Showing papers on "Kalman filter published in 2021"

Applied mathematics in integrated navigation systems

Abstract: Intended for those directly involved with the design, integration, and test and evaluation of navigation systems, this text/CD-ROM presents elements of basic mathematics, kinematics, equations describing navigation systems and their error models, and Kalman filtering. Detailed derivations are presen

FAST-LIO: A Fast, Robust LiDAR-Inertial Odometry Package by Tightly-Coupled Iterated Kalman Filter

Abstract: This letter presents a computationally efficient and robust LiDAR-inertial odometry framework. We fuse LiDAR feature points with IMU data using a tightly-coupled iterated extended Kalman filter to allow robust navigation in fast-motion, noisy or cluttered environments where degeneration occurs. To lower the computation load in the presence of a large number of measurements, we present a new formula to compute the Kalman gain. The new formula has computation load depending on the state dimension instead of the measurement dimension. The proposed method and its implementation are tested in various indoor and outdoor environments. In all tests, our method produces reliable navigation results in real-time: running on a quadrotor onboard computer, it fuses more than 1200 effective feature points in a scan and completes all iterations of an iEKF step within 25 ms. Our codes are open-sourced on Github. 1

Real-time optimal quantum control of mechanical motion at room temperature

Abstract: The ability to accurately control the dynamics of physical systems by measurement and feedback is a pillar of modern engineering1. Today, the increasing demand for applied quantum technologies requires adaptation of this level of control to individual quantum systems2,3. Achieving this in an optimal way is a challenging task that relies on both quantum-limited measurements and specifically tailored algorithms for state estimation and feedback4. Successful implementations thus far include experiments on the level of optical and atomic systems5–7. Here we demonstrate real-time optimal control of the quantum trajectory8 of an optically trapped nanoparticle. We combine confocal position sensing close to the Heisenberg limit with optimal state estimation via Kalman filtering to track the particle motion in phase space in real time with a position uncertainty of 1.3 times the zero-point fluctuation. Optimal feedback allows us to stabilize the quantum harmonic oscillator to a mean occupation of 0.56 ± 0.02 quanta, realizing quantum ground-state cooling from room temperature. Our work establishes quantum Kalman filtering as a method to achieve quantum control of mechanical motion, with potential implications for sensing on all scales. In combination with levitation, this paves the way to full-scale control over the wavepacket dynamics of solid-state macroscopic quantum objects in linear and nonlinear systems. Optimal quantum control of an optically trapped nanoparticle in its ground state is demonstrated at room temperature, using Kalman filtering to track its quantum trajectory in real time.

Seamless GPS/Inertial Navigation System Based on Self-Learning Square-Root Cubature Kalman Filter

Abstract: To improve the seamless navigation ability of an integrated Global Positioning System (GPS)/inertial navigation system in GPS-denied environments, a hybrid navigation strategy called the self-learning square-root- cubature Kalman filter (SL-SRCKF) is proposed in this article. The SL-SRCKF process contains two innovative steps: 1) it provides the traditional SRCKF with a self-learning ability, which means that navigation system observations can be provided continuously, even during long-term GPS outages; and 2) the relationship between the current Kalman filter gains and the optimal estimation error is established, which means that the optimal estimation accuracy can be improved by error compensation. The superiority of the proposed SL-SRCKF strategy is verified via experimental results and prominent advantages of this approach include: 1) the SL-SRCKF comprises two cycle filtering systems that work in a tightly coupled mode, and this allows more accurate error correction results to be obtained during GPS outages; 2) the system's error prediction ability is effectively improved by introducing a long short-term memory, which provides much better performance than other neural networks, such as random forest regression or the recursive neural network; and 3) under different (30, 60, and 100 s) GPS outage conditions, the long-term stability of SL-SRCKF is much better than that of other error correction approaches.

Tracking R of COVID-19: A new real-time estimation using the Kalman filter

Abstract: We develop a new method for estimating the effective reproduction number of an infectious disease ([Formula: see text]) and apply it to track the dynamics of COVID-19. The method is based on the fact that in the SIR model, [Formula: see text] is linearly related to the growth rate of the number of infected individuals. This time-varying growth rate is estimated using the Kalman filter from data on new cases. The method is easy to implement in standard statistical software, and it performs well even when the number of infected individuals is imperfectly measured, or the infection does not follow the SIR model. Our estimates of [Formula: see text] for COVID-19 for 124 countries across the world are provided in an interactive online dashboard, and they are used to assess the effectiveness of non-pharmaceutical interventions in a sample of 14 European countries.

