Kalman Filter Research Articles

Reinforcement learning-based estimation for spatio-temporal systems

State estimators such as Kalman filters compute an estimate of the instantaneous state of a dynamical system from sparse sensor measurements. For spatio-temporal systems, whose dynamics are governed by partial differential equations (PDEs), state estimators are typically designed based on a reduced-order model (ROM) that projects the original high-dimensional PDE onto a computationally tractable low-dimensional space. However, ROMs are prone to large errors, which negatively affects the performance of the estimator. Here, we introduce the reinforcement learning reduced-order estimator (RL-ROE), a ROM-based estimator in which the correction term that takes in the measurements is given by a nonlinear policy trained through reinforcement learning. The nonlinearity of the policy enables the RL-ROE to compensate efficiently for errors of the ROM, while still taking advantage of the imperfect knowledge of the dynamics. Using examples involving the Burgers and Navier-Stokes equations with parametric uncertainties, we show that in the limit of very few sensors, the trained RL-ROE outperforms a Kalman filter designed using the same ROM and yields accurate instantaneous estimates of high-dimensional states corresponding to unknown initial conditions and physical parameter values. The RL-ROE opens the door to lightweight real-time sensing of systems governed by parametric PDEs.

The Application and Potential Future Development of Artificial Intelligence in Education

With the coming of the era of artificial intelligence, the impact of artificial intelligence technology on basic education has been widely discussed, but there are still many problems and challenges. This paper focuses on the analysis of AI technology enabling basic education and the challenges in the application process. This paper concludes that artificial intelligence helps teachers carry out intelligent teaching and promotes students' personalized learning. But at the same time, AI also brings many challenges and risks, such as how to protect privacy and filter information in data overflow; And how to keep students creative while using AI. Based on this, this paper puts forward the following suggestions: the government should strengthen the investment and optimize the allocation of basic education resources; The government will explore the development of ethical norms and regulatory mechanisms applicable to artificial intelligence in the field of education; Schools to strengthen the training and introduction of teachers; Individual students combine artificial intelligence with real life.

Adaptive approach to spectrum monitoring in cognitive radio networks through signal detection optimization

The article considers the improvement of the adaptive algorithm of the spectral monitoring method for cognitive radio networks by introducing adaptive wavelet transforms and filters. The use of adaptive Morle and Dobechy wavelet transforms, as well as adaptive Kalman, LMS, and RLS filters is proposed, which allows dynamically changing parameters depending on the conditions of the radio environment. The comparative analysis with traditional methods showed that adaptive methods significantly increase the efficiency of signal detection in conditions of low SNR values, reducing the noise level, improving the accuracy of signal detection and reducing the probability of false alarms. The results of the study confirm the perspective of using adaptive methods to increase the reliability and efficiency of spectral monitoring in real operating conditions.

Comparison of the Wind Speed Estimation Algorithms of Wind Turbines Using a Drive Train Model and Extended Kalman Filter

To compare and validate wind speed estimation algorithms applied to wind turbines, wind speed estimators were designed in this study, based on two methods presented in the literature, and their performance was validated using the NREL 5MW model. The first method for wind speed estimation involves a three-dimensional (3D) look-up table-based approach, constructed using drive train differential equations. The second method involves applying a continuous–discrete extended Kalman filter. To verify and compare the performance of the algorithms designed using these different methods, feed-forward control algorithms, available power estimation algorithms, and a linear quadratic regulator, based on fuzzy logic (LQRF) control algorithms, were selected and applied as verification means, using the estimated wind speed as the input. Based on the simulation results, the performance of the two methods was compared. The method using drive train differential equations demonstrated superior performance in terms of reductions in the standard deviations of rotor speed and electrical power, as well as in its prediction accuracy for the available power.

Polar Motion Ultra-Short-Term Prediction of Least-Squares+Multivariate Autoregressive Hybrid Method by Using the Kalman Filter.

