Kalman Filter Algorithm Research Articles

Adaptive nonlinear Kalman filters based on credibility theory with noise correlation

To solve the divergence problem and overcome the difficulty in guaranteeing filtering accuracy during estimation of the process noise covariance or the measurement noise covariance with traditional new information-based nonlinear filtering methods, we design a new method for estimating noise statistical characteristics of nonlinear systems based on the credibility Kalman Filter (KF) theory considering noise correlation. This method first extends credibility to the Unscented Kalman Filter (UKF) and Extended Kalman Filter (EKF) based on the credibility theory. Further, an optimization model for nonlinear credibility under noise related conditions is established considering noise correlation. A combination of filtering smoothing and credibility iteration formula is used to improve the real-time performance of the nonlinear adaptive credibility KF algorithm, further expanding its application scenarios, and the derivation process of the formula theory is provided. Finally, the performance of the nonlinear credibility filtering algorithm is simulated and analyzed from multiple perspectives, and a comparative analysis conducted on specific experimental data. The simulation and experimental results show that the proposed credibility EKF and credibility UKF algorithms can estimate the noise covariance more accurately and effectively with lower average estimation time than traditional methods, indicating that the proposed algorithm has stable estimation performance and good real-time performance.

Kalman filter with impulse noised outliers: a robust sequential algorithm to filter data with a large number of outliers.

Impulse noised outliers are data points that differ significantly from other observations. They are generally removed from the data set through local regression or the Kalman filter algorithm. However, these methods, or their generalizations, are not well suited when the number of outliers is of the same order as the number of low-noise data (often called nominal measurement). In this article, we propose a new model for impulsed noise outliers. It is based on a hierarchical model and a simple linear Gaussian process as with the Kalman Filter. We present a fast forward-backward algorithm to filter and smooth sequential data and which also detects these outliers. We compare the robustness and efficiency of this algorithm with classical methods. Finally, we apply this method on a real data set from a Walk Over Weighing system admitting around 60 % of outliers. For this application, we further develop an (explicit) EM algorithm to calibrate some algorithm parameters.

State-of-charge estimation of lithium-ion battery: Joint long short-term memory network and adaptive extended Kalman filter online estimation algorithm

With the widespread use of lithium-ion batteries, estimating the State of Charge (SOC) has been one of the most critical tasks in the battery management system (BMS). In this paper, a joint long short-term memory recurrent neural network (LSTM-RNN) and adaptive extended Kalman filter (AEKF) algorithm is proposed to achieve accurate SOC estimation. The proposed algorithm generates an initial SOC estimation value through a trained LSTM-RNN with a sliding time window signal sequence as input. The initial estimation value is then used as a feedback input to the AEKF. The results show that only a 30-s time series as the input of the LSTM-RNN can achieve satisfactory estimation results. Compared with traditional adaptive extended Kalman filter and unscented Kalman filter (UKF), the proposed algorithm has a better performance of estimation accuracy under various discharging conditions, especially when applied at low temperatures. Finally, the SOC estimation results under four operating conditions and various temperatures show that the maximum error is less than 2.5 %, in particular, the root mean square error (RMSE) and the mean absolute error (MAE) are below 1.01 % and 0.64 %. The proposed algorithm is an effective SOC estimation method with good robustness and high estimation accuracy.

Research on Speech Denoising Algorithm for Equipment Trains in Fully Mechanized Mining Working Faces based on CEEMDAN High and Low Frequency Filtering