Combined State of Charge and State of Energy Estimation of Lithium-Ion Battery Using Dual Forgetting Factor-Based Adaptive Extended Kalman Filter for Electric Vehicle Applications

Abstract: With the increasing demand for Lithium-ion batteries in an electric vehicle (EV), it is always crucial to develop a highly accurate and low-cost state estimation method for the battery management system (BMS). Presently, the dual extended Kalman filter (DEKF) is extensively utilized for online SOC estimation. However, the problem of battery model parameter divergence from the true value greatly affects the estimation accuracy under realistic dynamic loading conditions. In this paper, the new dual forgetting factor-based adaptive extended Kalman filter (DFFAEKF) is proposed for SOC estimation. The proposed SOC estimation method is combined with the simple SOE estimation approach to develop the combined SOC and SOE estimation method. The quantitative relationships between SOC and SOE for all the test battery cells, which are established with the experimental data collected from different constant current discharge profiles are employed for SOE estimation. To evaluate the performance of the developed combined SOC and SOE estimation method, the three different chemistries battery cells are chosen for the testing under different dynamic loading profiles such as dynamic stress test (DST) and US06 drive cycle. For all the considered test battery cells, the experimental results indicated that the combined SOC and SOE estimation method using the proposed DFFAEKF can estimate the battery states under dynamic operating conditions with root mean square error (RMSE) less than 0.85% and 0.95% respectively. The proposed method also demonstrates fast convergence to its true value under erroneous initial conditions. Additionally, the order of worst-case big O notation complexity of the proposed DFFAEKF is equivalent to DEKF. Besides, the simplicity of the proposed method also supports to reduce the computational burden of the processor used in BMSs, and therefore it is well-suited for EV applications.

General Formulation of Kalman-Filter-Based Online Parameter Identification Methods for VSI-Fed PMSM

Abstract: This article proposes two Kalman-filter-based online identification schemes for permanent magnet synchronous machines (PMSMs), where the nonlinearity of a voltage-source inverter (VSI) is taken into account. One is formulated from an extended Kalman filter; the other uses a dual extended Kalman filter. They are generally formulated and can be applied to any identifiable electrical parameter combinations. The proposed schemes are further implemented on an industrial embedded control system. Their performance tests are conducted on a PMSM under static and dynamic conditions and compared with the extended Kalman filter without VSI nonlinearity compensation. The effectiveness of the proposed approaches is proved by the experimental results. Furthermore, a sensitivity analysis of the initial setup of parameter estimates has shown that the proposed estimators are robust against poor initial value choices. Real-time feasibility of the proposed estimators up to $\text{20}\;\text{kHz}$ is demonstrated via experiments.

R $^2$ LIVE: A Robust, Real-Time, LiDAR-Inertial-Visual Tightly-Coupled State Estimator and Mapping

Abstract: In this letter, we propose a robust, real-time tightly-coupled multi-sensor fusion framework, which fuses measurements from LiDAR, inertial sensor, and visual camera to achieve robust and accurate state estimation. Our proposed framework is composed of two parts: the filter-based odometry and factor graph optimization. To guarantee real-time performance, we estimate the state within the framework of error-state iterated Kalman-filter, and further improve the overall precision with our factor graph optimization. Taking advantage of measurements from all individual sensors, our algorithm is robust enough to various visual failure, LiDAR-degenerated scenarios, and is able to run in real time on an on-board computation platform, as shown by extensive experiments conducted in indoor, outdoor, and mixed environments of different scale (see attached video). Moreover, the results show that our proposed framework can improve the accuracy of state-of-the-art LiDAR-inertial or visual-inertial odometry. To share our findings and to make contributions to the community, we open source our codes on our Github.

