Unscented Kalman Filter Algorithm Research Articles

State Parameter Estimation of Intelligent Vehicles Based on an Adaptive Unscented Kalman Filter

The premise of vehicle intelligent decision making is to obtain vehicle motion state parameters accurately and in real-time. Several state parameters cannot be measured directly by vehicle sensors, so estimation algorithms based on filtering are effective solutions. The most representative algorithm is the Kalman filter, especially the standard unscented Kalman filter (UKF) that has been widely used in vehicle state estimation because of its superiority in dealing with nonlinear filtering problems. However, although the UKF assumes that the noise statistics of the system are known, due to the complex and changeable operating conditions, sensor aging and other factors, these noises vary. In order to realize high-precision vehicle state estimation, a noise-adaptive UKF algorithm is proposed in this article. The maximum a posteriori (MAP) algorithm is used to dynamically update the noise of the vehicle system, and it is embedded into the update step of the UKF to form an adaptive unscented Kalman filter (AUKF). The system will dynamically update the noise when noise statistics are unknown and prevent filter divergence by adjusting the mean and covariance of the estimated noise to improve accuracy. On this basis, the proposed method is verified by the joint simulation of CarSim and Matlab/Simulink, confirming that the AUKF performs better than the standard UKF in estimation accuracy and stability under different degrees of noise disturbance, and the estimation accuracy for the yaw rate, side slip angle and longitudinal velocity is improved by 20.08%, 40.98% and 89.91%, respectively.

Near real-time prediction of thermophysical parameters and time-dependent boundary heat flux of participating medium

The scattering coefficient (κs), absorption coefficient (κa), thermal conductivity (λ) and time-varying boundary heat flux (q(t)) of 1D participating medium are simultaneously determined in near real time. The forward problem of coupled conductive and radiative heat transfer is solved by finite volume method (FVM). The unscented Kalman filter (UKF) and corresponding smoothing technique (UKS) are employed to estimate the q(t), λ, κa and κs. To achieve non-intrusive detection, the measured signals on boundaries of the medium (such as radiative intensity on right boundary and temperatures on boundaries) are employed as inputs in the inverse problem. The effects of measurement error covariance, process error covariance, future measured signals, sampling interval and thermophysical properties on estimation results are thoroughly investigated. The UKS algorithm, when compared to the UKF algorithm, can improve the stability and accuracy of estimated q(t), λ, κa and κs. It is found that the UKS algorithm is efficient and accurate to solve the near real-time prediction of thermophysical parameters and boundary heat flux of participating medium even with measurement errors.

A comparative study of state of charge estimation methods of ultracapacitors for electric vehicles considering temperature characteristics

This paper systematically compares and evaluates three types SOC estimation methods for ultracapacitors (UCs) under different ambient temperatures. Firstly, based on the UC dynamic test data, the key parameters of Thevenin model are identified by genetic algorithm. Next, the polynomial fitting is employed to determine the relationship between parameters and ambient temperatures, and the temperature-varied model is established. At the same time, according to the extended Kalman filter (EKF), adaptive extended Kalman filter (AEKF) and unscented Kalman filter algorithm (UKF), three kinds UC SOC estimation methods are designed, which are suitable for different ambient temperatures. Then, the accuracy, robustness and self-correction ability of these SOC estimation methods are evaluated by using the urban dynamometer driving schedule test data at −10 °C, 10 °C, 25 °C and 40 °C. Finally, the results indicate that the AEKF algorithm is superior to the EKF and UKF, and its average absolute error and root mean square error are within 0.227 % and 0.318 % at different temperatures, respectively. In addition, the proposed temperature-varied model has a wider application.