The polar motion (PM, including two parameters PMx and PMy) ultra-short-term prediction (1-10 days) is demanded in the real-time navigation of satellites and spacecrafts. Improving the PMx and PMy ultra-short-term predictions accuracies are a key to optimize the performance of these related applications. Currently, the least squares (LS)+autoregressive (AR) hybrid method is regarded as one of the most capable approaches for ultra-short-term predictions of PMx and PMy. The Kalman filter has proven to be effective in improving the ultra-short-term prediction performance of the LS+AR hybrid method, but the PMx and PMy ultra-short-term predictions accuracies are still not able to satisfy some related applications. In order to improve the performance of PM ultra-short-term prediction, it is worth exploring the combinations of existing methods. Throughout the existing predicted methods, the LS+multivariate autoregressive (MAR) hybrid method by using the Kalman filter has the potential to improve the accuracy of PM ultra-short-term prediction. In addition, a PM prediction performance analysis of the LS+MAR hybrid method by using the Kalman filter, namely the LS+MAR+Kalman hybrid method, is still missing. In this contribution, we proposed the LS+MAR+Kalman hybrid method for PM ultra-short-term prediction. The data sets for PM predictions, which range from 1 to 10 days, have been tested based on the International Earth Rotation and Reference Systems Service Earth Orientation Parameter (IERS EOP) 14 C04 series to assess the performance of the LS+MAR+Kalman hybrid model. The experimental results illustrated that the LS+MAR+Kalman hybrid method can effectively execute PMy ultra-short-term predictions. The improvement of PMy prediction accuracy can rise up to 12.69% for 10-day predictions, and the improvement of ultra-short-term predictions is 7.64% on average.

Consensus formation control of wheeled mobile robots with mixed disturbances under input constraints

This paper addresses the problem of distributed consensus-based formation control for wheeled mobile robots (WMRs) under the influence of mixed disturbances, including both random noise and non-random disturbances. A consensus formation auxiliary subsystem is constructed based on the leader’s position estimated by the distributed estimator. A formation tracking subsystem for each robot is constructed based on the trajectory tracking error method. The above two subsystems are constructed into an extended formation modeling system. Further, a distributed model predictive control (DMPC) is designed to control this system without disturbance, and the controller is solved by means of a general-purpose neural network. A combination of Kalman filter (KF) and extended state observer (ESO) is intended to reduce the effect of both non-random disturbances and random noise, hence increasing the controller’s resilience to disturbances. Moreover, a composite control law is designed to ensure the controller’s effectiveness. Finally, simulation results demonstrate that the proposed control strategy is well-suited to addressing the problem, as it not only achieves accurate formation control but also effectively regulates the robot’s physical constraints while suppressing both non-random disturbances and random noise.

Long-term tracking for high-frequency surface wave radar based on heading constraint filtering combined ELM

Abstract Aiming at the problem of low measurement resolution and poor tracking accuracy in High-frequency surface wave radar (HFSWR) tracking field, a tracking method that combines the heading constraint filter and Extreme Learning Machine (ELM) is proposed. Compared with the existing research, the innovation of this study lies in proposing a two-stage tracking method based on the short-term stable state of the target, and similarity of long-term trajectory. Firstly, the heading constraint information is introduced into the estimator and improve the estimation accuracy. In multi-target tracking scenarios, many tracklets can be obtained. Then, the ELM learns robust features of tracklets to achieve the trajectory segment classification from the same target. This method can be widely applied to long-term tracking of cargo or passenger ships with fixed destinations, significantly improving tracking performance by utilizing implicit domain knowledge without additional information. The actual data of this paper comes from HFSWR on Bohai Bay. Both the simulation and actual measurement experiments show that the proposed cascaded tracking method achieves long-term continuous tracking, and generates more complete trajectories. Moreover, the proposed Extended Kalman filter based on pseudo-measurement and intercept parameters (IPM-EKF) exhibits better tracking stability and accuracy in limited scan steps. This study provides new ideas and methods for improving the tracking performance of special targets in the HFSWR field by utilizing motion features.

