Unscented Kalman Filter Research Articles

Recursive and batch Bayesian estimation of exponential non-viscous damping systems

Non-viscous damping systems include a convolutional integral and a kernel function in their equation of motion to incorporate time-hysteresis damping effects, which are present in dynamical behavior of most engineering materials yet are absent in commonly used viscous damping models. When an exponential kernel function is adopted by the non-viscous model, the unique damping characteristic is realized by an additional model parameter known as the relaxation parameter. The objective of this paper is to investigate various aspects of estimation problems on exponential non-viscous damping systems through recursive and batch Bayesian time-domain frameworks, with a focus on how the relaxation parameter introduces additional complexity in estimation problems compared to viscous damping systems. Two well-established algorithms are employed: the unscented Kalman filter (UKF) for recursive Bayesian estimation and the transitional Markov Chain Monte Carlo (TMCMC) for batch Bayesian estimation. We first analyze the complexity of estimation problems in SDOF viscous and non-viscous damping systems. The TMCMC algorithm offers a quantitative analysis that reveals greater uncertainty and stronger parameter correlation in non-viscous damping systems compared to viscous damping systems. Subsequently, the same SDOF systems are utilized to study recursive Bayesian estimation via UKF such as the effects of measurement data type, discretization, and initial conditions. Based on the results of the TMCMC algorithm, we study the dependence of UKF performance on the initial condition for various SDOF non-viscous damping systems with different levels of non-viscosity. In the end, a laboratory experiment compares the estimation results between viscous and non-viscous damping systems using both TMCMC and UKF.

Active rack control of steer-by-wire systems for vehicle lateral stability

This paper describes a stability control strategy based on a steer-by-wire system to improve the lateral stability and manoeuvrability of vehicles by integrating individual chassis control modules, such as electronic stability control (ESC) and active front steering (AFS). Because of the uncertainty of cornering stiffness, an adaptive sliding-mode control is implemented without using the cornering stiffness value. An adaptive parameter is used instead of the cornering stiffness in the slip angle estimation and the lateral stability control. An unscented Kalman filter is used to estimate the slip angle and adaptive sliding mode control is used in lateral stability control. An equivalent desired command is calculated in lateral stability control. An integrated AFS and four individual wheel-braking controls were utilised to achieve an optimal distribution of longitudinal and lateral tyre forces, aiming to attain the desired command for lateral stability. Optimal coordination of the control authority for the AFS and the ESC has been chosen to minimise the force of each tyre. Computer simulations and vehicle tests of a closed-loop driver–vehicle–controller system subjected to a double-lane change have been carried out to verify that the proposed control strategy works.

A novel adaptive unscented kalman filter algorithm for SOC estimation to reduce the sensitivity of attenuation coefficient

A new exponential adaptive strong tracking unscented Kalman filtering algorithm (ASTRUKF) is proposed to address the issues of slow tracking speed, untimely response of model parameter changes, and inaccurate noise statistical characteristics when estimating the State of Charge (SOC) of batteries at different temperatures, in order to reduce the sensitivity of attenuation coefficients. This algorithm improves upon the traditional method of calculating attenuation factor by incorporating the correlation between current and past residuals. It dynamically updates the Kalman gain and contribution rate using an exponential model, which increases the impact of current data. This algorithm also ensures the stability of the noise covariance matrix by stabilizing the attenuation factor within a fixed range. The contribution rate is utilized to estimate the statistical characteristics of detection noise, however it may exhibit bias. The ASTRUKF method exhibits a maximum estimation error of 10−8 at 0 °C and 10−12 at 15 and 25 °C. This value is well below the levels of the UKF and EKF algorithms. The ASTRUKF algorithm outperforms the UKF and EKF algorithms in terms of prediction accuracy at different temperatures. The ASTRUKF method is well-suited for estimating SOC and has excellent adaptability to temperature variations.