Minimum Error Entropy Kalman Filter

Abstract: To date, most linear and nonlinear Kalman filters (KFs) have been developed under the Gaussian assumption and the well-known minimum mean square error (MMSE) criterion. In order to improve the robustness with respect to impulsive (or heavy-tailed) non-Gaussian noises, the maximum correntropy criterion (MCC) has recently been used to replace the MMSE criterion in developing several robust Kalman-type filters. To deal with more complicated non-Gaussian noises such as noises from multimodal distributions, in this article, we develop a new Kalman-type filter, called minimum error entropy KF (MEE-KF), by using the minimum error entropy (MEE) criterion instead of the MMSE or MCC. Similar to the MCC-based KFs, the proposed filter is also an online algorithm with the recursive process, in which the propagation equations are used to give prior estimates of the state and covariance matrix, and a fixed-point algorithm is used to update the posterior estimates. In addition, the MEE extended KF (MEE-EKF) is also developed for performance improvement in the nonlinear situations. The high accuracy and strong robustness of MEE-KF and MEE-EKF are confirmed by experimental results.

Constrained Ensemble Kalman Filter for Distributed Electrochemical State Estimation of Lithium-Ion Batteries

Abstract: This article proposes a novel model-based estimator for distributed electrochemical states of lithium-ion (Li-ion) batteries. Through systematic simplifications of a high-order electrochemical–thermal coupled model consisting of partial differential-algebraic equations, a reduced-order battery model is obtained, which features an equivalent circuit form and captures local state dynamics of interest inside the battery. Based on the physics-based equivalent circuit model, a constrained ensemble Kalman filter (EnKF) is pertinently designed to detect internal variables, such as the local concentrations, overpotential, and molar flux. To address slow convergence issues due to weak observability of the battery model, the Li-ion's mass conservation is judiciously considered as a constraint in the estimation algorithm. The estimation performance is comprehensively examined under a wide operating range. It demonstrates that the proposed EnKF-based nonlinear estimator is able to accurately reproduce the physically meaningful state variables at a low computational cost and is significantly superior to its prevalent benchmarks for online applications.

Vehicle state and tyre force estimation: demonstrations and guidelines

Abstract: This paper presents an in-depth analysis of the application of different techniques for vehicle state and tyre force estimation using the same experimental data and vehicle models, except for the t...

Vehicle Localization During GPS Outages With Extended Kalman Filter and Deep Learning

Abstract: Integration of microelectromechanical system-based inertial navigation system (MEMS-INS) and global positioning system (GPS) is a promising approach to vehicle localization. However, such a scheme may have poor performance during GPS outages and is less robust to measurement noises in changeable urban environments. In this article, we give an improved extended Kalman filter (IEKF) using an adaptation mechanism to eliminate the influence of noises in MEMS-INS and mitigate dependence on the process model. Especially, to guarantee accurate position estimation of the INS, a deep learning framework with multiple long short-term memory (multi-LSTM) modules is proposed to predict the increment of the vehicle position based on Gaussian mixture model (GMM) and Kullback–Leibler (KL) distance. The IEKF and the multi-LSTM are then combined together to optimize vehicle positioning accuracy during GPS outages in changeable urban environments. Numerical simulations and real-world experiments have demonstrated the effectiveness of the combined IEKF and multi-LSTM method, with the root-mean-square error (RMSE) of predicted position reduced by up to 93.9%. Or specifically, the RMSEs during GPS outages with durations 30, 60, and 120 s are 2.34, 2.69, and 3.08 m, respectively, which obviously outperform the existing method.

A Novel Outlier-Robust Kalman Filtering Framework Based on Statistical Similarity Measure

Abstract: In this article, a statistical similarity measure is introduced to quantify the similarity between two random vectors. The measure is, then, employed to develop a novel outlier-robust Kalman filtering framework. The approximation errors and the stability of the proposed filter are analyzed and discussed. To implement the filter, a fixed-point iterative algorithm and a separate iterative algorithm are given, and their local convergent conditions are also provided, and their comparisons have been made. In addition, selection of the similarity function is considered, and four exemplary similarity functions are established, from which the relations between our new method and existing outlier-robust Kalman filters are revealed. Simulation examples are used to illustrate the effectiveness and potential of the new filtering scheme.

