Unscented Kalman Filter Research Articles

Enhancing physically-based flood forecasts through fusion of long short-term memory neural network with unscented Kalman filter

Accurate flood forecasts are vital for reservoir operation and flood prevention. The unscented Kalman filter (UKF) excels in improving physically-based models flood forecasting but depends on precise noise estimation, posing challenges in complex uncertainty quantification. In this study, we propose a novel approach, the deep fusion of a long short-term memory (LSTM) neural network and unscented Kalman filter (LSTM-UKF), to enhance flood forecasts by adaptively updating hydrological model states. The LSTM efficiently learns noise-related information from the estimation of Kalman Gain, obviating the need for intricate uncertainty recognition and approximation. For comparative analysis, the LSTM-UKF and UKF filters are constructed to correct Xinanjiang (XAJ) hydrological model states. Both filters utilize streamflow observations to update the XAJ model states and facilitate its flood forecasting performance. Comprehensive evaluations were conducted using 3-hourly meteor-hydrological sequences from the Jianxi and Tianyi basins in China, focusing on the accuracy, stability, and reliability of multi-step-ahead flood forecasts. Results indicate that the LSTM-UKF performs superior to the UKF, with maximal advancements in Nash-Sutcliffe efficiency coefficient (NSE) by 9.1%, maximal reduction in root mean square error (RMSE) by 18.7%, and maximal decrease in mean absolute error (MAE) by 22.6%. Additionally, the LSTM-UKF exhibits better robustness and stability in non-stationary flood events. The proposed LSTM-UKF mitigates the over-reliance on noise estimates, reducing systematic biases and error accumulation in state estimates and enhancing hydrological model generalizability in operational flood prevention platforms and systems.

A cooperative timestamp-free clock synchronization scheme based on fast unscented Kalman filtering for time-sensitive networking

Clock synchronization, built on the classical two-way message exchange scheme, is the key prerequisite for the normal operation of time-sensitive networking (TSN). In practical TSN, the imperfect oscillator caused by environmental changes leads to clock parameters drift. Moreover, synchronization errors accumulate in multi-hop networks, making it difficult for nodes at the edge of the network to achieve precise synchronization performance. Additionally, in some industrial and vehicular scenarios, the energy consumption and complexity of clock synchronization are important factors that need to be considered. To address these problems, this paper proposes a cooperative synchronization clock offset and clock skew joint tracking algorithm based on fast Unscented Kalman filter (FUKF). To further reduce the computation and energy consumption caused by clock synchronization, we introduce randomized singular value decomposition and timestamp-free exchange. The former uses small sub-matrices approximations to replace extremely high-dimensional matrices, reducing computational time in the update stage of the UKF. The latter reduces energy consumption by setting response intervals at the receiving end, eliminating the need for timestamp exchange during the synchronization process. Therefore, this algorithm can achieve long-term synchronization without requiring excessive computational and communication overhead. The results show that the proposed method, while maintaining accuracy unchanged, reduced the running time by 20% to 90% as the number of observations increased, thus verifying the effectiveness of the algorithm.

Data-driven dynamic inclination angle estimation of monorail crane under complex road conditions

Abstract Monorail cranes are crucial in facilitating auxiliary transportation within deep mining operations. As unmanned driving technology becomes increasingly prevalent in monorail crane operations, it encounters challenges such as low accuracy and unreliable attitude recognition, significantly jeopardizing the safety of monorail crane operations. Hence, this study proposes a dynamic inclination estimation methodology utilizing the Estimation-Focused-EKFNet algorithm. Firstly, based on the driving characteristics of the monorail crane, a dynamic inclination model of the monorail crane is established, based on which the dynamic inclination value can be calculated in real-time by the extended Kalman filter (EKF) estimator; however, given the complexity of the driving road conditions, in order to improve the dynamic inclination recognition accuracy, the CNN-LSTM-ATT algorithm combining the convolutional neural network (CNN), the long short-term memory (LSTM) neural network and the attention mechanism (ATT) is used to firstly predict the current dynamic camber is predicted by the CNN-LSTM-ATT algorithm combined with the CNN and the attention mechanism, and then the predicted dynamic inclination value is used as the observation value of the EKF estimator, which finally realizes that the EKF estimator can output the accurate dynamic inclination value in real-time. Experimental results indicate that, compared with the unscented Kalman filter, LSTM-ATT, and CNN-LSTM algorithms, the Estimation-Focused-EKFNet algorithm enhances dynamic inclination recognition in complex road conditions by at least 52.34%, significantly improving recognition reliability. Its recognition accuracy reaches 99.28%, effectively ensuring the safety of unmanned driving for monorail cranes.

