and single system positioning methods are gradually unable to meet the requirements of high accuracy and high reliability. Especially in complex and dynamic environments, GNSS signals are affected by multipath effects, occlusion, and interference, resulting in a significant decrease in positioning accuracy. Therefore, it is particularly important to develop a multi-frequency and multi-system GNSS positioning data fusion algorithm. This article used Kalman filtering technology and combined the data characteristics of multi-frequency and multi-system GNSS signals to study a new positioning data fusion algorithm. By comprehensively processing different GNSS systems and frequency signals, the positioning accuracy and anti-interference ability were significantly improved. The experimental results showed that the algorithm studied improved the average positioning accuracy by more than 6.23% in complex environments compared to traditional methods, and also exhibited good adaptability and stability under dynamic conditions. Fully utilizing the advantages of multi-frequency signals and combining advanced data fusion technology is an effective way to improve GNSS positioning performance, providing new ideas and methods for future intelligent navigation applications.

Real-Time Optimization of Discrete Element Models for Studying Asphalt Mixture Compaction Characteristics at the Meso-Scale

To enhance the quality of asphalt mixture compaction, the compaction mechanism, particularly at the meso-scale, must be thoroughly understood. Researchers have employed various technologies to study the compaction process. Among these, discrete element modeling (DEM) has been widely adopted due to its effectiveness in addressing particle-scale problems. However, improving simulation accuracy while maintaining computational efficiency remains a challenge. Therefore, this study aims to establish and optimize a DEM model for asphalt mixture gyratory compaction by integrating real-time laboratory SmartKli® sensing data. The Kalman filter was implemented as the fusion algorithm to enable real-time calibration. Two SmartKli sensors were positioned at different locations within specimens during both the laboratory Superpave gyratory compaction (SGC) test and DEM simulation to investigate the particle rotation characteristics. The results showed that the upper layer exhibited a higher degree of compaction than the lower layer. After calibration, particle rotation in the optimized DEM model more closely matched the laboratory SmartKli sensing data. Additionally, the changing trends of relative rotation for both SmartKli particles and coarse aggregate particles improved. The SmartKli simulation ball effectively represented the rotational behavior of its surrounding coarse aggregates, making its kinematic responses a reliable predictor of asphalt mixture compaction characteristics at the meso-scale.

State of Charge Estimation Based on Improved AILS-CSO Parameter Identification Algorithm

Abstract This paper introduces an adaptive inertial local search-cat-swarm optimization algorithm. The identification of parameters and estimation of charge state for lithium power batteries under diverse operational conditions were undertaken. In this approach, the equivalent circuit model of lithium power batteries is constructed using a second-order RC equivalent circuit model. Then, the cat swarm optimization algorithm is augmented with an adaptive adjustment algorithm for the inertial weight, thereby enhancing the accuracy of the identified battery parameters. Subsequently, the estimated voltage is then compared with the actual voltage in order to validate the feasibility of the algorithm. The root mean square error (RMSE) is less than 0.56%, and the maximum absolute error is 0.116 V. In conclusion, the state of charge of lithium batteries is estimated online under disparate working conditions via the integration of the extended Kalman filter algorithm, and a comparison is conducted. The maximum error is less than 1.74%, and the RMSE is less than 0.5%, indicating that the algorithm exhibits superior stability and estimation accuracy compared to the traditional recursive least squares method.

Motion and Inertia Estimation for Non-Cooperative Space Objects During Long-Term Occlusion Based on UKF-GP

This study addresses the motion and inertia parameter estimation problem of a torque-free, tumbling, non-cooperative space object (target) under long-term occlusions. To solve this problem, we employ a data-driven Gaussian process (GP) to simulate sensor measurements. In particular, we implement the multi-output GP to predict the projection measurements of a stereo-camera system onboard a chaser spacecraft. A product kernel, consisting of two periodic kernels, is used in the GP models to capture the periodic trends from non-periodic projection data. The initial guesses for the periodicity hyper-parameters of the GP models are intelligently derived from fast Fourier transform (FFT) analysis of the projection data. Additionally, we propose an unscented Kalman filter–Gaussian process (UKF-GP) fusion algorithm for target motion and inertia parameter estimation. The predicted projections from the GP models and their derivatives are used as the pseudo-measurements for UKF-GP during long-term occlusion. Results from Monte Carlo (MC) simulations demonstrate that, for varying tumbling frequencies, the UKF-GP can accurately estimate the target’s motion variables over hundreds of seconds, a capability the conventional UKF algorithm lacks.