This paper proposes a high and low frequency filtering denoising algorithm based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). CEEMDAN to address the issue of noise in speech signals obtained in the environment of fully mechanized mining face equipment trains. This algorithm first decomposes speech signals into multiple Intrinsic Mode Functions (IMFs) in different frequency domains through CEEMDAN, then uses Hilbert-Huang Transform (HHT) to obtain the instantaneous frequency and amplitude of IMFs, calculates the Euclidean distance between IMFs, normalizes it to obtain the average distance between IMFs, and divides the IMFs components into high and low frequency categories based on the average distance. Next, Optimally Modified Log Spectral Amplitude (OMLSA) algorithm and Kalman filtering algorithm are used for the high-frequency and low-frequency IMF components, respectively. Finally, the processed IMF components are reconstructed to obtain a denoised signal. After comparative experiments, the noise reduction algorithm proposed in this paper significantly improves the Signal to Noise Ratio (SNR), Peak Signal to Noise Ratio (PSNR), Mean Square Error (RMSE), and Mean Absolute Distance (MAE) of speech signals obtained in the environment of fully mechanized mining face equipment trains compared to other commonly used noise reduction algorithms.

A study of the attenuation stage of a global infectious disease.

Differences in control measures and response speeds between regions may be responsible for the differences in the number of infections of global infectious diseases. Therefore, this article aims to examine the decay stage of global infectious diseases. We demonstrate our method by considering the first wave of the COVID-19 epidemic in 2020. We introduce the concept of the attenuation rate into the varying coefficient SEIR model to measure the effect of different cities on epidemic control, and make inferences through the integrated adjusted Kalman filter algorithm. We applied the varying coefficient SEIR model to 136 cities in China where the total number of confirmed cases exceeded 20 after the implementation of control measures and analyzed the relationship between the estimated attenuation rate and local factors. Subsequent analysis and inference results show that the attenuation rate is significantly related to the local annual GDP and the longitude and latitude of a city or a region. We also apply the varying coefficient SEIR model to other regions outside China. We find that the fitting curve of the average daily number of new confirmed cases simulated by the variable coefficient SEIR model is consistent with the real data. The results show that the cities with better economic development are able to control the epidemic more effectively to a certain extent. On the other hand, geographical location also affected the effectiveness of regional epidemic control. In addition, through the results of attenuation rate analysis, we conclude that China and South Korea have achieved good results in controlling the epidemic in 2020.

In-Flight Calibration of Lorentz Actuators for Non-Contact Close-Proximity Formation Satellites with Cooperative Control

The non-contact close-proximity formation satellite (NCCPFS) is one of the technical solutions to improve the attitude performance, consisting of a payload module (PM) and a support module (SM). The non-contact Lorentz actuator (NCLA), as the core components of the NCCPFS, directly affect the attitude control performance of the entire satellite. In order to ensure the ultra-high attitude pointing performance and stability of the PM, an in-flight calibration method for the NCLAs based on minimum model error (MME) algorithm and Kalman filtering (KF) with cooperative control strategy is proposed in this article. In this method, the NCLAs generate a periodic nominal torque that causes the attitude of the PM to be periodically deflected. This periodic torque also reacts on the SM, and the SM counteracts this periodic torque through the flywheel to realize the cooperative tracking relative to the PM. Then, the gyroscope data are substituted into the MME algorithm to obtain the angular acceleration of the two modules, and the KF algorithm is adopted to observe the actual output torque of the NCLAs to complete the in-flight calibration of the NCLAs. Numerical simulation results show that the accuracy of the proposed calibration algorithm can reach about 8%, which proves the effectiveness of the proposed method.

Physics-informed deep learning with Kalman filter mixture for traffic state prediction

Accurate traffic forecasting is crucial for understanding and managing congestion for efficient transportation planning. However, conventional approaches often neglect epistemic uncertainty, which arises from incomplete knowledge across different spatiotemporal scales. This study addresses this challenge by introducing a novel methodology to establish dynamic spatiotemporal correlations that captures the unobserved heterogeneity in travel time through distinct peaks in probability density functions, guided by physics-based principles. We propose an innovative approach to modifying both prediction and correction steps of the Kalman Filter (KF) algorithm by leveraging established spatiotemporal correlations. Central to our approach is the development of a novel deep learning model called the Physics Informed-Graph Convolutional Gated Recurrent Neural Network (PI-GRNN). Functioning as the state-space model within the KF, the PI-GRNN exploits established correlations to construct dynamic adjacency matrices that utilize the inherent structure and relationships within the transportation network to capture sequential patterns and dependencies over time. Furthermore, our methodology integrates insights gained from correlations into the correction step of the KF algorithm that helps in enhancing its correctional capabilities. This integrated approach proves instrumental in alleviating the inherent model drift associated with data-driven methods, as periodic corrections through update step of KF refine the predictions generated by PI-GRNN. To the best of our knowledge, this study represents a pioneering effort in integrating deep learning and KF algorithms in this unique symbiotic manner. Through extensive experimentation with real-world traffic data, we demonstrate the superior performance of our model compared to the benchmark approaches.