Improving the accuracy of weighing systems in motion using dynamic neural networks

The paper is devoted to solving the problem of weighing vehicles in motion as part of modern information technologies and automated intelligent systems for managing urban resources and infrastructure. The aim of the work is to improve the accuracy of measurements in systems for weighing vehicles in motion in heavy traffic as part of intelligent urban infrastructure management systems, thereby contributing to the efficiency and sustainability of urban processes. The scientific novelty is the use of models in the form of neural networks with time delays to process data from weighing sensors. The application of this approach makes it possible to improve the accuracy of mass measurement in weighing systems in motion under conditions of intense traffic by taking into account the dynamic and nonlinear properties of the weighing process. The practical usefulness of the developed method lies in the development of new innovative weighing systems as part of modern information technologies and automated intelligent systems for managing urban resources and infrastructure. Testing the method on a simulation model of the WIM process demonstrated advantages in weighing accuracy compared to traditional methods using static and linear models. Experimental data showed a reduction in the root mean square error compared to the traditional method based on Kalman filters, which confirms the effectiveness of the proposed approach.

Estimation of SOC for Li-ion battery-powered three-wheeled electric vehicle using machine learning methods

Abstract The Battery Management System (BMS) serves as the heart of the electric vehicle system, in which estimating the state of charge (SOC) is the crucial part of the BMS to ensure the durability, reliability, and sustainability of the battery pack. Due to its nonlinear characteristics, accurately estimating the SOC for a slow degradation of the charge is highly cumbersome. The literature provides a series of machine learning algorithms (MLA) to estimate and predict the SOC of lithium-ion (Li-ion) battery systems for electric vehicle (EV) applications. The literature has proposed various MLA, coulomb counting, and different Kalman filter methods to address this challenge and estimate the SOC of Li-ion battery systems for EV applications. This research looks at the differences and similarities between the coulomb counting method, the unscented Kalman filter method, and a number of machine learning algorithms. These include linear regression, polynomial linear regression, support vector regression, decision trees, random forests, artificial neural networks (ANN), and long short-term memory (LSTM). The goal is to assess the MLAs' accuracy in estimating battery SOC. Analyzing model errors optimizes the battery's performance parameter. We identify ANN and LSTM as the two most efficient methods for accurate SOC estimation in an EV-operated BMS system by evaluating the performance indices of the aforementioned machine learning methodologies. Once again, the LSTM model for SOC estimation has proven to be highly accurate in analyzing the discrepancy between the actual and predicted traveling ranges of the designed prototype. We design a MATLAB/SIMULINK EV powertrain by collecting realtime data from the Li-ion battery pack, analyzing the SOC variation data, and using the previously mentioned MLA in the Python platform to estimate the SOC and its accuracy. It highlights the effectiveness of advanced MLAs in improving SOC estimation, thereby enhancing the performance and reliability of EV battery systems.

Enhancing the state-of-charge estimation of lithium-ion batteries using a CNN-BiGRU and AUKF fusion model

Accurate estimation of lithium-ion batteries’ state of charge (SOC) is crucial for the safety of energy storage devices, preventing issues such as overcharging or discharging. This paper introduces a fusion model combining convolutional neural network (CNN), bidirectional gated recurrent unit (BiGRU), and adaptive unscented Kalman filter (AUKF). This method's advantage lies in integrating Kalman filtering with the benefits of neural networks, eliminating the need for complex hyperparameter tuning and battery model construction. Initially, CNN-BiGRU maps variables like voltage, current, and temperature to SOC for initial estimation. The AUKF algorithm then filters these SOC outputs, minimizing fluctuations and enhancing accuracy. This approach ultimately leads to precise and stable SOC estimates. To validate the model's effectiveness, lithium-ion battery datasets across various temperatures were extensively trained and tested. The CNN-BiGRU-AUKF model demonstrated consistent performance under these conditions, with a maximum MSE of 0.00011, MAE under 0.0092, Max AE around 0.02, and a maximum RMSE of 0.017. Compared to similar methods, the proposed approach demonstrates superior SOC estimation accuracy and computational efficiency. Additionally, the model's scalability was validated using training and testing data for SOC estimates from a different type of lithium battery.

Active Vibration Control and Parameter Optimization of Genetic Algorithm for Partially Damped Composites Beams.