Research on collaborative multi-UAV localization method based on combination navigation information

In challenging environments, unmanned aerial vehicle (UAV) systems often encounter unstable satellite signals and communication link interference. This paper proposes an integrated navigation method that integrates inertial navigation system (INS), global navigation satellite system (GNSS), and visual navigation system (VNS). Utilizing data from onboard sensors, this method merges relative navigation information from feature tracking of multiple UAVs with each UAV’s absolute navigation data. It includes specially designed transmission rules to reduce data exchange between UAVs. Each UAV uses an adaptive unscented Kalman filter (AUKF) method, which is enhanced into a collaborative AUKF (C-AUKF) using a message passing-based approach. Experiments in a simulated mission scenario revealed that the C-AUKF, in comparison to using extended Kalman filter (EKF), significantly improved flight test performance across the entire testing area, with a cumulative deviation of only 10.22 m, about 0.85% of the total flight distance. These results demonstrate that the proposed method not only meets accuracy requirements for position and velocity in integrated navigation but also significantly enhances multi-UAV navigation precision, particularly in scenarios with global positioning system (GPS) interference.

Exchange rate stability and expectation management under heterogeneous expectations

This study develops a heterogeneous agent model comprising fundamentalists, chartists, carry traders, and stabilizers to determine the RMB exchange rate. The stabilizers act as agents of the central bank and relevant government agencies to manage expectations when the exchange rate appreciates or depreciates excessively. Using the unscented Kalman filter method, our study finds that the principal parameters of the heterogeneous agent model are statistically and economically significant, and the heterogeneous agent model can adequately characterize the main features of expectation management. Furthermore, the stabilizers can significantly reduce excess volatility and promote market exchange rates to their fundamental values. Additionally, the timing of the stabilizers' actions is consistent with that of the central bank's implementation of expectation management.

Picking funds in China

This study compiles data on actively managed mutual funds in China spanning from 2007 to 2020 to construct portfolios of superior funds using the Fund Confidence Set (FCS) algorithm. Time-varying alphas and betas are estimated using an adaptive unscented Kalman filter with maximum posterior and random weighting rather than the extended Kalman filter. Moreover, an exponential smoother is integrated into the FCS algorithm, leading to improvements in portfolios’ performance. These two modifications to the FCS algorithm further enhance the performance of superior fund portfolios, producing an average monthly excess return of up to 1.88 %.

Complex‐step derivative‐based extended Kalman filter for state estimation in twin rotor MIMO system

AbstractThis paper presents the design of a complex‐step extended Kalman filter (CS‐EKF) to estimate the states of the twin‐rotor MIMO system (TRMS) which is a non‐linear system. Since the model of TRMS is quite complex and contains discontinuous functions, it is very difficult to calculate the Jacobian matrix in the TRMS analytically by hand. This makes it difficult to implement control methods that require Jacobian matrix calculation for TRMS. Herein, to calculate the Jacobian matrix, the CS‐EKF uses the complex‐step derivative approach, which is a numerical technique and offers near‐analytical accuracy in a single function evaluation. The effectiveness of the CS‐EKF is demonstrated through simulation and real‐time experiments. Also, The CS‐EKF is compared to the finite‐difference extended Kalman filter (FD‐EKF) and the unscented Kalman filter (UKF) in terms of estimation accuracy, computational load, and ease of implementation.

Mass property estimation on TSE(3) via unscented Kalman filter using RCS thrusters

Estimation of spacecraft mass properties in the presence of noise is a nontrivial problem that, when properly addressed, can substantially reduce the crew time devoted to cargo management, control effort expended to manage fuel mass, or both. The estimation of such properties is treated here using a dual unscented Kalman filter (UKF) where the dynamics of the rigid-body spacecraft are formulated on the special Euclidean group SE(3) and its tangent bundle TSE(3) to avoid singularity and nonuniqueness issues found in attitude parameterization sets. The dual UKF on TSE(3) is developed, and a specific methodology is proposed for the estimation of the constant mass properties. An excitation approach is employed in the mass property estimation scheme. Arbitrary sensor suite placements are considered and implemented in the measurement model to capture real-world spacecraft behavior. Furthermore, a reaction control system with duty cycle constraints and noisy thrust values is implemented to account for uncertainty in the excitation inputs. With these features, the methods contained herein are found to be effective at estimating mass properties.