Using Vehicle‐Induced DAS Signals for Near‐Surface Characterization With High Spatiotemporal Resolution

AbstractVehicle‐induced seismic waves, generated as vehicles traverse the ground surface, carry valuable information for imaging the underlying near‐surface structure. These waves propagate differently in the subsurface depending on soil properties at various spatial locations. By leveraging wave propagation characteristics, such as surface‐wave velocity and attenuation, this study presents a novel method for near‐surface monitoring. Our method employs passing vehicles as active, non‐dedicated seismic sources and leverages pre‐existing telecommunication fibers as large‐scale and cost‐effective roadside sensors empowered by Distributed Acoustic Sensing (DAS) technology. A specialized Kalman filter algorithm is integrated for automated DAS‐based traffic monitoring to accurately determine vehicles' location and speed. Then, our approach uniquely leverages vehicle trajectories to isolate space‐time windows containing high‐quality surface waves. With known vehicle (i.e., seismic source) locations, we can effectively mitigate artifacts associated with suboptimal distribution of sources in conventional ambient noise interferometry. Compared to ambient noise interferometry, our approach enables the synthesis of virtual shot gathers with a high signal‐to‐noise ratio and spatiotemporal resolution at reduced computational costs. We validate the effectiveness of our method using the Stanford DAS‐2 array, with a focus on capturing spatial heterogeneity and monitoring temporal variations in soil seismic properties during rainfall events. Specifically, in non‐built‐up areas, we observed an evident decrease in phase velocity and group velocity and an increase in attenuation due to the rainfall. Our findings illustrate our method's sensitivity and resolution in discerning variations across different spatial locations and demonstrate that our method is a promising advancement for high‐resolution near‐surface imaging in urban settings.

Human-Following Strategy for Orchard Mobile Robot Based on the KCF-YOLO Algorithm

Autonomous mobile robots play a vital role in the mechanized production of orchards, where human-following is a crucial collaborative function. In unstructured orchard environments, obstacles often obscure the path, and personnel may overlap, leading to significant disruptions to human-following. This paper introduces the KCF-YOLO fusion visual tracking method to ensure stable tracking in interference environments. The YOLO algorithm provides the main framework, and the KCF algorithm intervenes in assistant tracking. A three-dimensional binocular-vision reconstruction method was used to acquire personnel positions, achieving stabilized visual tracking in disturbed environments. The robot was guided by fitting the personnel’s trajectory using an unscented Kalman filter algorithm. The experimental results show that, with 30 trials in multi-person scenarios, the average tracking success rate is 96.66%, with an average frame rate of 8 FPS. Additionally, the mobile robot is capable of maintaining a stable following speed with the target individuals. Across three human-following experiments, the horizontal offset Error Y does not exceed 1.03 m. The proposed KCF-YOLO tracking method significantly bolsters the stability and robustness of the mobile robot for human-following in intricate orchard scenarios, offering an effective solution for tracking tasks.