Dynamic synergistic modelling for cobalt removal process in zinc hydrometallurgy and the research of parameter estimation based on unscented Kalman filter

AbstractThe cobalt removal process with arsenic salt of zinc hydrometallurgy has serious non‐linearity, uncertainty, and mutual coupling. Its accurate dynamic modelling has always been a challenging problem. On the basis of in‐depth analysis of cobalt removal process and reaction mechanism, considering the cascade relationship between the reactors, a dynamic synergistic continuously stirred tank reactor (SCSTR) mechanism model of the cobalt removal process was constructed. Aiming at the unknown parameters in the SCSTR model, the idea of the Kalman filter was introduced, and the unknown parameters were characterized as unknown states; a method of estimating the unknown model parameters was developed using the augmented state equation and the unscented Kalman filter (UKF) algorithm. Simulation results with industrial data of a zinc smeltery showed that the parameter estimation model has high accuracy, and the estimated parameters can be used in the SCSTR model. An intensive simulation analysis of the dynamic characteristics of the complete SCSTR model was carried out to verify the influence of different input disturbances on the output ion concentration of each reactor, which demonstrated the excellent dynamic performance and potential of the model. Ultimately, according to the industrial calculation analysis, the SCSTR model has a guiding effect on the addition of zinc powder in the reactors, overcomes the blindness in the production process, and provides a momentous basis for the optimization control of the cobalt removal process.

A Self-Calibration SOC Estimation Method for Lithium-Ion Battery

Accurate state of charge (SOC) estimation is essential for the battery management system (BMS). In engineering, inappropriate selection of equivalent circuit model (ECM) and model parameters is common for lithium-ion batteries. It can result in systematic errors (i.e., modeling errors) in the state-space equation, thus affecting the SOC estimation accuracy. Aiming at that, this paper proposes a self-calibration method to enhance SOC estimation. In the method, a novel state-space equation containing an unknown systematic error term is developed based on the Thevenin model. A self-calibration unscented Kalman filter (SC-UKF) algorithm is then introduced for recursive SOC estimation. The algorithm can automatically recognize and calibrate the unknown systematic error in the state equation, while also reducing the random noise effect through data fusion with the measurement equation. Test results demonstrate that the method can effectively correct the Thevenin modeling error and improve SOC estimation accuracy. Furthermore, the proposed method is computationally simple and convenient for engineering applications without increasing model complexity.

A Novel UWB Positioning Method Based on a Maximum-Correntropy Unscented Kalman Filter

Aiming at the problem of measurement-information abnormal-error and nonlinear filtering in UWB navigation and positioning, an ultra wideband position algorithm based on a maximum cross-correlation entropy unscented Kalman filter is proposed. The algorithm first obtains the predictive state estimate and the covariance matrix through traceless transformation. Then, it reconstructs observation information using the nonlinear regression method based on the maximum cross-correlation entropy criterion, which enhances the robustness of the unscented Kalman filter algorithm for heavy-tailed noise. The simulation and actual test results show that this algorithm has better positioning accuracy and stability than the traditional filter algorithm in a non Gaussian noise environment. This algorithm effectively solves the problem that UWB indoor location is easily affected by indoor environments, resulting in fixed deviation for that location.

Research on Attitude Detection and Flight Experiment of Coaxial Twin-Rotor UAV.

Aiming at the problem that the single sensor of the coaxial UAV cannot accurately measure attitude information, a pose estimation algorithm based on unscented Kalman filter information fusion is proposed. The kinematics and dynamics characteristics of coaxial folding twin-rotor UAV are studied, and a mathematical model is established. The common attitude estimation methods are analyzed, and the extended Kalman filter algorithm and unscented Kalman filter algorithm are established. In order to complete the test of the prototype of a small coaxial twin-rotor UAV, a test platform for the dynamic performance and attitude angle of the semi-physical flight of the UAV was established. The platform can analyze the mechanical vibration, attitude angle and noise of the aircraft. It can also test and analyze the characteristics of the mechanical vibration and noise produced by the UAV at different rotor speeds. Furthermore, the static and time-varying trends of the pitch angle and yaw angle of the Kalman filter attitude estimation algorithm is further analyzed through static and dynamic experiments. The analysis results show that the attitude estimation of the UKF is better than that of the EKF when the throttle is between 0.2σ and 0.9σ. The error of the algorithm is less than 0.6°. The experiment and analysis provide a reference for the optimization of the control parameters and flight control strategy of the coaxial folding dual-rotor aircraft.

