Adaptive Unscented Kalman Filter Research Articles

Innovation Adaptive UKF Train Location Method Based on Kinematic Constraints

To address the issue of reduced positioning accuracy caused by satellite signal interruptions when trains pass through long tunnels, a novel train positioning method based on an innovative adaptive unscented Kalman filter (UKF) under kinematic constraints is proposed. This method aims to improve the accuracy of the location of trains during operation. By considering the dynamic characteristics of the train, a dynamic kinematic-constrained inertial navigation system (INS)/odometer (ODO) combination positioning system is established. This system utilizes kinematic constraints to correct the accumulated errors of the INS. Additionally, the algorithm incorporates real-time estimation of the measurement noise covariance using innovation sequences. The updated adaptive estimation algorithm is applied within the UKF framework for nonlinear filtering, forming the innovative adaptive UKF algorithm. At each time step, the difference between the ODO sensor data and the INS output is used as the measurement input for the innovative adaptive UKF algorithm, enabling global estimation. This process ultimately yields the actual positioning result for the train. Simulation results demonstrate that the innovative adaptive UKF train positioning method, incorporating kinematic constraints, effectively mitigates the impact of satellite signal interruptions. Compared with the traditional INS/ODO positioning method, the innovative adaptive UKF method reduces position errors by 34.35% and speed errors by 36.33%. Overall, this method enhances navigation accuracy, minimizes train positioning errors, and meets the requirements of modern train positioning systems.

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

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

Application of IMU/GPS Integrated Navigation System Based on Adaptive Unscented Kalman Filter Algorithm in 3D Positioning of Forest Rescue Personnel.

Utilizing reliable and accurate positioning and navigation systems is crucial for saving the lives of rescue personnel and accelerating rescue operations. However, Global Navigation Satellite Systems (GNSSs), such as GPS, may not provide stable signals in dense forests. Therefore, integrating multiple sensors like GPS and Inertial Measurement Units (IMUs) becomes essential to enhance the availability and accuracy of positioning systems. To accurately estimate rescuers' positions, this paper employs the Adaptive Unscented Kalman Filter (AUKF) algorithm with measurement noise variance matrix adaptation, integrating IMU and GPS data alongside barometric altitude measurements for precise three-dimensional positioning in complex environments. The AUKF enhances estimation robustness through the adaptive adjustment of the measurement noise variance matrix, particularly excelling when GPS signals are interrupted. This study conducted tests on two-dimensional and three-dimensional road scenarios in forest environments, confirming that the AUKF-algorithm-based integrated navigation system outperforms the traditional Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Adaptive Extended Kalman Filter (AEKF) in emergency rescue applications. The tests further evaluated the system's navigation performance on rugged roads and during GPS signal interruptions. The results demonstrate that the system achieves higher positioning accuracy on rugged forest roads, notably reducing errors by 18.32% in the north direction, 8.51% in the up direction, and 3.85% in the east direction compared to the EKF. Furthermore, the system exhibits good adaptability during GPS signal interruptions, ensuring continuous and accurate personnel positioning during rescue operations.

A new online SOC estimation method using broad learning system and adaptive unscented Kalman filter algorithm

The accurate estimation of lithium batteries’ state of charge (SOC) is important for extending battery life and preventing accidents. To improve the battery model’s adaptability to variations in actual operating conditions, this paper proposes a new hybrid SOC estimation method. The battery model is first built based on the broad learning system (BLS) to simulate the battery’s voltage characteristics. Subsequently, the adaptive unscented Kalman filter algorithm is applied for SOC estimation. We introduce the Bernstein inequality (BI) to guide the BLS model’s online update process. With the BI method, the redundant incremental data is not used for battery model updates, which improves the model’s online learning efficiency. Finally, dynamic test operation data is collected from different temperatures to validate the proposed SOC estimation algorithm. Experimental results manifest that the SOC estimation error can be limited to 0.51 %. In addition, the proposed method has satisfactory training and online learning time consumption.