The paper partially covered Active Constrained Layer Damping (ACLD) cantilever beams' dynamic modeling, active vibration control, and parameter optimization techniques as the main topic of this research. The dynamic model of the viscoelastic sandwich beam is created by merging the finite element approach with the Golla Hughes McTavish (GHM) model. The governing equation is constructed based on Hamilton's principle. After the joint reduction of physical space and state space, the model is modified to comply with the demands of active control. The control parameters are optimized based on the Kalman filter and genetic algorithm. The effect of various ACLD coverage architectures and excitation signals on the system's vibration is investigated. According to the research, the genetic algorithm's optimization iteration can quickly find the best solution while achieving accurate model tracking, increasing the effectiveness and precision of active control. The Kalman filter can effectively suppress the impact of vibration and noise exposure to random excitation on the system.

Performance evaluation and analysis for hydraulic active suspension using the collaborative control method

Hydraulic active suspension has the coupling characteristics of integrated mechanical-hydraulic-control system, and its performance is also affected by external interference, noise interference, and other factors. Therefore, a novel controller is presented to achieve system-level optimal performances by using the collaborative control method. The proposed collaborative method is provided an implementation framework, and includes outer loop control of Linear Quadratic Regulator (LQR), inside loop control of modified linearized active disturbance rejection control (M-LADRC) and Kalman filter, and so on. In addition, the semi-physical simulation method is used to the simulation and test, and the force tracking control test for hydraulic servo system and Kalman filter test are carried out. Finally, the performance of semi-physical active suspension is compared with that of the ideal active suspension and passive suspension under the different road profile excitation. The superiority and effectiveness are verified for the collaborative control method. The collaborative controller has improved the suspension system performance and is more practical, which is beneficial for the application of the achievements.

Development and observation of a three-dimensional scanning coaxial Mie lidar for dynamic monitoring of near-surface aerosol plumes

Accurate three-dimensional spatiotemporal distribution information on near-surface aerosols is of great significance for environmental research. In this study, a 3D scanning coaxial Mie lidar (3D-STML) was developed to achieve a fast three-dimensional scanning observation of aerosol diffusion processes in near-surface areas. 3D-STML generates high-spatiotemporal resolution images of aerosol extinction coefficient in real-time and captures the dynamic changes of aerosols in near real-time. By optimizing the design of the light guide mirror and the telescope sub-mirror, the system has a small overlap. Based on this, a highly stable and high-speed mechanical rotation mechanism was developed to enable three-dimensional observations. The integration of a solid-state high-repetition-rate pulsed laser and a coaxial, optical system for the transmitter and receiver ensures rapid tracking of aerosol plumes. To meet the observation requirements of near-surface aerosols, an aerosol inversion algorithm combining the Fernald and Klett methods was designed and developed. For aerosol plume monitoring needs, an aerosol plume-tracking algorithm based on Kalman filtering was developed to track the spatiotemporal evolution of aerosols automatically. Experimental results demonstrated that 3D-STML is capable of detecting aerosols in a range from 15 m to 4 km, with a distance resolution of 1.5 m and a time resolution of 0.083 s. It can effectively track and capture aerosol plumes. It can be used for large-scale, long-term observation of near-surface aerosols and for monitoring the spatiotemporal evolution of aerosol plumes.

Impact of Data Corruption and Operating Temperature on Performance of Model-Based SoC Estimation

Electric vehicles (EVs) are becoming popular around the world. Making a lithium battery (LIB) pack with a robust battery management system (BMS) for an EV to operate under different complex environments is both a challenge and a requirement for engineers. A BMS can intelligently manage LIB systems by estimating the battery state of charge (SoC). Due to the nonlinear characteristics of LIB, influenced by factors such as the harsh environment and data corruption caused by electromagnetic interference (EMI) inside electric vehicles, SoC estimation should consider available capacity, model parameters, operating temperature and reductions in data sampling time. The widely used model-based algorithms, such as the extended Kalman filter (EKF) have limitations. Therefore, a detailed review of the balance between temperature, data sampling time, and different model-based algorithms is necessary. Firstly, a state of charge—open-circuit voltage (SoC-OCV) curve of LIB is obtained by the polynomial curve fitting (PCF) method. Secondly, a first-order RC (1-RC) equivalent circuit model (ECM) is applied to identify the battery parameters using a forgetting factor-based recursive least squares algorithm (FF-RLS), ensuring accurate internal battery parameters for the next step of SoC estimation. Thirdly, different model-based algorithms are utilized to estimate the SoC of LIB under various operating temperatures and data sampling times. Finally, the experimental data by dynamic stress test (DST) is collected at temperatures of 10 °C, 25 °C, and 40 °C, respectively, to verify and analyze the impact of operating temperature and data sampling time to provide a practical reference for the SoC estimation.