Enhanced Object Detection in Autonomous Vehicles through LiDAR—Camera Sensor Fusion

To realize accurate environment perception, which is the technological key to enabling autonomous vehicles to interact with their external environments, it is primarily necessary to solve the issues of object detection and tracking in the vehicle-movement process. Multi-sensor fusion has become an essential process in efforts to overcome the shortcomings of individual sensor types and improve the efficiency and reliability of autonomous vehicles. This paper puts forward moving object detection and tracking methods based on LiDAR—camera fusion. Operating based on the calibration of the camera and LiDAR technology, this paper uses YOLO and PointPillars network models to perform object detection based on image and point cloud data. Then, a target box intersection-over-union (IoU) matching strategy, based on center-point distance probability and the improved Dempster–Shafer (D–S) theory, is used to perform class confidence fusion to obtain the final fusion detection result. In the process of moving object tracking, the DeepSORT algorithm is improved to address the issue of identity switching resulting from dynamic objects re-emerging after occlusion. An unscented Kalman filter is utilized to accurately predict the motion state of nonlinear objects, and object motion information is added to the IoU matching module to improve the matching accuracy in the data association process. Through self-collected data verification, the performances of fusion detection and tracking are judged to be significantly better than those of a single sensor. The evaluation indexes of the improved DeepSORT algorithm are 66% for MOTA and 79% for MOTP, which are, respectively, 10% and 5% higher than those of the original DeepSORT algorithm. The improved DeepSORT algorithm effectively solves the problem of tracking instability caused by the occlusion of moving objects.

Research on a Path Tracking Control Strategy for Autonomous Vehicles Based on State Parameter Identification

With the rapid development of autonomous driving technology, estimating and controlling key vehicle state parameters under complex road conditions have become critical challenges. This study combines Unscented Kalman Filtering (UKF) and Sliding Mode Control (SMC) methods to propose an integrated control model for achieving more efficient control. First, a three-degrees-of-freedom vehicle dynamics model based on the Dugoff tire model is constructed to accurately estimate key vehicle state parameters. Next, UKF is used to estimate road friction coefficients and key vehicle state parameters, and its performance is compared with Extended Kalman Filtering (EKF) under various conditions. The results show the superiority of UKF in identifying road friction coefficients. Based on SMC theory, a sliding surface is designed, and the functional relationship between state variables and control variables is derived to establish the corresponding control model. Joint simulations using Carsim and Simulink under different conditions validate the real-time performance and effectiveness of the designed UKF-SMC integrated control strategy in the presence of external disturbances and system uncertainties. Simulation results indicate that this strategy effectively enhances the overall performance and safety of autonomous vehicles, providing an accurate real-time solution capable of handling complex and variable road conditions. The proposed UKF-SMC integrated control strategy not only proves its theoretical superiority but also demonstrates promising practical applications in simulation experiments. This study provides reliable technical support for the development of autonomous driving technology under complex road conditions.

Online parameter identification based predictive pressure control for train electro-pneumatic braking systems with thermal effect

The electro-pneumatic braking system with ON/OFF solenoid valves has been widely used in trains due to its advantages and superiority. The undesirable impact of the thermal effect on the electro-pneumatic braking system leads to frequent valve switching, degradation of the pressure tracking performance and sometimes instability. This article presents an adaptive model predictive control approach to solve the pressure control problem under temperature uncertainty based on a switched unscented Kalman filter. First, a nonlinear switched dynamical model with the uncertain temperature parameter is derived for the electro-pneumatic braking system by comprehensively integrating its nonlinear, discontinuous dynamics and thermal effect. Using a switched unscented Kalman filter on the presented model of the system, the temperature parameter is accurately estimated to improve the model’s accuracy. Based on the corrected system model and the designed adaptive model predictive control method, the pressure tracking performance and the valves’ switchings of the electro-pneumatic braking system are improved, and the stability is guaranteed. The simulations and the experiments conducted for a braking system prototype confirm the performance validity of the proposed method.