Analysis of the neural mechanism of spectra decrease in MCI by a thalamo-cortical coupled neural mass model

Objective. In order to deeply understand the neurophysiological mechanism of the spectra decrease in mild cognitive impairment (MCI), this paper studies a new neural mass model, which can simulate various intracerebral electrophysiological activities. Approach. In this study, a thalamo-cortical coupled neural mass model (TCC-NMM) is proposed. The influences of the coupling coefficients and other key parameters on the model spectra are simulated. Then, the unscented Kalman filter (UKF) algorithm is used to reversely identify the parameters in the TCC-NMM. Furthermore, the TCC-NMM and UKF are combined to analyze the spectra reduction mechanism of electroencephalogram (EEG) signals in MCI patients. The independent sample t-test is carried out to statistical analyze the differences of the identified parameters between MCI and normal controls. The Pearson correlation analysis is used to analyze the intrinsic relationship between parameters and the scores of the comprehensive competence assessment scale. Main results. The simulation results show that the decreased cortical synaptic connectivity constants C 1 can result in spectra decrease of the TCC-NMM outputs. The real EEG analysis results show that the identified values of parameter C 1 are significant lower in the MCI group than in control group in frontal and occipital areas and the parameters C 1 are positively correlated with the Montreal Cognitive Assessment (MoCA) scores in the two areas. This consistency suggests that the cortical synaptic connectivity loss from pyramidal cells to excitatory interneurons (eIN) may be one of the neural mechanisms of EEG spectra decrease in MCI. Significance. (a) In this study, a new mathematical model TCCNMM based on anatomy and neurophysiology is proposed. (b) All key parameters in TCC-NMM are studied in detail through the forward and reverse analysis and the influence of these parameters on the output spectra of the model is pointed out. (c) The possible neural mechanism of the decreased spectra in MCI patients is pointed out by the joint analysis of simulation in forward with TCC-NMM and analysis of the actual EEG signals in reverse with UKF identification algorithm. (d) We find that the identified parameter C1 of MCI patients is significantly lower than that of the control group, which is consistent with the simulation analysis of TCC-NMM. So, we suggest that the decreased MCI alpha power spectrum is likely related to the cortical synaptic connection loss from pyramidal cells to eIN.

State of charge estimation under different temperatures using unscented Kalman filter algorithm based on fractional-order model with multi-innovation

In this study, a battery test platform is built to study and analyze the battery model. A fractional-order model (FOM) of battery is developed by combining the second-order equivalent circuit model with fractional calculus theory. By combining the multi-innovation with the unscented Kalman filter algorithm based on FOM, a fractional-order multi innovation unscented Kalman filter algorithm is proposed. Under different temperatures and dynamic conditions, the tracking of terminal voltage and the estimation results of SOC using the proposed algorithm are compared and analyzed. In order to verify the accuracy and robustness of the proposed algorithm, the tracking effect of the terminal voltage and the estimation results of SOC under different initial SOC values are investigated. The experimental results indicate that the FOM is more accurate than the integer-order model in reflecting the battery characteristics. Under different temperatures, dynamic conditions, and initial SOC values, the values of mean absolute error (MAE) and root mean squared error (RMSE) of the proposed algorithm are the lowest, which verifies the effectiveness of the proposed algorithm. The maximum values of MAE and RMSE of SOC estimation results of the proposed algorithm are 1.04 % and 0.9122 %, respectively, indicating that the proposed algorithm has high accuracy and good robustness.

A joint state-of-health and state-of-energy estimation method for lithium-ion batteries through combining the forgetting factor recursive least squares and unscented Kalman filter

The state of energy (SOE) estimation of lithium-ion batteries is the basis of the mileage prediction of electric vehicles. However, its accurate estimation is affected by various factors such as the state of health (SOH) and temperature. In this study, a joint SOH-SOE estimation method combining the forgetting factor recursive least squares (FFRLS) and the unscented Kalman filter algorithm is proposed to improve the SOE estimation accuracy under complex and dynamic working conditions. The FFRLS algorithm is used to identify and update the battery model parameters and the open circuit voltage curves online, and the ordinary least squares algorithm is used to update battery capacity. The experiments show that the proposed algorithm can achieve satisfactory estimation accuracy under different battery aging degrees and temperatures. SOH and SOE estimation errors are within 4 % and 3 %, respectively. Even at a low temperature of −10 °C, the SOE estimation error is less than 4 %.