Research on Vision-Based Servoing and Trajectory Prediction Strategy for Capturing Illegal Drones

A proposed strategy for managing airspace and preventing illegal drones from compromising security involves the use of autonomous drones equipped with three key functionalities. Firstly, the implementation of YOLO-v5 technology allows for the identification of illegal drones and the establishment of a visual-servo system to determine their relative position to the autonomous drone. Secondly, an extended Kalman filter algorithm predicts the flight trajectory of illegal drones, enabling the autonomous drone to compensate in advance and significantly enhance the capture success rate. Lastly, to ensure system robustness and suppress interference from illegal drones, an adaptive fast nonsingular terminal sliding mode technique is employed. This technique achieves finite time convergence of the system state and utilizes delay estimation technology for the real-time compensation of unknown disturbances. The stability of the closed-loop system is confirmed through Lyapunov theory, and a model-based hardware-in-the-loop simulation strategy is adopted to streamline system development and improve efficiency. Experimental results demonstrate that the designed autonomous drone accurately predicts the trajectory of illegal drones, effectively captures them using a robotic arm, and maintains stable flight throughout the process.

Orthotope-search-expansion-based extended zonotopic Kalman filter design for a discrete-time linear parameter-varying system with a dual-noise term

A novel algorithm utilizing an extended zonotopic Kalman filter based on the orthotope search expansion method is introduced to solve the state estimation problem in discrete-time linear parameter-varying systems when the dual noise of the systems is assumed to be bounded but unknown. First, to identify unknown parameters, an orthotope search expansion method is proposed with a measurement strip constraint. Subsequently, based on the parameter identification orthotopic set, an extended zonotopic Kalman filter algorithm is proposed to derive an estimation interval that wraps the true state of the system. Next, by minimizing the size of the zonotope, the optimal gain matrix for the extended zonotopic Kalman filter algorithm is determined. Finally, the proposed methods are demonstrated for their effectiveness and accuracy through the presentation of two simulation examples.

Research on the Method of Light Intensity Detection based on Kalman Filtering

A light intensity detection algorithm using Kalman filtering is proposed for the usage of data fusion in multi-sensor scenarios, like industrial control, machine vision, and navigation systems. In traditional measurements, the result is often faced with noise interference, causing accuracy problems. This algorithm Kalman filtering can be a good solution to noise signal reduction and provide optimal estimation in various domains that need prediction. As Kalman filtering is suitable for light intensity measurements, This work experimented with the steps shown below. First, the light intensity data is reported by sensors, and the mean and standard deviation of the measurement data are calculated; Second, by introducing a Kalman filtering model into the detecting model, the precision of estimating is improved, and the reliability of the system is enhanced; Finally, the data and diagram are exported by Matlab, and the Kalman filtering algorithm is compared with classical algorithms like moving average, median filtering. The experimental data shows Kalman filtering can be better applied to state estimation and signal processing domains, and the average light intensity data is 949.744. This result supports that Kalman filtering provides a robust and efficient method and it bed-covers the future research in improving the precision in light intensity measurements.

State estimation of buses: A hybrid algorithm of deep neural network and unscented Kalman filter considering mass identification

Accurately obtaining vehicle state parameters is a crucial prerequisite for active safety control. However, key stability parameters of buses, such as sideslip angle and roll angle, are difficult to measure directly. Moreover, changes in the bus mass during the driving route can impact the vehicle state. To tackle these challenges, we identify the bus mass before state estimation, and propose a hybrid state estimation algorithm based on deep neural network (DNN) and unscented Kalman filter (UKF). First, the mass is identified using the recursive least squares (RLS) method based on longitudinal dynamics at each start of bus, and the yaw and roll moment of inertia are adaptively adjusted based on the identified mass. Second, a composite DNN combining the convolutional neural network (CNN), gated recurrent unit (GRU), and attention mechanism is designed to estimate sideslip and roll angles. As for the training dataset, it is acquired from different maneuvers simulated by TruckSim. Third, a UKF estimator is established based on 4-degree of freedom (DOF) vehicle dynamics model and magic tire formula, and the estimated values of DNN are inserted into UKF estimator as virtual observations. Finally, the proposed hybrid algorithm is validated through simulation maneuvers and real driving maneuvers based on MATLAB/Simulink and TruckSim software. The comparative results demonstrate that the proposed algorithm outperforms individual DNN estimation and UKF estimation, enhancing both estimation accuracy and reliability.

