Improve Estimation Accuracy Research Articles

Robust-stein estimator for overcoming outliers and multicollinearity

Linear regression models with correlated regressors can negatively impact the performance of ordinary least squares estimators. The Stein and ridge estimators have been proposed as alternative techniques to improve estimation accuracy. However, both methods are non-robust to outliers. In previous studies, the M-estimator has been used in combination with the ridge estimator to address both correlated regressors and outliers. In this paper, we introduce the robust Stein estimator to address both issues simultaneously. Our simulation and application results demonstrate that the proposed technique performs favorably compared to existing methods.

Doubly selective channel estimation and equalization based on ICI/ISI mitigation for OQAM-FBMC systems

Over a doubly selective channel, broadband transmission systems face challenges in channel estimation and equalization. High mobility causes inter-carrier interference (ICI), while multipath transmission induces inter-symbol interference (ISI). In this paper, we present a mitigation method of ICI/ISI for the offset quadrature amplitude-modulated filter bank multi-carrier (OQAM-FBMC) system. It features low inherent imaginary interference (IMI) sensitivity and high efficiency. Specifically, a pilot indices optimization algorithm and a sparse adaptive orthogonal subspace pursuit (SAOSP) algorithm are presented based on the 2-D channel modeling scheme. The guard pilots are first added to mitigate the effect of ICI. Then the index optimization and SAOSP algorithms are applied to achieve a high-accuracy estimation of sparse channel coefficients. In addition, a threshold judgment suboptimal minimum mean square error (MMSE) equalization method is presented based on the variability of the interference power. The method uses normalized interference power thresholds to estimate the ISI dimension and reduce the equalization data, thus mitigating the effect of ISI and achieving efficient equalization. To verify the above methods, single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) models are built. Simulation results indicate a 3-5 dB improvement in channel estimation accuracy. The suboptimal MMSE equalization results are close to the optimal MMSE with about four orders of magnitude reduction in complexity.

Robust Estimation of Vehicle Dynamic State Using a Novel Second-Order Fault-Tolerant Extended Kalman Filter

<div>The vehicle dynamic state is essential for stability control and decision-making of intelligent vehicles. However, these states cannot usually be measured directly and need to be obtained indirectly using additional estimation algorithms. Unfortunately, most of the existing estimation methods ignore the effect of data loss on estimation accuracy. Furthermore, high-order filters have been proven that can significantly improve estimation performance. Therefore, a second-order fault-tolerant extended Kalman filter (SOFTEKF) is designed to predict the vehicle state in the case of data loss. The loss of sensor data is described by a random discrete distribution. Then, an estimator of minimum estimation error covariance is derived based on the extended Kalman filter (EKF) framework. Finally, experimental tests demonstrate that the SOFTEKF can reduce the effect of data loss and improve estimation accuracy by at least 10.6% compared to the traditional EKF and fault-tolerant EKF.</div>

Performance models of data parallel DAG workflows for large scale data analytics

Directed Acyclic Graph (DAG) workflows are widely used for large-scale data analytics in cluster-based distributed computing systems. The performance model for a DAG on data-parallel frameworks (e.g., MapReduce) is a research challenge because the allocation of preemptable system resources among parallel jobs may dynamically vary during execution. This resource allocation variation during execution makes it difficult to accurately estimate the execution time. In this paper, we tackle this challenge by proposing a new cost model, called Bottleneck Oriented Estimation (BOE), to estimate the allocation of preemptable resources by identifying the bottleneck to accurately predict task execution time. For a DAG workflow, we propose a state-based approach to iteratively use the resource allocation property among stages to estimate the overall execution plan. Furthermore, to handle the skewness of various jobs, we refine the model with the order statistics theory to improve estimation accuracy. Extensive experiments were performed to validate these cost models with HiBench and TPC-H workloads. The BOE model outperforms the state-of-the-art models by a factor of five for task execution time estimation. For the refined skew-aware model, the average prediction error is under 3% when estimating the execution time of 51 hybrid analytics (HiBench) and query (TPC-H) DAG workflows.