Online state of charge estimation of LiFePO4 battery based on EKF-AUKF algorithm with reference compensation for estimation results

The state of charge(SOC) is an important index in Battery Management System(BMS) for smart grids and electric vehicles, whose accuracy is affected by model and sensor errors. In this paper, an online SOC estimation method based on EKF-AUKF algorithm with reference compensation for estimation results is proposed. Firstly, a joint estimation method based on extended Kalman filter(EKF) and adaptive unscented Kalman filter(AUKF) algorithm is adopted to estimate SOC under Beijing bus dynamic stress test(BBDST) condition. The result shows that the estimation error is within 2 %. Secondly, the characteristics of EKF-AUKF algorithm under voltage and current sampling errors are analyzed over the whole SOC range. The results indicate that voltage measurement error increases SOC estimation error. Then, an online reference is built by calculating the sum of the estimation result of ampere-hour counting(AHC) method and constant deviation, and then the difference between the estimation result of EKF-AUKF algorithm and online reference can be obtained. The absolute value of the difference is used to compare with limit deviation value and compensate the SOC of EKF-AUKF method by different compensation coefficients. Finally, the effectiveness of the proposed method is verified under different operating conditions. The experimental results show that the proposed method can greatly improve the SOC estimation accuracy under large voltage error.

Optimized Longitudinal and Lateral Control Strategy of Intelligent Vehicles Based on Adaptive Sliding Mode Control

To improve the tracking accuracy and robustness of the path-tracking control model for intelligent vehicles under longitudinal and lateral coupling constraints, this paper utilizes the Kalman filter algorithm to design a longitudinal and lateral coordinated control (LLCC) strategy optimized by adaptive sliding mode control (ASMC). First, a three-degree-of-freedom (3-DOF) vehicle dynamics model was established. Next, under the fuzzy adaptive Unscented Kalman filter (UKF) theory, the vehicle state parameter estimation and road adhesion coefficient (RAC) observer were designed to estimate vehicle speed (VS), yaw rate (YR), sideslip angle (SA), and RAC. Then, a layered control concept was adopted to design the path-tracking controller, with a target VS, YR, and SA as control objectives. An upper-level adaptive sliding mode controller was designed using RBF neural networks, while a lower-level tire force distribution controller was designed using distributed sequential quadratic programming (DSQP) to obtain an optimal tire driving force. Finally, the control strategy was validated using Carsim and Matlab/Simulink software under different road adhesion coefficients and speeds. The findings indicate that the optimized control strategy is capable of adaptively adjusting control parameters to accommodate various complex conditions, enhancing the tracking precision and robustness of vehicles even further.

Design and implementation of an adaptive unscented Kalman filter with interval Type-3 fuzzy set for an attitude and heading reference system considering gyroscope bias

Low-cost microelectromechanical sensors used in attitude and heading reference systems (AHRS) suffer from unstable on–off biases, scaling errors, and nonlinearities that lead to an increase of navigation errors over time. To damp these errors and uncertainties from ultimate attitude and heading angles, the bias term of gyroscopes is augemented in under estimation state vector for high frequency feedback compensation. In this paper, an adaptive estimation algorithm to combine the strong tracking filter (STF) and interval type-3 fuzzy set (IT3FS) with an unscented Kalman filter (UKF) is proposed to deal with the large uncertainties in the microelectromechanical AHRS. The UKF, involving strong capability of dealing with nonlinearity, is limited by large instable bias uncertainty. By combining the STF to adaptively tuning of the UKF gain matrix and the IT3FS to determine the STF fading factor as well, the new IT3FS-STUKF algorithm is developed for high estimation performance against the significant uncertainties. To validate the proposed IT3FS-STUKF, real experiments are conducted with ground vehicles in urban areas, which show an improved accuracy compared to the extended Kalman filter (EKF) at reasonable computational burden.