Unscented Kalman filter application for state estimation of a Qball-X4 quadrotor

In the process of controlling the quadrotor, accurate state estimation plays a crucial role. For positioning purposes, the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are employed to determine the position of moving subjects. The Qball-X4 quadrotor is a highly nonlinear object, and when combined with Gauss interference, it can compromise the accuracy of the EKF. To address these challenges, this study focuses on assessing the suitability of the UKF nonlinear filtering method for estimating the state of the Qball-X4 quadrotor. This estimation is based on measurements from the gyroscope and Global Positioning System (GPS). To simulate real-life conditions, measurement noise has been deliberately introduced into the sensors. Rigorous testing under various conditions has emphasized the superior performance of the UKF filter in estimating the state of the quadrotor. This paper presents a valuable method to enhance the accuracy and reliability of the navigation system for the Qball-X4 quadrotor.

Identification of amplitude-dependent aerodynamic damping from free vibration data using iterative unscented kalman filter

This study presents an innovative approach employing an iterative Unscented Kalman Filter (IUKF) for the identification of amplitude-dependent nonlinear aerodynamic damping using wind tunnel free vibration data. The wind-structure interaction system is represented as a single-degree-of-freedom system, with the amplitude-dependent aerodynamic damping modeled as a polynomial function of structural displacement and velocity. The augmented state variables, encompassing structural vibration frequency and polynomial coefficients for aerodynamic damping, are concurrently estimated from free vibration data using the UKF technique. To enhance the robustness of the identification results against variations in initial conditions, the UKF is applied iteratively by assigning the estimated polynomial coefficients as new initial values for the state variables. Validation of the IUKF-based method is performed through a numerical example featuring a typical bridge deck sectional model, as well as experimental data from two spring-suspended sectional models experiencing vertical vortex-induced vibration (VIV) and torsional post-flutter limit cycle oscillation. The feasibility of identifying amplitude-dependent aerodynamic damping for amplitude range not covered by the displacement signal is examined.

A hierarchical estimation of road grade based on tire force observation

Road grade is important for autonomous vehicles, but it is difficult to measure directly. To address this issue, a hierarchical estimation of road grade is suggested based on the observation of tire forces. First, a 7-degree-of-freedom (DOF) dynamics model, including vehicle longitudinal, lateral, and yaw motions together with wheel rotations, is developed while considering the road grade. Subsequently, a dual-layer road grade estimation strategy is proposed based on an unscented Kalman filter (UKF). The lower-layer UKF estimates the longitudinal and lateral tire forces for road grade observation, and the upper-layer UKF is employed to estimate the road grade by considering the vehicle’s lateral acceleration and yaw rate. Finally, CarSim and MATLAB joint simulations and road tests are performed under different conditions to validate the correctness and effectiveness of the proposed estimation method. The results show that the proposed tire force observation-based estimator exhibits a lower mean absolute error and root mean square error on sloping roads and combined curved and sloping roads, and presents a better overall estimation performance on road grade compared with the widely used kinematics and dynamics model-based estimators.

Acceleration Slip Regulation Control Method for Distributed Electric Drive Vehicles under Icy and Snowy Road Conditions

To achieve a rapid and stable dynamic response of the drive anti-slip system for distributed electric vehicles on low-friction surfaces, this paper proposes an adaptive acceleration slip regulation control strategy based on wheel slip rate. An attachment coefficient fusion estimation algorithm based on an improved singular value decomposition unscented Kalman filter is designed. This algorithm combines Sage–Husa with the unscented Kalman filter for adaptive improvement, allowing for the quick and accurate determination of the road friction coefficient and, subsequently, the optimal slip rate. Additionally, a slip rate control strategy based on dynamic adaptive compensation sliding mode control is designed, which introduces a dynamic weight integral function into the control rate to adaptively adjust the integral effect based on errors, with its stability proven. To verify the performance of the road estimator and slip rate controller, a model is built with vehicle simulation software, and simulations are conducted. The results show that under icy and snowy road conditions, the designed estimator can reduce estimation errors and respond rapidly to sudden changes. Compared to traditional equivalent controllers, the designed controller can effectively reduce chattering, decrease overshoot, and shorten response time. Especially during road transitions, the designed controller demonstrates better dynamic performance and stability.

Non-Line-of-Sight Positioning Method for Ultra-Wideband/Miniature Inertial Measurement Unit Integrated System Based on Extended Kalman Particle Filter

In the field of unmanned aerial vehicle (UAV) control, high-precision navigation algorithms are a research hotspot. To address the problem of poor localization caused by non-line-of-sight (NLOS) errors in ultra-wideband (UWB) systems, an UWB/MIMU integrated navigation method was developed, and a particle filter (PF) algorithm for data fusion was improved upon. The extended Kalman filter (EKF) was used to improve the method of constructing the importance density function (IDF) in the traditional PF, so that the particle sampling process fully considers the real-time measurement information, increases the sampling efficiency, weakens the particle degradation phenomenon, and reduces the UAV positioning error. We compared the positioning accuracy of the proposed extended Kalman particle filter (EKPF) algorithm with that of the EKF and unscented Kalman filter (UKF) algorithm used in traditional UWB/MIMU data fusion through simulation, and the results proved the effectiveness of the proposed algorithm through outdoor experiments. We found that, in NLOS environments, compared with pure UWB positioning, the accuracy of the EKPF algorithm in the X- and Y-directions was increased by 35% and 39%, respectively, and the positioning error in the Z-direction was considerably reduced, which proved the practicability of the proposed algorithm.