County Scale Corn Yield Estimation Based on Multi-source Data in Liaoning Province

Corn as a dominant and productive cereal crop has been recognized as indispensable to the global food system and industrial raw materials. China’s corn consumption reached 2.82 × 108 t in 2021, but its production was only 2.65 × 108 t, and China’s corn industry is still in short supply. Timely and reliable corn yield estimation at a large scale is imperative and prerequisite to prevent climate risk and meet the growing demand for corn. While crop growth models are well suited to simulate yield formation, they lack the ability to provide fast and accurate estimates of large-scale yields, owing to the sheer quantity of data they require for parameterization. This study was conducted in the typical rain-fed corn belt, Liaoning province, to evaluate the applicability of our modeling practices. We developed the factors using climate data and MCD43A4 production, and built a county-level corn yield estimation model based on correlation analysis and corn growth mechanisms. We used corn yield data from the county between 2007 and 2017, leaving out 2017 for verification. The results show that our model, with an R2 (the Coefficient of Determination) of 0.82 and an RMSE (Root Mean Square Error) of 279.33 kg/hm2, significantly improved estimation accuracy compared to only using historical records and climate data. Our model’s R2 was 0.34 higher than the trend yield estimation model and 0.27 higher than the climate yield estimation model. Additionally, RMSE was reduced by 300–400 kg/hm2 compared to the other two models. The improvement in performance achieved by adding remote sensing information to the model was due to the inclusion of variables such as monitored corn growth state, which corrected the model predictions. Our work demonstrates a simple, scalable, and accurate method for timely estimation of corn yield at the county level with publicly available multiple-source data, which can potentially be employed in situations with sparse ground data for estimating crop yields.

Continuous motion finger joint angle estimation utilizing hybrid sEMG-FMG modality driven transformer-based deep learning model

Continuous motion joint angle estimation plays an important role in human–machine interaction (HMI). However, it is still a challenge to estimate continuous motion finger joint angles (CMFJA) accurately. To improve CMFJA estimation accuracy, we used hybrid surface electromyography-force myography (sEMG-FMG) modality as the decoding scheme since combining two sensing modalities could potentially compensate and correct for single sensing modality, and proposed a biosignals driven convolution neural networks (CNN) and Transformer model (BioCNN-T) to estimate CMFJA motivated by the potential of the Transformer architecture, which extracts local features through CNN, and captures dependencies between global features through Transformer encoder. The metacarpophalangeal joint angles of 6 hand movements commonly used in daily life were selected as estimation objects. The experimental results show that CMFJA estimation by hybrid sEMG-FMG modality can achieve higher accuracy than single modality. And we found that the addition of convolution block before Transformer encoder plays a positive role in improving estimation accuracy and pixel-level fusion is the most suitable among the information fusion strategies appearing in the paper. What’s more, compare with the CNN and long short-term memory neural networks (CNN-LSTM), the BioCNN-T has higher accuracy and less computing cost. (Average normalized root mean square error, 0.0456 ± 0.0030 versus 0.0539 ± 0.0035; Inference time, 9.12 × 10-6 s versus 3.20 × 10-4 s). To our knowledge, our work is a pioneer in the use of hybrid sEMG-FMG modality and Transformer architecture to estimate CMFJA. The Implications of it have promising potential in flexible and fine-grained HMI.

An Intelligent Framework for Estimating Software Development Projects using Machine Learning

The IT industry has faced many challenges related to software effort and cost estimation. A cost assessment is conducted after software effort estimation, which benefits customers as well as developers. The purpose of this paper is to discuss various methods for the estimation of software effort and cost in the context of software engineering, such as algorithmic methods, expert judgment methods, analogy-based estimation methods, and machine learning methods, as well as their different aspects. In spite of this, estimation of the effort involved in software development are subject to uncertainty. Several methods have been developed in the literature for improving estimation accuracy, many of which involve the use of machine learning techniques. A machine learning framework is proposed in this paper to address this challenging problem. In addition to being completely independent of algorithmic models and estimation problems, this framework also features a modular architecture. It has high interpretability, learning capability, and robustness to imprecise and uncertain inputs.