Online numerical simulation method based on adaptive unscented Kalman filter for shear wall structures

Hybrid test method is an effective approach to evaluate the seismic performance of engineering structures. Particularly, online numerical simulation method (ONSM) based on unscented Kalman filter (UKF) model updating significantly improves the accuracy of the hybrid test results. However, the sensitivity of UKF to the initial values of the state vector, state covariance, and observation noise covariance may lead to the distortion of hybrid test results. To address these issues, one novel ONSM based on adaptive UKF (ONSM-AUKF) is proposed in this paper. The AUKF algorithm incorporates an adaptive variance module to maintain equilibrium. This not only reduces the sensitivity of UKF to the initial parameter settings, prevents filter divergence, but also enhances the accuracy and stability of estimation. The proposed ONSM-AUKF accurately identifies the constitutive model parameters by utilizing measured data from specimens through the AUKF algorithm, which improves the accuracy and the stability of parameter estimation. The simulation results indicate that AUKF algorithm has the capability to decrease the sensitivity of initial parameter settings, thus enhancing the stability and robustness of parameter estimation in comparison to the UKF algorithm. The experimental results validate the feasibility and effectiveness of the proposed ONSM-AUKF, as well as the advantages of the ONSM-AUKF over the ONSM-UKF. The results indicate that the proposed ONSM-AUKF may have broad application prospect in evaluating the seismic performance of various of complex engineering structures.

Research on Vehicle Stability Control Based on a Union Disturbance Observer and Improved Adaptive Unscented Kalman Filter

This paper considers external disturbances imposed on vehicle systems. Based on a vehicle dynamics model of the vehicle with three degrees of freedom (3-DOFs), a union disturbance observer (UDO) composed of a nonlinear disturbance observer (NDO) and an extended state observer (ESO) was designed to obtain external disturbances and unmodeled items. Meanwhile, an improved adaptive unscented Kalman filter (iAUKF) with anti-disturbance and anti-noise properties is proposed, based on the UDO and the unscented Kalman filter (UKF) method, to evaluate the sideslip angle of vehicle systems. Finally, a vehicle yaw stability controller was designed based on UDO and the global fast terminal sliding mode control (GFTSMC) method. The results of co-simulation demonstrated that the proposed UDO was effectively able to observe external disturbances and unmodeled items. The proposed iAUKF, which considers external disturbances, not only achieves adaptive updating and adjustment of filtering parameters under different sensor noise intensities but can also resist external disturbances, improving the estimation accuracy and robustness of the UKF. In the anti-disturbance performance test, the maximum estimation error of the sideslip angle of the iAUKF under the three working conditions was less than 0.1°, 0.02°, and 0.5°, respectively. Based on the UDO and the GFTSMC, a vehicle yaw stability controller is described, which improves the accuracy of control and the robustness of the vehicle’s stability control system and greatly strengthens the driving safety of the vehicle.

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.

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.

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 %.

A Robust Monocular and Binocular Visual Ranging Fusion Method Based on an Adaptive UKF.

Visual ranging technology holds great promise in various fields such as unmanned driving and robot navigation. However, complex dynamic environments pose significant challenges to its accuracy and robustness. Existing monocular visual ranging methods are susceptible to scale uncertainty, while binocular visual ranging is sensitive to changes in lighting and texture. To overcome the limitations of single visual ranging, this paper proposes a fusion method for monocular and binocular visual ranging based on an adaptive Unscented Kalman Filter (AUKF). The proposed method first utilizes a monocular camera to estimate the initial distance based on the pixel size, and then employs the triangulation principle with a binocular camera to obtain accurate depth. Building upon this foundation, a probabilistic fusion framework is constructed to dynamically fuse monocular and binocular ranging using the AUKF. The AUKF employs nonlinear recursive filtering to estimate the optimal distance and its uncertainty, and introduces an adaptive noise-adjustment mechanism to dynamically update the observation noise based on fusion residuals, thus suppressing outlier interference. Additionally, an adaptive fusion strategy based on depth hypothesis propagation is designed to autonomously adjust the noise prior of the AUKF by combining current environmental features and historical measurement information, further enhancing the algorithm's adaptability to complex scenes. To validate the effectiveness of the proposed method, comprehensive evaluations were conducted on large-scale public datasets such as KITTI and complex scene data collected in real-world scenarios. The quantitative results demonstrate that the fusion method significantly improves the overall accuracy and stability of visual ranging, reducing the average relative error within an 8 m range by 43.1% and 40.9% compared to monocular and binocular ranging, respectively. Compared to traditional methods, the proposed method significantly enhances ranging accuracy and exhibits stronger robustness against factors such as lighting changes and dynamic targets. The sensitivity analysis further confirmed the effectiveness of the AUKF framework and adaptive noise strategy. In summary, the proposed fusion method effectively combines the advantages of monocular and binocular vision, significantly expanding the application range of visual ranging technology in intelligent driving, robotics, and other fields while ensuring accuracy, robustness, and real-time performance.