Kalman Filter-Based Data Fusion of Wi-Fi RTT and PDR for Indoor Localization

Abstract: The Fine Time Measurement (FTM) protocol introduced by IEEE 802.11 includes a new ranging method, named Wi-Fi Round Trip Time (Wi-Fi RTT), which can be used for indoor localization. Pedestrian Dead Reckoning (PDR) can provide accurate pedestrian tracking through inertial sensors in a short time. Information fusion of PDR and existing wireless technology is widely used in indoor localization to ensure the robustness and stability. In this paper, we propose a fusion indoor localization method of Wi-Fi RTT and PDR. Firstly, an adaptive filtering system consisting of multiple Extended Kalman Filter (EKF) and a new outlier detection method is proposed to reduce the localization error of Wi-Fi RTT. Secondly, the fusion algorithm based on the Federated Filter (FF) and observability is designed to combine Wi-Fi RTT with PDR. Finally, to further improve the localization performance of the fusion algorithm, a real-time smoothing method with fixed interval is used. We evaluate the proposed method in four different scenarios. The results show that the proposed indoor localization method has better stability and robustness, and the average localization error decreased by 37.4-67.6% compared with the classic EKF-based method.

Adaptive Ensemble-Based Electrochemical-Thermal-Degradation State Estimation of Lithium-Ion Batteries

Abstract: A computationally efficient state estimation method for lithium-ion (Li-ion) batteries is proposed based on a degradation-conscious high-fidelity electrochemical-thermal model for advanced battery management systems. The computational burden caused by the high-dimensional nonlinear nature of the battery model is effectively eased by adopting an ensemble-based state estimator using the singular evolutive interpolated Kalman filter (SEIKF). Unlike the existing schemes, it shows that the proposed algorithm intrinsically ensures mass conservation without imposing additional constraints, leading to a battery state estimator simple to tune and fast to converge. The model uncertainty caused by battery degradation and the measurement errors are properly addressed by the proposed scheme as it adaptively adjusts the error covariance matrices of the SEIKF. The performance of the proposed adaptive ensemble-based Li-ion battery state estimator is examined by comparing it with some well-established nonlinear estimation techniques that have been used previously for battery electrochemical state estimation, and the results show that excellent performance can be provided in terms of accuracy, computational speed, as well as robustness.

State-of-Charge and State-of-Health Estimation for Lithium-Ion Batteries Based on Dual Fractional-Order Extended Kalman Filter and Online Parameter Identification

Abstract: Accurate state-of-charge (SOC) and state-of-health (SOH) estimations of batteries are of great significance for electric vehicles A combined SOC and SOH estimation method for lithium-ion batteries based on a dual extended Kalman filter (EKF) and fractional-order model (FOM) is proposed A fractional second-order RC model is established and model parameters are identified offline by an adaptive genetic algorithm (AGA) One of the dual filters is used to jointly estimate the SOC and SOH (ohmic internal resistance and capacity), and another is employed to update the model parameters online Compared with single filter with fixed parameters, the dual filters can obtain more accurate SOC estimation and model voltage prediction The SOC root-mean square errors (RMSEs) decrease from 687%, 850% and 732% to 048%, 063% and 086% under the Federal Urban Driving Schedule (FUDS), the Dynamic Stress Test (DST) and the US06 Highway Driving Schedule tests, respectively, and the model voltage RMSEs decrease from 886 mV, 793 mV and 684 mV to 49 mV, 57 mV and 38 mV, respectively at room temperature The accuracy of the SOH estimation is also verified under these three tests The convergence and robustness of the proposed method are discussed and verified by using the wrong initial state value and noise analysis

State of charge estimation with the adaptive unscented Kalman filter based on an accurate equivalent circuit model

Abstract: The accurate estimation of the state of charge (SOC) plays an important role in optimizing the energy management of electric vehicles. To improve the estimation accuracy of SOC, this study proposes a SOC estimation method with the adaptive unscented Kalman filter (AUKF) based on an accurate equivalent circuit model. First, combined with the n-RC equivalent circuit model, the relationship curve between SOC and open-circuit voltage (OCV) is fitted via parameter identification. Next, the accuracy advantage of the n-RC model is proven by comparing and analyzing the voltage response curves of different n-RC models and several common equivalent circuit models. Moreover, the accuracy of the n-RC model becomes higher with the increasing n. Then the numerical validation experiments are established based on the AUKF algorithm, and the constant current discharge experiment, hybrid pulse experiment, robustness verification experiment are carried out. Finally, to effectively evaluate this estimation approach, in addition to setting up a control group experiment based on the extended Kalman filter (EKF) algorithm and unscented Kalman filter (UKF) algorithm. The experiment results show that, compared with the other two algorithms, the SOC estimation method based on AUKF is more accurate.