Robust UKF orbit determination method with time-varying forgetting factor for angle/range-based integrated navigation system

The angle/range-based integrated navigation system is a favorable navigation solution for deep space explorers. However, the statistical characteristics of the measurement noise are time-varying, leading to inaccuracies in the derived measurement covariance even causing filter divergence. To reduce the gap between theoretical and actual covariances, some adaptive methods use empirically determined and unchanged forgetting factors to scale innovations within the sliding window. However, the constant weighting sequence cannot accurately adapt to the time-varying measurement noise in dynamic processes. Therefore, this paper proposes an Adaptive Robust Unscented Kalman Filter with Time-varying forgetting factors (TFF-ARUKF) for the angle/range integrated navigation system. Firstly, based on a statistically linear regression model approximating the nonlinear measurement model, the M-estimator is adopted to suppress the interference of outliers. Secondly, the covariance matching method is combined with the Huber linear regression problem to adaptively adjust the measurement noise covariance used in the M-estimation. Thirdly, to capture the time-varying characteristics of the measurement noise in each estimation, a new time-varying forgetting factors selection strategy is designed to dynamically adjust the adaptive matrix used in the covariance matching method. Simulations and experimental analysis compared with EKF, AMUKF, ARUKF, and Student’s t-based methods have validated the effectiveness and robustness of the proposed algorithm.

Autonomous wireless positioning system using crowdsourced Wi-Fi fingerprinting and self-detected FTM stations

Wi-Fi positioning system (WPS) has been proven as an effective way to realize universal indoor navigation for smart city-related applications. The localization ability of the existing WPS is affected by the low precision of the crowdsourced database and the unknown location of local wireless stations. This paper develops an integrated indoor localization framework using crowdsourced Wi-Fi fingerprinting and self-detected Wi-Fi Fine Time Measurement (FTM) stations (IL-CFSW). A novel crowdsourced mobile sensors data modeling algorithm with self-calibrated parameters is proposed, and modeled trajectories are further segmented and matched with the existing pedestrian indoor network to enhance the performance of the final database generation. Furthermore, the iteration unscented Kalman filter (iUKF) is adopted to recognize the position and calibrate the bias of existing Wi-Fi FTM anchors combined with the hybrid distance measurement model. Finally, an enhanced particle filter with error ellipse constraint is developed to fuse different location sources and indoor network information. Comprehensive experimental results present that the developed IL-CFSW can achieve autonomous 3D indoor localization performance in multi-floor contained scenes and meter-level positioning accuracy is achieved with the consideration of pedestrian indoor network information.

Battery lumped fractional‐order hysteresis thermoelectric coupling model for state of charge estimation adaptive to time‐varying core temperature conditions

AbstractAs electric vehicles become more common, there is increasing concern regarding their battery reliability and safety. The estimation accuracy is strongly correlated with the performance of the battery model. The lumped fractional‐order hysteresis thermoelectric coupling model (LFHTCM), considering temperature and hysteresis effects, is established in this paper. Firstly, the fractional‐order hysteresis sub‐model is established based on the Grunwald‐Letnikov (G‐L) fractional calculus principle and the recursive model of hysteresis voltage. Then, the thermal sub‐model is established by integrating the Bernardi heating mechanism and the heat transfer model. The fractional‐order sub‐model provides voltage to the thermal sub‐model for heat generation calculation. The thermal sub‐model provides temperature to the fractional‐order model for parameter correction. Finally, the fractional‐order unscented Kalman filtering (FOUKF) algorithm was developed to estimate the state of charge (SOC) of the battery. Experimental results confirmed the effectiveness of the model, with its estimation enhancing the utilization, operational optimization, and calibration of batteries in practical applications.