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.

Robust adaptive non‐linear alignment algorithm for SINS/DVL integrated navigation system based on variational Bayesian

AbstractThe problem of dynamic attitude alignment for strapdown inertial navigation system (SINS) and Doppler velocity log (DVL) integrated navigation has become a research hotspot. Underwater complex environment makes DVL output vulnerable to non‐Gaussian noise pollution, which makes it difficult to converge the SINS misalignment angle to within 1° based on analytical coarse alignment. This is to say, the performance of SINS fine alignment via Kalman filter will be degraded because the model of initial alignment exhibits non‐linearity. The inaccurate and/or unknown prior information of measurement noise statistical characteristics will also degrade the filtering performance. To ensure the SINS/DVL alignment accuracy under non‐linear, non‐Gaussian and uncertain conditions, this paper proposed a robust adaptive unscented Kalman filter (UKF) based on Variational Bayesian (VB) method (VBRAUKF). The proposed VBRAUKF improves the adaptability and robustness of UKF from the following two main aspects. Firstly, an adaptive estimation strategy for the measurement noise covariance is designed based on the VB algorithm, which can restrain the effect of inaccurate observation model and improve the adaptive ability of the filtering method. Secondly, an expansion factor is designed based on Mahalanobis distance algorithm, which can restrain the effect of non‐Gaussian noise and improve the robustness of the filtering method. The experimental results for the problem of the SINS/DVL dynamic alignment under mixed Gaussian noise and/or outlier conditions demonstrate the superiority of the proposed VBRAUKF over the traditional ones.

Hybrid State Estimation: Integrating Physics-Informed Neural Networks with Adaptive UKF for Dynamic Systems

In this paper, we present a novel approach to state estimation in dynamic systems by combining Physics-Informed Neural Networks (PINNs) with an adaptive Unscented Kalman Filter (UKF). Recognizing the limitations of traditional state estimation methods, we refine the PINN architecture with hybrid loss functions and Monte Carlo Dropout for enhanced uncertainty estimation. The Unscented Kalman Filter is augmented with an adaptive noise covariance mechanism and incorporates model parameters into the state vector to improve adaptability. We further validate this hybrid framework by integrating the enhanced PINN with the UKF for a seamless state prediction pipeline, demonstrating significant improvements in accuracy and robustness. Our experimental results show a marked enhancement in state estimation fidelity for both position and velocity tracking, supported by uncertainty quantification via Bayesian inference and Monte Carlo Dropout. We further extend the simulation and present evaluations on a double pendulum system and state estimation on a quadcopter drone. This comprehensive solution is poised to advance the state-of-the-art in dynamic system estimation, providing unparalleled performance across control theory, machine learning, and numerical optimization domains.

Multi-interest adaptive unscented Kalman filter based on improved matrix decomposition methods for lithium-ion battery state of charge estimation

Accurately predicting the state of charge (SOC) is crucial to improving Li-ion battery performance. However, available model-based estimation approaches still face challenges in handling model uncertainty and measurement noise effects on parameter identification. Besides, the widely used unscented Kalman filter (UKF) algorithm has limitations in electric vehicles as it requires the error covariance matrix to maintain positive definiteness, limiting its applicability under certain conditions. This study introduces the bias-compensated forgetting factor recursive least squares (BCFFRLS) method for parameter estimation within the second-order RC equivalent circuit model specific to the INR18650-20R battery. Furthermore, we propose a novel algorithm named the optimization multi-interest adaptive unscented Kalman filter (O-MIAUKF). This algorithm is designed to address stability and robustness issues with traditional UKF encounters in dynamic environments. Experimental validation demonstrates that the O-MIAUKF algorithm excels in maintaining strong stability and robustness in various working conditions, accurately estimating SOC even with a non-positive covariance matrix. The SOC estimation error remains stable at 0.8 %, which is lower than that of the current Extended Kalman Filter (EKF), UKF, and Dual Extended Kalman Filter (DEKF).