Recursive Filtering of Distributed Cyber-Physical Systems With Attack Detection

Abstract: This article is concerned with the distributed recursive filtering of cyber-physical systems consisting of a set of spatially distributed subsystems. Due to the vulnerability of communication networks, the transmitted data among subsystems could be subject to deception attacks. In this article, attackers do not have enough knowledge of the full network topology and the system parameters and therefore cannot carry out stealth attacks. For this scenario, a defense strategy dependent on the received innovation is proposed to identify the occurring attacks as far as possible. In light of identified attacks, a novel distributed filter is constructed and its gain is designed via a set of recursive formulas on the upper bound of covariance of filtering errors. The utilization of upper bound is to avoid the calculational challenge of cross-covariance matrices and realize the requirement of distributed implementation, simultaneously. Furthermore, the developed scheme only depends on the neighboring information and the information from the subsystem itself, and thereby satisfying the requirement of the scalability. Finally, a standard IEEE 39-bus power system is utilized to verify the effectiveness of the proposed filtering scheme.

Analysis of Adaptive Image Retrieval by Transition Kalman Filter Approach based on Intensity Parameter

Abstract: The information changes in image pixel of retrieved records is very common in image process. The image content extraction is containing many parameters to reconstruct the image again for access the information. The intensity level, edge parameters are important parameter to reconstruct the image. The filtering techniques used to retrieve the image from query images. In this research article, the adaptive function kalman filter function performs for image retrieval to get better accuracy and high reliable compared to previous existing method includes Content Based Image Retrieval (CBIR). The kalman filter is incorporated with adaptive feature extraction for transition framework in the fine tuning of kalman gain. The feature vector database analysis provides transparent to choose the images in retrieval function from query images dataset for higher retrieval rate. The virtual connection is activated once in single process for improving reliability of the practice. Besides, this research article encompasses the adaptive updating prediction function in the estimation process. Our proposed framework construct with adaptive state transition Kalman filtering technique to improve retrieval rate. Finally, we achieved 96.2% of retrieval rate in the image retrieval process. We compare the performance measure such as accuracy, reliability and computation time of the process with existing methods.

Tightly Coupled Integration of INS and UWB Using Fixed-Lag Extended UFIR Smoothing for Quadrotor Localization

Abstract: Accurate indoor localization information of the quadrotor plays an important role in many Internet-of-Things applications. To improve the estimation accuracy and robustness, a fixed-lag extended finite impulse response smoother (FEFIRS) algorithm is proposed for fusing the inertial navigation system (INS) and ultra wideband (UWB) data tightly, which employs a distance between the UWB reference nodes and a blind node measured by the INS and UWB. The FEFIRS algorithm consists of an extended unbiased finite impulse response (EFIR) filter and a fixed-lag unbiased FIR (UFIR) smoother. The EFIR filter is employed to improve the robustness, and the fix-lag UFIR smoother is capable of improving the accuracy. Based on extensive test investigations employing real data, the proposed FEFIRS has higher accuracy and robustness than the Kalman-based solutions in the tightly integrated INS/UWB-based indoor quadrotor localization.

Linear and Nonlinear Regression-Based Maximum Correntropy Extended Kalman Filtering

Abstract: The extended Kalman filter (EKF) is a method extensively applied in many areas, particularly, in nonlinear target tracking. The optimization criterion commonly used in EKF is the celebrated minimum mean square error (MMSE) criterion, which exhibits excellent performance under Gaussian noise assumption. However, its performance may degrade dramatically when the noises are heavy tailed. To cope with this problem, this paper proposes two new nonlinear filters, namely the linear regression maximum correntropy EKF (LRMCEKF) and nonlinear regression maximum correntropy EKF (NRMCEKF), by applying the maximum correntropy criterion (MCC) rather than the MMSE criterion to EKF. In both filters, a regression model is formulated, and a fixed-point iterative algorithm is utilized to obtain the posterior estimates. The effectiveness and robustness of the proposed algorithms in target tracking are confirmed by an illustrative example.