Kalman tracking and parameter estimation of continuous gravitational waves with a pulsar timing array

Abstract Continuous nanohertz gravitational waves from individual supermassive black hole binaries may be detectable with pulsar timing arrays. A novel search strategy is developed, wherein intrinsic achromatic spin wandering is tracked simultaneously with the modulation induced by a single gravitational wave source in the pulse times of arrival. A two-step inference procedure is applied within a state-space framework, such that the modulation is tracked with a Kalman filter, which then provides a likelihood for nested sampling. The procedure estimates the static parameters in the problem, such as the sky position of the source, without fitting for ensemble-averaged statistics such as the power spectral density of the timing noise, and therefore complements traditional parameter estimation methods. It also returns the Bayes factor relating a model with a single gravitational wave source to one without, complementing traditional detection methods. It is shown via astrophysically representative software injections in Gaussian measurement noise that the procedure distinguishes a gravitational wave from pure noise down to a characteristic wave strain of h0 ≈ 2 × 10−15. Full posterior distributions of model parameters are recovered and tested for accuracy. There is a bias of ≈0.3 rad in the marginalised one-dimensional posterior for the orbital inclination ι, introduced by dropping the so-called ‘pulsar terms’. Smaller biases $\lesssim 10~{{\%}}$ are also observed in other static parameters.

A multilevel lightweight fish respiratory frequency measurement method – Segmentation instead of detection

Respiratory frequency is an important physiological parameter for fish health. Traditional respiration detection methods have inherent frequency measurement error problems, and segmentation provides an innovative technique for respiration measurement. By shifting the focus from detection to segmentation, this approach provides robust and reliable support for measuring fish respiratory frequency accurately. However, the existing segmentation network models face challenges related to their large scale, high computational demands, and limited deployability at the edge. To overcome these challenges, this paper introduces an easily portable, high-precision segmentation method based on lightweight network and network slimming technique, named PM-YOLOv5s-seg (Prune MobileNetv3-YOLOv5s Segmentation). PM-YOLOv5s-seg utilizes the MobileNetv3 network as its segmentation backbone, enabling the extraction of essential fish mouth features. Simultaneously, it employs depth separable convolution to reduce network parameters and calculation amounts. Furthermore, the model undergoes additional sparsification via channel pruning, significantly improving its efficiency. Finally, respiratory frequency modeling is performed on the obtained fish mouth segmentation results, utilizing innovative techniques such as Ellipse fitting, Kalman filtering, and polynomial fitting methods. Comparison with the state-of-the-art methods demonstrates the superiority of the multilevel lightweight segmentation model PM-YOLOv5s-seg in terms of detection accuracy, computational efficiency, and model size. This model achieves an optimal balance between the speed and accuracy in fish respiratory frequency measurement, which holds significant implications for fish welfare as well as disease detection.

TWPT: Through-Wall Position Detection and Tracking System Using IR-UWB Radar Utilizing Kalman Filter-Based Clutter Reduction and CLEAN Algorithm

Against the backdrop of rapidly advancing Artificial Intelligence of Things (AIOT) and sensing technologies, there is a growing demand for indoor location-based services (LBSs). This paper proposes a through-the-wall localization and tracking (TWPT) system based on an improved ultra-wideband (IR-UWB) radar to achieve more accurate localization of indoor moving targets. The TWPT system overcomes the limitations of traditional localization methods, such as multipath effects and environmental interference, using the high penetration and high accuracy of IR-UWB radar based on multi-sensor fusion technology. In the study, an improved Kalman filter (KF) algorithm is used for clutter reduction, while the CLEAN algorithm, combined with a compensation mechanism, is utilized to increase the target detection probability. Finally, a three-point localization estimation algorithm based on multi-IR-UWB radar is applied for the precise position and trajectory estimation of the target. Experimental validation indicates the TWPT system achieves a high positioning accuracy of 96.91%, with a root mean square error (RMSE) of 0.082 m and a Maximum Position Error (MPE) of 0.259 m. This study provides a highly accurate and precise solution for indoor TWPT based on IR-UWB radar.