Gaze Estimation via Strip Pooling and Multi-Criss-Cross Attention Networks

Deep learning techniques for gaze estimation usually determine gaze direction directly from images of the face. These algorithms achieve good performance because face images contain more feature information than eye images. However, these image classes contain a substantial amount of redundant information that may interfere with gaze prediction and may represent a bottleneck for performance improvement. To address these issues, we model long-distance dependencies between the eyes via Strip Pooling and Multi-Criss-Cross Attention Networks (SPMCCA-Net), which consist of two newly designed network modules. One module is represented by a feature enhancement bottleneck block based on fringe pooling. By incorporating strip pooling, this residual module not only enlarges its receptive fields to capture long-distance dependence between the eyes but also increases weights on important features and reduces the interference of redundant information unrelated to gaze. The other module is a multi-criss-cross attention network. This module exploits a cross-attention mechanism to further enhance long-range dependence between the eyes by incorporating the distribution of eye-gaze features and providing more gaze cues for improving estimation accuracy. Network training relies on the multi-loss function, combined with smooth L1 loss and cross entropy loss. This approach speeds up training convergence while increasing gaze estimation precision. Extensive experiments demonstrate that SPMCCA-Net outperforms several state-of-the-art methods, achieving mean angular error values of 10.13° on the Gaze360 dataset and 6.61° on the RT-gene dataset.

High-Precision State of Charge Estimation of Urban-Road-Condition Lithium-Ion Batteries Based on Optimized High-Order Term Compensation-Adaptive Extended Kalman Filtering

It is significant to improve the accuracy of estimating the state of charge (SOC) of lithium-ion batteries under different working conditions on urban roads. In this study, an improved second-order polarized equivalent circuit (SO-PEC) modeling method is proposed. Accuracy test using segmented parallel exponential fitting parameter identification method. Online parameter identification using recursive least squares with variable forgetting factors(VFFRLS). An optimized higher-order term compensation-adaptive extended Kalman filter (HTC-AEKF) is proposed in the process of estimating SOC. The algorithm incorporates a noise-adaptive algorithm that introduces noise covariance into the recursive process in real-time to reduce the impact of process noise and observation noise on the accuracy of SOC estimation. Multiple iterations are performed for some of the processes in the extended Kalman filter(EKF) to compensate for the accuracy impact of missing higher-order terms in the linearization process. Model validation results show over 98% accuracy. The results after comparing with the EKF algorithm show a 4.1% improvement in SOC estimation accuracy under Hybrid Pulse Power Characterization(HPPC) working conditions. 2.7% improvement in accuracy in Dynamic Stress Test(DST) working conditions. 2.1% improvement in Beijing Bus Dynamic Stress Test(BBDST) working conditions. The superiority of the algorithm is demonstrated.

Modification of the radiation-based Abtew reference evapotranspiration model under humid climate, Northeast India

Abstract This study aimed to improve the Abtew model for reference evapotranspiration (ET0) calculation in Northeast India using seven temperature-based solar radiation models. The temperature-based models require only air temperature as input data, which can be easily measured in most locations worldwide. The performance of the improved Abtew models (A1-A7), along with the Stephen Stewart model (SS), the Irmak model (Ir), and the modified Turc model (MT), was evaluated under the climatic conditions of Dibrugarh, Northeast India, using statistical indices such as mean absolute error (MAE), root mean square error (RMSE), standard error (SE), coefficient of correlation (r), coefficient of determination (R2), and index of agreement (D). The results showed that the seven improved Abtew models (RMSE = 0.40–0.53 mm/day; D = 0.81–0.93) outperformed the four physical models (RMSE = 0.43–2.77 mm/day; D = 0.49–0.91) for the ET0 estimate at Dibrugarh. The statistical analysis identified that the A6 model ranked highest for Dibrugarh. This study highlights the significant improvement in ET0 estimation accuracy by utilizing temperature-based solar radiation models in the Abtew model. Therefore, we strongly recommend using the A6 model to estimate ET0, which requires only temperature data as input, for estimating ET0 under the climatic conditions of Dibrugarh, Northeast India.