State of Charge Estimation of Composite Energy Storage Systems with Supercapacitors and Lithium Batteries

Abstract: This paper studies the state of charge (SOC) estimation of supercapacitors and lithium batteries in the hybrid energy storage system of electric vehicles. According to the energy storage principle of the electric vehicle composite energy storage system, the circuit models of supercapacitors and lithium batteries were established, respectively, and the model parameters were identified online using the recursive least square (RLS) method and Kalman filtering (KF) algorithm. Then, the online estimation of SOC was completed based on the Kalman filtering algorithm and unscented Kalman filtering algorithm. Finally, the experimental platform for SOC estimation was built and Matlab was used for calculation and analysis. The experimental results showed that the SOC estimation results reached a high accuracy, and the variation range of estimation error was [−0.94%, 0.34%]. For lithium batteries, the recursive least square method is combined with the 2RC model to obtain the optimal result, and the estimation error is within the range of [−1.16%, 0.85%] in the case of comprehensive weighing accuracy and calculation amount. Moreover, the system has excellent robustness and high reliability.

The New Trend of State Estimation: From Model-Driven to Hybrid-Driven Methods

Abstract: State estimation is widely used in various automated systems, including IoT systems, unmanned systems, robots, etc. In traditional state estimation, measurement data are instantaneous and processed in real time. With modern systems' development, sensors can obtain more and more signals and store them. Therefore, how to use these measurement big data to improve the performance of state estimation has become a hot research issue in this field. This paper reviews the development of state estimation and future development trends. First, we review the model-based state estimation methods, including the Kalman filter, such as the extended Kalman filter (EKF), unscented Kalman filter (UKF), cubature Kalman filter (CKF), etc. Particle filters and Gaussian mixture filters that can handle mixed Gaussian noise are discussed, too. These methods have high requirements for models, while it is not easy to obtain accurate system models in practice. The emergence of robust filters, the interacting multiple model (IMM), and adaptive filters are also mentioned here. Secondly, the current research status of data-driven state estimation methods is introduced based on network learning. Finally, the main research results for hybrid filters obtained in recent years are summarized and discussed, which combine model-based methods and data-driven methods. This paper is based on state estimation research results and provides a more detailed overview of model-driven, data-driven, and hybrid-driven approaches. The main algorithm of each method is provided so that beginners can have a clearer understanding. Additionally, it discusses the future development trends for researchers in state estimation.

A Novel Heavy-Tailed Mixture Distribution Based Robust Kalman Filter for Cooperative Localization

Abstract: In cooperative localization for autonomous underwater vehicles (AUVs), the practical stochastic noise may be heavy-tailed, and nonstationary distributed because of acoustic speed variation, multipath effect of acoustic channel, and changeable underwater environment. To address such noise, a novel heavy-tailed mixture (HTM) distribution is first proposed in this article, and then expressed as a hierarchical Gaussian form by employing a categorical distributed auxiliary vector. Based on that, a novel HTM distribution based robust Kalman filter is proposed, where the one-step prediction, and measurement likelihood probability density functions are, respectively, modeled as an HTM distribution, and a Normal-Gamma-inverse Wishart distribution. The proposed filter is verified by a lake experiment about cooperative localization for AUVs. Compared with the cutting-edge filter, the proposed filter has been improved by 50.27% in localization error but no more than twice computational time is required.

Kalman filter based short term prediction model for COVID-19 spread

Abstract: Corona Virus Disease 2019 (COVID19) has emerged as a global medical emergency in the contemporary time. The spread scenario of this pandemic has shown many variations. Keeping all this in mind, this article is written after various studies and analysis on the latest data on COVID19 spread, which also includes the demographic and environmental factors. After gathering data from various resources, all data is integrated and passed into different Machine Learning Models in order to check its appropriateness. Ensemble Learning Technique, Random Forest, gives a good evaluation score on the tested data. Through this technique, various important factors are recognized and their contribution to the spread is analyzed. Also, linear relationships between various features are plotted through the heat map of Pearson Correlation matrix. Finally, Kalman Filter is used to estimate future spread of SARS-Cov-2, which shows good results on the tested data. The inferences from the Random Forest feature importance and Pearson Correlation gives many similarities and few dissimilarities, and these techniques successfully identify the different contributing factors. The Kalman Filter gives a satisfying result for short term estimation, but not so good performance for long term forecasting. Overall, the analysis, plots, inferences and forecast are satisfying and can help a lot in fighting the spread of the virus.