Kalman filtering based on dynamic perception of measurement noise

In this work, we focus on the online state estimation problem for linear systems in non-Gaussian measurement noise. Specifically, the measurement noise is modeled as a Gaussian mixture model (GMM). Then, Kalman innovation is used to approximate the current measurement noise, and dynamically perceive its responsiveness to each sub-model of the GMM. The responsiveness from different Gaussian scales is mapped to a new cost function, while the corresponding Kalman filter algorithm is derived. The theoretical steady-state error and computational complexity analysis of the algorithm are also given. The simulation and real experimental results agree with the theoretical predictions and demonstrate the superior performance of the proposed algorithm.

Vehicle Multi-Object Detection and Tracking Algorithm Based on Improved You Only Look Once 5s Version and DeepSORT

The increasing popularity of vehicles has led to traffic congestion and frequent traffic accidents. Intelligent transportation technology is an effective solution to this problem. In order to improve the accuracy and effectiveness of vehicle detection and tracking, this paper combined the improved YOLOv5s model with the optimized DeepSORT tracking algorithm to detect and track vehicles on traffic roads. Firstly, in the detection model of YOLOv5s, the Attention-based Intra-scale Feature Interaction (AIFI) module is introduced to detect vehicles more quickly and accurately. Secondly, the Kalman filtering (KF) algorithm of DeepSORT is optimized to improve the accuracy of predictions of the vehicle state by using the width to replace the length-to-width ratio of the vehicle prediction box in the original KF algorithm. Finally, in the re-recognition network of DeepSORT, the original Convolutional Neural Network (CNN) model is replaced by an improved ResNet36 as the backbone network for feature extraction. The experimental results show that, compared with the original algorithm, when examining the performance of the improved algorithm in terms of target detection, the recall rate, average accuracy (mAP), and detection speed, are increased by 7.7%, 15.5%, and 14.2%, respectively; in terms of multi-object tracking performance, such as multi-object tracking precision (MOTP) and multi-object tracking accuracy (MOTA), improvements of 14.84% and 9.62%, respectively, are obtained and the total number of times a trajectory is fragmented (Frag) is reduced by 32.52%.These results indicate that the proposed algorithm can meet the requirements of accuracy, real-time detection, and stable vehicle detection and tracking on traffic roads.

Pedestrian tracking method based on S-YOFEO framework in complex scene

A real-time stable multi-target tracking method based on the enhanced You Only Look Once-v8 (YOLOv8) and the optimized Simple Online and Realtime Tracking with a Deep association metric (DeepSORT) for multi-target tracking (S-YOFEO) is proposed with the aim of addressing the issue of target ID transformation and loss caused by the increase of practical background complexity. For the purpose of further enhancing the representation of small-scale features, a small target detection head is first introduced to the detection layer of YOLOv8 in this paper with the aim of collecting more detailed information by increasing the detection resolution of YOLOv8. Secondly, the Omni-Scale Network (OSNet) feature extraction network is implemented to enable accurate and efficient fusion of the extracted complex and comparable feature information, taking into account the restricted computational power of DeepSORT’s original feature extraction network. Again, a novel adaptive forgetting Kalman filter algorithm (FSA) is devised to enhance the precision of model prediction and the effectiveness of parameter updates to adjust to the uncertain movement speed and trajectory of pedestrians in real scenarios. Following that, an accurate and stable association matching process is obtained by substituting Efficient-Intersection over Union (EIOU) for Complete-Intersection over Union (CIOU) in DeepSORT to boost the convergence speed and matching effect during association matching. Last but not least, One-Shot Aggregation (OSA) is presented as the trajectory feature extractor to deal with the various noise interferences in the complex scene. OSA is highly sensitive to information of different scales, and its one-time aggregation property substantially decreases the computational overhead of the model. According to the trial results, S-YOFEO has made some developments as its precision can reach 78.2% and its speed can reach 56.0 frames per second (FPS).