Calibration Method for Relativistic Navigation System Using Parallel Q-Learning Extended Kalman Filter.

For the relativistic navigation system where the position and velocity of the spacecraft are determined through the observation of the relativistic perturbations including stellar aberration and starlight gravitational deflection, a novel parallel Q-learning extended Kalman filter (PQEKF) is presented to implement the measurement bias calibration. The relativistic perturbations are extracted from the inter-star angle measurement achieved with a group of high-accuracy star sensors on the spacecraft. Inter-star angle measurement bias caused by the misalignment of the star sensors is one of the main error sources in the relativistic navigation system. In order to suppress the unfavorable effect of measurement bias on navigation performance, the PQEKF is developed to estimate the position and velocity, together with the calibration parameters, where the Q-learning approach is adopted to fine tune the process noise covariance matrix of the filter automatically. The high performance of the presented method is illustrated via numerical simulations in the scenario of medium Earth orbit (MEO) satellite navigation. The simulation results show that, for the considered MEO satellite and the presented PQEKF algorithm, in the case that the inter-star angle measurement accuracy is about 1 mas, after calibration, the positioning accuracy of the relativistic navigation system is less than 300 m.

Joint Model Parameter Identification and EKF Algorithm for the SOC Estimation of LFP Battery

Abstract Accurately estimating the state of charge (SOC) of batteries is crucial for achieving the safety and efficient driving of electric vehicles. To address the negative impact of voltage platform flatness and accumulated errors in current sampling, the SOC estimation method jointing model parameter identification and extended Kalman filter (EKF) algorithm is proposed and verified through simulation in this paper. Firstly, the parameter identification method is obtained based on the second-order dual polarization model, and effective identification of the parameters under different SOC is achieved using experimental conditions of hybrid pulse power characteristic and constant current discharge. On this basis, a function model with SOC as the independent variable and model parameters as the dependent variable is established by jointing model parameter identification and EKF algorithm, and the iterative estimation of SOC is achieved through the 1stopt and cftool methods. Finally, the SOC estimation accuracy of the proposed method is validated under three operating conditions that adopt the latest standards and are closer to the actual driving environment. The simulation results show that the SOC estimation method jointing model parameter identification and EKF algorithm has higher accuracy and smaller fluctuations than the traditional AH integration method, and the mean squared error (MSE) of estimation for the four test conditions are less than 0.29%, 0.72% and 0.25%, respectively.

Characterizing the dynamics, reactivity and controllability of moods in depression with a Kalman filter.

Mood disorders involve a complex interplay between multifaceted internal emotional states, and complex external inputs. Dynamical systems theory suggests that this interplay between aspects of moods and environmental stimuli may hence determine key psychopathological features of mood disorders, including the stability of mood states, the response to external inputs, how controllable mood states are, and what interventions are most likely to be effective. However, a comprehensive computational approach to all these aspects has not yet been undertaken. Here, we argue that the combination of ecological momentary assessments (EMA) with a well-established dynamical systems framework-the humble Kalman filter-enables a comprehensive account of all these aspects. We first introduce the key features of the Kalman filter and optimal control theory and their relationship to aspects of psychopathology. We then examine the psychometric and inferential properties of combining EMA data with Kalman filtering across realistic scenarios. Finally, we apply the Kalman filter to a series of EMA datasets comprising over 700 participants with and without symptoms of depression. The results show a naive Kalman filter approach performs favourably compared to the standard vector autoregressive approach frequently employed, capturing key aspects of the data better. Furthermore, it suggests that the depressed state involves alterations to interactions between moods; alterations to how moods responds to external inputs; and as a result an alteration in how controllable mood states are. We replicate these findings qualitatively across datasets and explore an extension to optimal control theory to guide therapeutic interventions. Mood dynamics are richly and profoundly altered in depressed states. The humble Kalman filter is a well-established, rich framework to characterise mood dynamics. Its application to EMA data is valid; straightforward; and likely to result in substantial novel insights both into mechanisms and treatments.