Implementation of unknown parameter estimation procedure for hybrid and discrete non‐linear systems

AbstractThe application of the hybrid extended Kalman filter (HEKF), hybrid unscented Kalman filter (HUKF), hybrid particle filter (HPF), and hybrid extended Kalman particle filter (HEKPF) is discussed for hybrid non‐linear filter problems, when prediction equations are continuous‐time and the update equations are discrete‐time, and also the discrete extended Kalman filter (DEKF), discrete unscented Kalman filter (DUKF), discrete particle filter (DPF), and discrete extended Kalman particle filter (DEKPF) for discrete‐time non‐linear filter problems, when prediction equations and update equations are discrete‐time. In order to assess the performance of the filters, the authors consider the non‐linear dynamics for a re‐entry vehicle. The filters are used in two hybrid and discrete states to estimate the position, velocity, and drag parameter associated with the re‐entry vehicle. Theoretical topics concerning estimating the drag parameter of a vehicle in re‐entry phase have been dealt with. Drag parameter estimation is carried out using a combination of hybrid filters and discrete filters as an effective estimator and fixed value, forgetting factor, and Robbins‐Monro stochastic approximation methods as the noise covariance matrix adjuster of the parameter.

Battery parameter identification for unmanned aerial vehicles with hybrid power system

Unmanned aerial vehicles (UAVs) nowadays are getting soaring importance in many aspects like agricultural and military fields. A hybrid power system is a promising solution toward high energy density and power density demands for UAVs as it integrates power sources like internal combustion engine (ICE), fuel cell (FC) and lowcapacity lithium-polymer (LIPO) batteries. For robust energy management, accurate state-of-charge (SOC) estimation is indispensable, which necessitates open circuit voltage (OCV) determination and parameter identification of battery. The presented research demonstrates the feasibility of carrying out incremental OCV test and even dynamic stress test (DST) by making use of the hybrid powered UAV system itself. Based on battery relaxation terminal voltage as well as current wave excitation, novel methods for OCV determination and parameter identification are proposed. Results of SOC estimation against DST through adaptive unscented Kalman filter (AUKF) algorithm show that parameters and OCV identified with longer relaxation time don’t yield better SOC estimation accuracy. Besides, it also discloses that OCV played the vital role in affecting SOC estimation accuracy. A detailed analysis is presented showing that mean discharging rate and current wave amplitude are the major factors which affect the quality of OCV identified related to SOC estimation accuracy.

Artificial neural network based on strong track and square root UKF for INS/GNSS intelligence integrated system during GPS outage

When INS/GNSS (inertial navigation system/global navigation satellite system) integrated system is applied, it will be affected by the insufficient number of visible satellites, and even the satellite signal will be lost completely. At this time, the positioning error of INS accumulates with time, and the navigation accuracy decreases rapidly. Therefore, in order to improve the performance of INS/GNSS integration during the satellite signals interruption, a novel learning algorithm for neural network has been presented and used for intelligence integrated system in this article. First of all, determine the input and output of neural network for intelligent integrated system and a nonlinear model for weighs updating during neural network learning has been established. Then, the neural network learning based on strong tracking and square root UKF (unscented Kalman filter) is proposed for iterations of the nonlinear model. In this algorithm, the square root of the state covariance matrix is used to replace the covariance matrix in the classical UKF to avoid the filter divergence caused by the negative definite state covariance matrix. Meanwhile, the strong tracking coefficient is introduced to adjust the filter gain in real-time and improve the tracking capability to mutation state. Finally, an improved calculation method of strong tracking coefficient is presented to reduce the computational complexity in this algorithm. The results of the simulation test and the field-positioning data show that the proposed learning algorithm could improve the calculation stability and robustness of neural network. Therefore, the error accumulation of INS/GNSS integration is effectively compensated, and then the positioning accuracy of INS/GNSS intelligence integrated system has been improved.