State of health estimation of lithium-ion battery using dual adaptive unscented Kalman filter and Coulomb counting approach

Several charging and discharging processes of lithium-ion batteries (LIBs) can lead to a battery fading and degradation effect. This may cause sudden faults, leakages, and explosions. As a result, it is highly important to estimate the state of health (SoH) of the battery to avoid any battery problems. This article proposes a novel hybrid dual adaptive unscented Kalman filter (DAUKF)-Coulomb counting approach (CCA) to efficiently state of charge (SoC) and SoH estimation of LIBs. The Gazelle optimization algorithm (GOA) is utilized in identifying LIB model parameters under various SoC conditions. It is used for minimizing the integral squared error between measured and estimated battery voltages. The battery model includes loading, fading, and various dynamic conditions. The GOA-based model has better results than other models by >8 %. The proposed hybrid DAUKF-CCA is compared with the dual adaptive extended Kalman filter (DAEKF)-CCA and other multiple algorithms. The fitness function consists of integral squared error between estimated and measured SoC of LIBs. The simulation results of the DAUKF-CCA are verified by a comparison with the measurement results performed using commercial Panasonic LiBs. The SoC results using the DAUKF-CCA are very close to the measurement results and the error is <1 %. The proposed DAUKF-CCA can ensure that the SoC and SoH estimation of LIBs is efficiently achieved.

Enhanced extended-input LSTM with an adaptive singular value decomposition UKF for LIB SOC estimation using full-cycle current rate and temperature data

Accurately estimating the state of charge (SOC) of lithium-ion batteries by the battery management system (BMS) is crucial for efficient energy management and power distribution control in electric vehicles (EVs). By far, data-driven methods have been extensively used in estimating the SOC of lithium-ion batteries to efficiently operate EVs with limited resources. However, the learning ability of these methods needs further enhancement. Therefore, this paper aims to analyze the SOC performance of an extended-input long short-term memory (ELSTM) model. The inputs of the ELSTM are improved with identified battery parameters based on an adaptive multi-timescale identification method with frequency difference decomposition. Second, an adaptive singular value decomposition-transformed unscented Kalman filter (ASVDUKF) is proposed to integrate all unknown variables and guarantee the positive definiteness of the error covariance matrix into a vector to form a multi-fusion model that robustly outputs the denoised and optimized SOCs based on the estimations of the ELSTM. The SOC results demonstrate that the ELSTM outperforms the LSTM, which uses conventional input data. Following that, the ELSTM-ASVDUKF model ensures high accuracy and stability with optimal mean absolute error, root-mean-square error, and mean absolute percentage error of 0.0939%, 0.1074%, and 0.1257%, respectively. The proposed model is validated using various full-cycle current rate and temperature data from two different batteries, establishing it as a promising solution for future development.

A fractional order model of auxiliary power batteries suitable for hydrogen fuel cell hybrid systems heavy-duty trucks

Aiming at the problem that the existing battery fractional order model is not suitable for the auxiliary power battery of hydrogen fuel cell heavy-duty trucks, considering the characteristics of multiple influencing factors and nonlinearity in actual driving processes, a fractional order model of auxiliary power batteries is proposed based on the hydrogen fuel cell heavy-duty trucks model and the batteries' fractional order model. Then, to solve the charge state estimation error increases due to the high frequency and large rate charging and discharging, H∞ filter is introduced into the adaptive unscented Kalman filter to optimize the charge state estimation in the model. Additionally, the model's parameters are identified using the evolutionary algorithm and the recursive least squares technique based on the forgetting factor. Finally, the model is verified by dynamic conditions. The results show that compared with the auxiliary power batteries' fractional order model, the optimized model reduces the MAE by 0.08% and the RMSE by 0.22% when estimating voltage, and reduces the MAE by 0.25% and the RMSE by 2.66% when estimating SOC. Therefore, the optimized fractional order model of auxiliary power battery has higher accuracy and applicability.