Measuring the Magnetic Dipole Moment and Magnetospheric Fluctuations of Accretion-powered Pulsars in the Small Magellanic Cloud with an Unscented Kalman Filter

Many accretion-powered pulsars rotate in magnetocentrifugal disequilibrium, spinning up or down secularly over multiyear intervals. The magnetic dipole moment μ of such systems cannot be inferred uniquely from the time-averaged aperiodic X-ray flux 〈L(t)〉 and pulse period 〈P(t)〉, because the radiative efficiency of the accretion is unknown and degenerate with the mass accretion rate. Here, we circumvent the degeneracy by tracking the fluctuations in the unaveraged time series L(t) and P(t) using an unscented Kalman filter, whereupon μ can be estimated uniquely, up to the uncertainties in the mass, radius, and distance of the star. The analysis is performed on Rossi X-ray Timing Explorer observations for 24 X-ray transients in the Small Magellanic Cloud, which have been monitored regularly for ∼16 yr. As well as independent estimates of μ, the analysis yields time-resolved histories of the mass accretion rate and the Maxwell stress at the disk–magnetosphere boundary for each star, and hence auto- and cross-correlations involving the latter two state variables. The inferred fluctuation statistics convey important information about the complex accretion physics at the disk–magnetosphere boundary.

SOC and SOH state estimation of lithium battery based on ffrls and kalman filter

Abstract In the energy storage System, the Battery Management System (BMS) is responsible for the charge and discharge control and energy balance control of the lithium battery, and the accuracy of lithium battery state estimation is directly affected by the control effect of BMS. In order to ensure the normal operation of lithium batteries, this paper selects the State of Charge (SOC) and State of Health (SOH) of lithium batteries as the research object and accurately estimates the SOC and SOH of lithium batteries as the research goal. The equivalent circuit model based on lithium battery is established, and the identification model parameters are based on the recursive least squares method with forgetting factor. Based on the Thevenin equivalent circuit model, the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are used to estimate the SOC of the battery, respectively. FFRLS and Double Extended Kalman Filter (DEKF) are used to estimate the ohm internal resistance in the equivalent model based on lithium battery, and then the SOH is estimated.

Interacting multiple model-based yaw stability control for distributed drive electric vehicle via adaptive model predictive control algorithm

The vehicle lateral stability control is a challenging problem due to the tire nonlinearity and the immeasurable sideslip angle. Thus, an adaptive model predictive control (AMPC) scheme based on interacting multiple model (IMM) vehicle sideslip angle observer is proposed in this paper. First, the observer is composed of the Extended Kalman filter (EKF) and the Unscented Kalman filter (UKF), which improves the real-time performance as well as the observation accuracy. Then, a multi-objective controller based on adaptive vehicle model prediction is designed using model predictive control algorithm. This controller aims to achieve a balance between the actuation and state constraints. The T-S fuzzy algorithm is used to observe the tire cornering stiffness and design an adaptive vehicle model. By utilizing the appropriate objective function and a quadratic programing solver, the controller output is obtained to achieve vehicle stability control. Finally, the effectiveness of the designed AMPC scheme under various working conditions is verified by Carsim-Simulink joint simulation platform and hardware-in-the-loop (HIL) test.

Subsea pipeline inspection gauges fluctuating friction control under time-varying disturbance

To suppress friction fluctuations during the operation of a pipeline inspection gauge (PIG) and to avoid speed deviations, which may lead to poor detection accuracy and jamming, an adaptive backstepping controller with improved unscented Kalman filter (UKF) was proposed in this paper. Firstly, the friction model was derived, and based on this, the nonlinear dynamic model of PIG was established. Then, an adaptive backstepping controller was designed to estimate the dynamic parameters of the system and stabilize the operating velocity of the PIG by controlling the friction, and adaptive noise based UKF was applied to obtain more accurate feedback estimated signals to deal with the time-varying disturbances in the environment. An active control PIG prototype and a pipeline experimental platform was built, and experiments were conducted under various conditions. Under all conditions, compared to the uncontrolled system, the proposed control strategy can reduce the fluctuation range of friction values by more than 59%, reduce the velocity fluctuation range by more than 88%, and maintain the velocity control error within 4%. Compared to the other controllers, the proposed controller demonstrated better performance in terms of control precision and robustness, verifying the effectiveness and reliability of the proposed controller.

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.