Kinematic Parameter Identification and Error Compensation of Industrial Robots Based on Unscented Kalman Filter with Adaptive Process Noise Covariance

Kinematic calibration plays a pivotal role in enhancing the absolute positioning accuracy of industrial robots, with parameter identification and error compensation constituting its core components. While the conventional parameter identification method, based on linearization, has shown promise, it suffers from the loss of high-order system information. To address this issue, we propose an unscented Kalman filter (UKF) with adaptive process noise covariance for robot kinematic parameter identification. The kinematic model of a typical 6-degree-of-freedom industrial robot is established. The UKF is introduced to identify the unknown constant parameters within this model. To mitigate the reliance of the UKF on the process noise covariance, an adaptive process noise covariance strategy is proposed to adjust and correct this covariance. The effectiveness of the proposed algorithm is then demonstrated through identification and error compensation experiments for the industrial robot. Results indicate its superior stability and accuracy across various initial conditions. Compared to the conventional UKF algorithm, the proposed approach enhances the robot’s accuracy stability by 25% under differing initial conditions. Moreover, compared to alternative methods such as the extended Kalman algorithm, particle swarm optimization algorithm, and grey wolf algorithm, the proposed approach yields average improvements of 4.13%, 26.47%, and 41.59%, respectively.

Position prediction of underwater gliders based on a new heterogeneous model ensemble method

An underwater glider (UG) is a promising unmanned underwater vehicle driven by buoyancy that can perform long-period and large-scale ocean observations. Due to the lack of inertial sensors and the low-speed relative to the ocean current, it is difficult to determine the exact position of the UG. Besides, the position of the UG is of great significance for acoustic applications. Therefore, this paper proposes a new heterogeneous model ensemble method (HMEM) based on the whale algorithm (WOA) optimized backpropagation neural network with complement ensemble empirical mode decomposition (CEEMD-BPNN) and the physical model. The physical model can deduce the underwater position of the UG considering the ambient environment, and the WOA-CEEMD-BPNN is adopted to predict the surface position with historical data. Then, the new heterogeneous model ensemble method integrates these two with an unscented Kalman filter according to the predicted surface position. To evaluate the performance of the HMEM, the evaluation index is introduced, and the sea trial conducted by the Petrel-II glider is used as a case study. The experiment demonstrates that the MAE and RMSE of the HMEM are 0.51 km and 0.76 km, respectively, and the mean time difference is 3.08 × 102 s, which outperforms the dynamic model and can achieve accurate position prediction for long periods.

Preoperative diffusion tensor imaging: Fiber-trajectory-distribution-based tractography to identify facial nerve in vestibular schwannoma.

Tractography of the facial nerve based on diffusion MRI is instrumental before surgery for the resection of vestibular schwannoma, but no excellent methods usable for the suppression of motion and image noise have been proposed. The aim of this study was to effectively suppress noise and provide accurate facial nerve reconstruction by extend a fiber trajectory distribution function based on the fourth-order streamline differential equations. Preoperative MRI from 33 patients with vestibular schwannoma who underwent surgical resection were utilized in this study. First, T1WI and T2WI were used to obtain mask images and regions of interest. Second, probabilistic tractography was employed to obtain the fibers representing the approximate facial nerve pathway, and these fibers were subsequently translated into orientation information for each voxel. Last, the voxel orientation information and the peaks of the fiber orientation distribution were combined to generate a fiber trajectory distribution function, which was used to parameterize the anatomical information. The parameters were determined by minimizing the cost between the trajectory of fibers and the estimated directions. Qualitative and visual analyses were used to compare facial nerve reconstruction with intraoperative recordings. Compared with other methods (SD_Stream, iFOD1, iFOD2, unscented Kalman filter, parallel transport tractography), the fiber-trajectory-distribution-based tractography provided the most accurate facial nerve reconstructions. The fiber-trajectory-distribution-based tractography can effectively suppress the effect of noise. It is a more valuable aid for surgeons before vestibular schwannoma resection, which may ultimately improve the postsurgical patient's outcome.