Accurate Tracking of Agile Trajectories for a Tail-Sitter UAV Under Wind Disturbances Environments

To achieve more robust and accurate tracking control of high maneuvering trajectories for a tail-sitter fixed-wing unmanned aerial vehicle (UAV) operating within its full envelope in outdoor environments, a novel control approach is proposed. Firstly, the study rigorously demonstrates the differential flatness property of tail-sitter fixed-wing UAV dynamics using a comprehensive aerodynamics model, which incorporates wind effects without simplification. Then, utilizing the derived flatness functions and the treatments for singularity, the study presents a complete process of the differential flatness transform. This transformation maps the desired maneuver trajectory to a state-input trajectory, facilitating control design. Leveraging an existing controller from the reference literature, trajectory tracking is implemented. Subsequently, a low-cost wind estimation method operating during all flight phases is proposed to estimate the wind effects involved in the model. The wind estimation method involves generating a virtual wind measurement utilizing a low-fidelity tail-sitter model. The virtual wind measurement is integrated with real wind data obtained from the pitot tube and processed through fusion using an extended Kalman filter. Finally, the effectiveness of our methods is confirmed through comprehensive real-world experiments conducted in outdoor settings. The results demonstrate superior robustness and accuracy in controlling challenging agile maneuvering trajectories compared to the existing method. Additionally, the test results highlight the effectiveness of our method in wind estimation.

HFR-YOLO v3 model for multi-object detection and unscented Kalman filtering based object tracking in vehicle driving footage

HFR-YOLO v3 model for multi-object detection and unscented Kalman filtering based object tracking in vehicle driving footage

Research on the effect of biosensing technology on the dissemination of health information in ideological and political education

Biosensing technologies, which monitor physiological responses such as Heart Rate Variability (HRL), Skin Conductance Level (SCL), and Electroencephalogram (EEG) activity, offer a novel approach to enhancing the dissemination of health information in ideological and political education (IPE). In this context, health information encompasses topics such as mental health, stress management, and healthy lifestyle practices, all crucial to students’ overall well-being. Traditional health education methods cannot often capture real-time physiological and emotional responses, which can improve engagement and learning outcomes. This research explores the effectiveness of biosensing technology in enhancing the dissemination of health information within IPE. It examines how physiological data can be utilized to assess student engagement, emotional responses, and learning outcomes related to health. A mixed-methods approach was adopted, combining quantitative data from wearable biosensors (heart rate monitors, Galvanic Skin Response (GSR) sensors, EEG headsets) with qualitative feedback from students. Physiological data were preprocessed using signal filtering techniques, such as the Savitzky-Golay Filter, and features such as heart rate variability, skin conductance, and EEG alpha waves were extracted using the Kalman Filter (KF). A Modified Runge-Kutta Optimizer Integrated with Deep Belief Networks (MRKO-DBN) classifier was employed to predict student engagement based on these features. The research revealed that physiological responses, particularly heart rate variability and skin conductance, were strongly correlated with student engagement. The MRKO-DBN model achieved accuracy in predicting engagement. Qualitative feedback further confirmed that Biosensing technology significantly improved students’ engagement. Integrating Biosensing technology into health education within ideological and political contexts offers significant potential for enhancing student engagement and learning outcomes. By providing real-time, personalized feedback, it fosters a more interactive and responsive learning environment.

Improved accuracy of the whole body Center of Mass position through Kalman filtering

Improved accuracy of the whole body Center of Mass position through Kalman filtering

A Novel Real-Time Autonomous Localization Algorithm Based on Weighted Loosely Coupled Visual–Inertial Data of the Velocity Layer

IMUs (inertial measurement units) and cameras are widely utilized and combined to autonomously measure the motion states of mobile robots. This paper presents a loosely coupled algorithm for autonomous localization, the ICEKF (IMU-aided camera extended Kalman filter), for the weighted data fusion of the IMU and visual measurement. The algorithm fuses motion information on the velocity layer, thereby mitigating the excessive accumulation of IMU errors caused by direct subtraction on the positional layer after quadratic integration. Furthermore, by incorporating a weighting mechanism, the algorithm allows for a flexible adjustment of the emphasis placed on IMU data versus visual information, which augments the robustness and adaptability of autonomous motion estimation for robots. The simulation and dataset experiments demonstrate that the ICEKF can provide reliable estimates for robot motion trajectories.