Double layer weighted unscented Kalman underwater target tracking algorithm based on sound speed profile

For target tracking in underwater wireless sensor networks, the inhomogeneous medium refracts the sound waves and bends their propagation path, which reduces the measurement accuracy of sensor nodes. In addition, since the information measured by nodes are different, modification effects of nodes to the predicted states of tracking algorithm are variable. Based on the problems, this paper constructs Fisher information matrix to weight target state information contained in nodes using acoustic time-of-flight as the measurements. With the information-weighted measurements, we propose a double layer weighted unscented Kalman tracking algorithm based on sound speed profile (SSP_DLWUKF). SSP_DLWUKF consists of outer layer unscented Kalman filter (UKF) algorithm and inner layer UKF algorithm. The inner layer UKF is used to predict target state, update the weights of the outer layer particles and weight the measurements. The outer layer UKF is utilized to modify target states predicted by inner layer UKF. The simulation results show that the mean tracking error of SSP_DLWUKF is about 55.81% of that of double layer unscented Kalman filter (DLUKF) algorithm, 71.29% that of UKF and 50.58% that of particle filter (PF). Simulation and experiment demonstrate that SSP_DLWUKF can utilize measurements to effectively reduce tracking errors and improve tracking accuracy.

Robust Initial Alignment Based on Unscented Information Kalman Filter

The velocity of the odometer (OD) and Doppler velocity log (DVL) is easily contaminated by non-Gaussian noise, and the prior information of the state vector is usually hard to estimate accuracy enough, which will lead to the performance of alignment to decline or even divergent. Considering the error characteristic model has very significant nonlinear characteristics, a robust unscented information Kalman filter (RUIKF) algorithm for dynamic initial alignment is proposed in this article to suppress the influence of interference noise. The RUIKF algorithm first calculates the Mahalanobis distance (MD) between observation and the innovation of observation, and an amplification factor is designed to modify the estimation of the measurement noise covariance matrix and then take the modified measurement noise covariance matrix to update the measurement. The state error is estimated by the RUIKF to modify the strapdown inertial navigation system (SINS) navigation solution. Initial alignment experiments are carried out by the RUIKF and unscented information Kalman filter (UIKF) algorithm, respectively, under the conditions of outliers and mixed Gaussian distribution noise. The results show that the RUIKF can suppress the effect of outliers and non-Gaussian noise when the velocity of the OD (or DVL) is contaminated. The experiment results also verify the feasibility and effectiveness of the RUIKF algorithm on the SINS/DVL/OD integrated dynamic initial alignment.

State of Charge Estimation of Lithium-Ion Battery Using Robust Kernel Fuzzy Model and Multi-Innovation UKF Algorithm Under Noise

Accurate and robust state of charge (SOC) estimation of lithium-ion batteries is very important to prolong battery life and prevent catastrophic failures. However, the accuracy of SOC estimation is seriously affected by unknown noise, uncertain interference and temperature. In this article, a novel model fusion method is presented to achieve precise SOC estimation in the case of non-Gaussian noise and outliers. A state-space model of battery system is first developed to conduct SOC estimate. Then, a novel robust kernel Takagi–Sugeno fuzzy method to minimize the mean and variance of model error is developed to characterize the electrical performance of battery. This modeling strategy uses local nonlinear modeling mechanism, which the nonlinear relationship between data can be well represented, thus it can obtain a superior modeling performance. Finally, a multi-innovation unscented Kalman filter (UKF) algorithm considering the historical state information is designed to incorporate with the robust fuzzy model to filter out the noise in the observation and update the SOC estimation. Additional stability analysis shows the convergence of the proposed multi-innovation UKF algorithm. Experiments and verifications show that the presented estimation architecture is effective and has better modeling ability compared with several common methods.