Temperature homogenization control of parabolic trough solar collector field based on hydraulic calculation and extended Kalman filter

Parabolic Trough Collector fields serve as the heat-absorbing components in large-scale commercial solar trough power plants. However, they frequently encounter challenges related to uneven spatial distribution of solar irradiation and heat transfer fluid flow. These disparities often lead to temperature inhomogeneity across the field, thereby jeopardizing both the safety and economic efficiency of the collector field. To address these issues, this study first introduces a proportional-integral and feedforward based flow control strategy designed to stabilize the fluid outlet temperature in the collector field. Subsequently, a flow allocation scheme aimed at achieving temperature uniformity across individual collector loops is presented. This scheme relies on the effective irradiation estimates for each collector loop, calculated using the extended Kalman filter algorithm and a suggested hydraulic model. Simulation results demonstrate that these control strategies not only stabilize the outlet temperature of the collector field at the desired set value but also significantly diminish temperature variances among individual collector loops, with reduced computational overhead. The maximum temperature difference between loops can be reduced from 126.3 °C to 12.7 °C under uneven radiation intensity, ranging from 563 W/m2 to 885 W/m2, by the proposed temperature homogenization control strategy.

Multicomponent collaborative time-frequency state-space model for vibration signal decomposition under nonstationary conditions

The implementation of prognostics and health management strategies is essential for enhancing the safety and maintenance of rotating equipment in chemical plants. The examination of vibration signal behaviours under variable-speed conditions and the development of signal decomposition methods in such contexts are of substantial theoretical and practical relevance. This paper proposes a novel multicomponent collaborative time-frequency state-space method for the decomposition of vibration signals. The method employs a multi-component proportional model to accurately describe the synchronisation of high-frequency components with the rotational frequency component. Based on this framework, the instantaneous frequency change curves of multiple components are input into the Vold–Kalman filter algorithm for precise decomposition of multicomponent vibration signals under variable-speed conditions. Experimental results demonstrate the effectiveness of the proposed method in achieving accurate instantaneous frequency tracking and signal decomposition, showing clear advantages over traditional methods.

Design and construction of INS/GPS navigation system based on adaptive Kalman filter algorithm

Design and construction of INS/GPS navigation system based on adaptive Kalman filter algorithm

Based on historical weather data to predict summer field-scale maize yield: Assimilation of remote sensing data to WOFOST model by ensemble Kalman filter algorithm

Effective support for agricultural production-management strategies relies on the accurate monitoring of crop growth and grain yield estimation at the field scale, making it an urgent need for the development of precision agriculture. Crop models are capable of simulating the growth and development of crops. In addition, Unmanned Aerial Vehicle (UAV) provides high temporal and spatial resolution for remote sensing, which can quickly and accurately obtain the crop growth status of small and medium-sized areas. This research utilized multispectral remote sensing information collected via UAV, alongside the WOFOST (World Food Studies) model, to evaluate the growth of summer maize within the experimental site. By utilizing vegetation indices derived from the UAV remote sensing data, the LAI (Leaf Area Index) of summer maize was ascertained, which further revealed a robust correlation between LAI and NDVI (Normalized Difference Vegetation Index). The model parameters were calibrated using crop and soil data from the Irrigation Experiment Station of Northwest A&F University. Verification indices revealed good consistency with a normalized root mean square error (nRMSE) of around 25 %, indicating that the model was suitable for simulating summer maize growth in this region. The ensemble Kalman filter algorithm was utilized to assimilate the remote sensing observation data with the WOFOST model, and the results showed that assimilation improved the accuracy of the yield simulation for each treatment. The optimal assimilation frequency should be more than three times, and assimilation during the flowering and grain-filling stages of summer maize could obtain better yield simulation results. By assimilating remote sensing observation data with 33 years of historical meteorological data from the Yangling Meteorological Station using the ensemble Kalman filter algorithm, this study predicted the yield and obtained a relative error of less than 5 %. The predicted yield value obtained on September 6 was more accurate than the predicted yield obtained at other times.