State updating of the Xin'anjiang model: joint assimilating streamflow and multi-source soil moisture data via the asynchronous ensemble Kalman filter with enhanced error models

Abstract. Assimilating either soil moisture or streamflow individually has been well demonstrated to enhance the simulation performance of hydrological models. However, the runoff routing process may introduce a lag between soil moisture and outlet discharge, presenting challenges in simultaneously assimilating the two types of observations into a hydrological model. The asynchronous ensemble Kalman filter (AEnKF), an adaptation of the ensemble Kalman filter (EnKF), is capable of utilizing observations from both the assimilation moment and the preceding periods, thus holding potential to address this challenge. Our study first merges soil moisture data collected from field soil moisture monitoring sites with China Meteorological Administration Land Data Assimilation System (CLDAS) soil moisture data. We then employ the AEnKF, equipped with improved error models, to assimilate both the observed outlet discharge and the merged soil moisture data into the Xin'anjiang model. This process updates the state variables of the model, aiming to enhance real-time flood forecasting performance. Tests involving both synthetic and real-world cases demonstrates that assimilation of these two types of observations simultaneously substantially reduces the accumulation of past errors in the initial conditions at the start of the forecast, thereby aiding in elevating the accuracy of flood forecasting. Moreover, the AEnKF with the enhanced error model consistently yields greater forecasting accuracy across various lead times compared to the standard EnKF.

A hybrid data assimilation method based on real-time Ensemble Kalman filtering and KNN for COVID-19 prediction

This study introduces a hybrid data assimilation method that significantly improves the predictive accuracy of the time-dependent Susceptible-Exposed-Asymptomatic-Infected-Quarantined-Removed (SEAIQR) model for epidemic forecasting. The approach integrates real-time Ensemble Kalman Filtering (EnKF) with the K-Nearest Neighbors (KNN) algorithm, combining dynamic real-time adjustments with pattern recognition techniques tailored to the specific dynamics of epidemics. This hybrid methodology overcomes the limitations of single-model predictions in the face of increasingly complex transmission pathways in modern society. Numerical experiments conducted using COVID-19 case data from Xi’an, Shaanxi Province, China (December 9, 2021, to January 8, 2022) demonstrate a marked improvement in forecasting accuracy relative to traditional models and other data assimilation approaches. These findings underscore the potential of the proposed method to enhance the accuracy and reliability of predictive models, providing valuable insights for future epidemic forecasting and disease control strategies.

A Robust Kalman Filter Based on the Pearson Type VII-Inverse Wishart Distribution: Symmetrical Treatment of Time-Varying Measurement Bias and Heavy-Tailed Noise

This paper introduces a novel robust Kalman filter designed to leverage symmetrical properties within the Pearson Type VII-Inverse Wishart (PVIW) distribution, enhancing state estimation accuracy in the presence of time-varying biases and non-stationary heavy-tailed (NSHT) noise. The filter includes a shape parameter from the normal distribution and an extra variable from the Gamma distribution, which are used to symmetrically adjust the average and variation measures of the data to fit better under difficult noise conditions. To deal with unknown noise that changes over time, the filter uses the Inverse Wishart distribution to model and estimate the scale matrix deviations, making it easier to adapt to changes. The filter also uses a technique called Variational Bayesian to estimate both the state and the parameters at the same time. The results from simulations show that this new filter greatly improves the accuracy and strength of the estimation compared to the usual Kalman filters that assume a normal distribution, especially when there is non-stationary heavy-tailed noise. The main objective is to improve estimation in signal processing and control systems where heavy-tailed noise is prevalent.

Clamping Force Estimation for Electro-Mechanical Brake Based on Friction Torque Fusion Approach

Electromechanical brakes (EMB) are anticipated to become the standard brake system in the future, gaining favor among researchers and automobile manufacturers due to their numerous advantages. However, to achieve cost competitiveness, expensive load cells used to measure the clamping force on the disc must be replaced with a clamping force estimation algorithm. To do this, an algorithm is first developed to estimate the pad contact point, which represents the point of contact between the pad and the disc, to determine where the clamping force occurs. Subsequently, this paper proposes a novel Kalman filter approach utilizing friction torque fusion for clamping force estimation. Specifically, the estimation performance is enhanced by incorporating both dynamic and static friction torque models. The proposed estimation algorithm is validated by comparing its results with the actual clamping force measured using a load cell sensor. Furthermore, experimental tests are conducted to confirm whether the proposed estimation algorithm maintains its performance under various control reference conditions, and overall, the estimation error was within about 5% in this paper.