A method for state of charge and state of health estimation of lithium-ion battery based on adaptive unscented Kalman filter

The state of lithium-ion battery is a key indicator for the battery management system (BMS) of electric vehicles (EVs). State of charge (SOC) and state of health (SOH) of the power cell are the main parameters of the BMS during operation. In this paper, an adaptive unscented Kalman filter algorithm (AUKF) is presented for the joint estimation of SOC and SOH of lithium-ion batteries. Firstly, this paper develops a 2-RC equivalent circuit model and identifies the model parameters using recursive least squares algorithm with forgetting factor. Then, the SOC and SOH of the battery are estimated simultaneously by AUKF. Finally, the accuracy of the proposed method is verified under different operating conditions. The experiment results show that the maximum SOC estimation error is under 0.08% by the proposed method. Compared with the unscented Kalman filtering (UKF), it is shown that the proposed method is more accurate and reliable. An effective method is provided for state estimation for battery management system.

Co-Estimation of State-of-Charge and State-of-Health for Lithium-Ion Batteries Considering Temperature and Ageing

State-of-charge (SOC) estimation of lithium-ion batteries (LIBs) is the basis of other state estimations. However, its accuracy can be affected by many factors, such as temperature and ageing. To handle this bottleneck issue, we here propose a joint SOC-SOH estimation method considering the influence of the temperature. It combines the Forgetting Factor Recursive Least Squares (FFRLS) algorithm, Total Least Squares (TLS) algorithm, and Unscented Kalman Filter (UKF) algorithm. First, the FFRLS algorithm is used to identify and update the parameters of the equivalent circuit model in real time under different battery ageing degrees. Then, the TLS algorithm is used to estimate the battery SOH to improve the prior estimation accuracy of SOC. Next, the SOC is calculated by the UKF algorithm, and finally, a more accurate SOH can be obtained according to the UKF-based SOC trajectory. The battery-in-the-loop experiments are utilized to verify the proposed algorithm. For the cases of temperature change up to 35 °C and capacity decay up to 10%, our joint estimator can achieve ultra-low errors, bounded by 2%, respectively, for SOH and SOC. The proposed method paves the way for the advancement of battery use in applications, such as electric vehicles and microgrid applications.

State of charge estimation of lithium‐ion battery based on extended Kalman filter and unscented Kalman filter techniques

AbstractLithium‐ion batteries (LIBs) are currently the most widely used energy storage technologies in electric vehicles (EVs) due to their higher power density, greater energy density, longer life, fast charging capabilities, and low discharge rate. The brain of rechargeable batteries is referred to be the battery management system (BMS). The operation of the battery is monitored & regulated by an electronic system called BMS. Most significantly, it prevents the battery from exceeding its safety limits. One of the important parameters of BMS is the state of charge (SOC); it determines the battery's remaining capacity of accessible stored energy, battery lifespan, and cell balancing. As a result, an accurate SOC calculation is essential for BMS, and it is used for safer operations that avoid overcharging and discharging for the optimum battery life. The primary ambition of this article is to find an accurate and robust SOC estimation based on extended Kalman filter (EKF) and unscented Kalman filter (UKF) techniques. RMS error, average error, minimum error, and maximum error are used to compare the EKF method and UKF method. Two resistor‐capacitor (2RC) equivalent circuit model has been considered for the dynamic performance of the battery. The waveforms are displayed, and errors are simulated for SOC estimate using the EKF and UKF algorithms, taking the same initial SOC into consideration at a time. The UKF algorithm outperforms the EKF approach in terms of dynamic results when comparing the two methods.

Joint state estimation of power battery based on UKPF

Accurate estimation of power battery state is an important function in battery management system. In order to accurately estimate power battery SOC and SOH and improve the performance of long-term estimation of battery SOC, a joint estimation method of power battery state based on UKPF was proposed in this paper. The particle filter algorithm was added on the basis of the unscented Kalman filter algorithm, and the particle filter algorithm was optimized by the unscented Kalman filter algorithm, which improved the particle degradation problem and improved the accuracy of battery state estimation. Based on the time scale transformation, the battery state estimation was completed, and the SOC and SOH were estimated at short and long time scales, respectively. The SOH estimation results were updated to the model parameters for SOC estimation. The results show that the joint estimation method can accurately estimate battery SOC and SOH with an error of less than 3%.

A comparative study of the unscented Kalman filter and particle filter estimation methods for the measurement of the road adhesion coefficient

Abstract. The measurement of the road adhesion coefficient is of great significance for the vehicle active safety control system and is one of the key technologies for future autonomous driving. With a focus on the problems of interference uncertainty and system nonlinearity in the estimation of the road adhesion coefficient, this work adopts a vehicle model with 7 degrees of freedom (7-DOF) and the Dugoff tire model and uses these models to estimate the road adhesion coefficient in real time based on the particle filter (PF) algorithm. The estimations using the PF algorithm are verified by selecting typical working conditions, and they are compared with estimations using the unscented Kalman filter (UKF) algorithm. Simulation results show that the road adhesion coefficient estimator error based on the UKF algorithm is less than 7 %, whereas the road adhesion coefficient estimator error based on the PF algorithm is less than 0.1 %. Thus, compared with the UKF algorithm, the PF algorithm has a higher accuracy and control effect with respect to estimating the road adhesion coefficient under different road conditions. In order to verify the robustness of the road adhesion coefficient estimator, an automobile test platform based on a four-wheel-hub-motor car is built. According to the experimental results, the estimator based on the PF algorithm can realize the road surface identification with an error of less than 1 %, which verifies the feasibility and effectiveness of the algorithm with respect to estimating the road adhesion coefficient and shows good robustness.

A Novel Adaptive Back Propagation Neural Network-Unscented Kalman Filtering Algorithm for Accurate Lithium-Ion Battery State of Charge Estimation

Accurate State of Charge (SOC) estimation for lithium-ion batteries has great significance with respect to the correct decision-making and safety control. In this research, an improved second-order-polarization equivalent circuit (SO-PEC) modelling method is proposed. In the process of estimating the SOC, a joint estimation algorithm, the Adaptive Back Propagation Neural Network and Unscented Kalman Filtering algorithm (ABP-UKF), is proposed. It combines the advantages of the robust learning rate in the Back Propagation (BP) neural network and the linearization error reduction in the Unscented Kalman Filtering (UKF) algorithm. In the BP neural network part, the self-adjustment of the learning factor accompanies the whole estimation process, and the improvement of the self-adjustment algorithm corrects the shortcomings of the UKF algorithm. In the verification part, the model is validated using a segmented double-exponential fit. Using the Ampere-hour integration method as the reference value, the estimation results of the UKF algorithm and the Back Propagation Neural Network and Unscented Kalman Filtering (BP-UKF) algorithm are compared, and the estimation accuracy of the proposed method is improved by 1.29% under the Hybrid Pulse Power Characterization (HPPC) working conditions, 1.28% under the Beijing Bus Dynamic Stress Test (BBDST) working conditions, and 2.24% under the Dynamic Stress Test (DST) working conditions. The proposed ABP-UKF algorithm has good results in estimating the SOC of lithium-ion batteries and will play an important role in the high-precision energy management process.

Adaptive particle filter for state estimation with application to non‐linear system

Particle filtering (PF) has certain application value, but the disadvantage is that there is a phenomenon of particle degradation. In order to reduce the impact of this problem, this paper presents a new adaptive PF approach to improve the estimate accuracy. From the perspective of selecting an appropriate important density functions, in this filter, the particles are first updated using the Spherical Simplex Unscented Kalman Filter algorithm, and then the particles are updated using the Adaptive Extended Kalman filter algorithm. Simultaneously, from the perspective of improving the resampling method, a new resampling technique based on the random resampling method has been designed and fused to this filter. The comparison and analysis of two simulation schemes have been conducted to assess the performance of the designed filtering algorithm. The simulation results show the effectiveness of the proposed approach.