Aboveground Biomass Retrieval in Tropical and Boreal Forests Using L-Band Airborne Polarimetric Observations

Forests play a crucial part in regulating global climate change since their aboveground biomass (AGB) relates to the carbon cycle, and its changes affect the main carbon pools. At present, the most suitable available SAR data for wall-to-wall forest AGB estimation are exploiting an L-band polarimetric SAR. However, the saturation issues were reported for AGB estimation using L-band backscatter coefficients. Saturation varies depending on forest structure. Polarimetric information has the capability to identify different aspects of forest structure and therefore shows great potential for reducing saturation issues and improving estimation accuracy. In this study, 121 polarimetric decomposition observations, 10 polarimetric backscatter coefficients and their derived observations, and six texture features were extracted and applied for forest AGB estimation in a tropical forest and a boreal forest. A parametric feature optimization inversion model (Multiple linear stepwise regression, MSLR) and a nonparametric feature optimization inversion model (fast iterative procedure integrated into a K-nearest neighbor nonparameter algorithm, KNNFIFS) were used for polarimetric features optimization and forest AGB inversion. The results demonstrated the great potential of L-band polarimetric features for forest AGB estimation. KNNFIFS performed better both in tropical (R2 = 0.80, RMSE = 22.55 Mg/ha, rRMSE = 14.59%, MA%E = 12.21%) and boreal (R2 = 0.74, RMSE = 19.82 Mg/ha, rRMSE = 20.86%, MA%E = 20.19%) forests. Non-model-based polarimetric features performed better compared to features extracted by backscatter coefficients, model-based decompositions, and texture. Polarimetric observations also revealed site-dependent performances.

Phase-shifting interferometry based on dynamic mode decomposition.

A phase retrieval algorithm in phase-shifting interferometry is presented based on dynamic mode decomposition (DMD). The complex-valued spatial mode obtained from the DMD of phase-shifted interferograms allows the derivation of the phase estimate. At the same time, the oscillation frequency associated with the spatial mode provides the phase step estimate. The performance of the proposed method is compared to methods based on least squares and principle component analysis. The simulation and experimental results demonstrate the improvement in the phase estimation accuracy and noise robustness offered by the proposed method and thus substantiate its practical applicability.

Multi‐Task Learning for Simultaneous Retrievals of Passive Microwave Precipitation Estimates and Rain/No‐Rain Classification

AbstractSatellite‐based precipitation estimations provide frequent, large‐scale measurements. Deep learning has recently shown significant potential for improving estimation accuracy. Most studies have employed a two‐stage framework, which is a sequential architecture of a rain/no‐rain binary classification task followed by a rain rate regression task. This study proposes a novel precipitation retrieval framework in which these two tasks are simultaneously trained using multi‐task learning approach (MTL). Furthermore, a novel network architecture and loss function were designed to reap the benefits of MTL. The proposed two‐task model successfully achieved a better performance than the conventional single‐task model possibly due to efficient knowledge transfer between tasks. Furthermore, the product intercomparison showed that our product outperformed existing products in rain rate retrieval and also yielded better skills in the rain/no‐rain retrieval task.

Delay Prediction for ASIC HLS: Comparing Graph-Based and Nongraph-Based Learning Models

While high-level synthesis (HLS) tools offer faster design of hardware accelerators with different area versus delay tradeoffs, HLS-based delay estimates often deviate significantly from results obtained from ASIC logic synthesis (LS) tools. Current HLS tools rely on simple additive delay models which fail to capture the downstream optimizations performed during LS and technology mapping. Inaccurate delay estimates prevent fast and accurate design-space exploration without performing time-consuming LS tasks. In this work, we exploit different machine learning models which automatically learn to map the different downstream optimizations onto the HLS critical paths. In particular, we compare graph-based and nongraph-based learning models to investigate their efficacy, devise hybrid models to get the best of the both worlds. To carry out our learning-assisted methodology, we create a dataset of different HLS benchmarks and develop an automated framework, which extends a commercial HLS toolchain, to extract essential information from LS critical path and automatically matches this information to HLS path. This is a nontrivial task to perform manually due to difference in level of abstractions. Finally, we train the proposed hybrid models through inductive learning and integrate them in the commercial HLS toolchain to improve delay prediction accuracy. Experimental results demonstrate significant improvements in delay estimation accuracy across a wide variety of benchmark designs. We demonstrate that the graph-based models can infer essential structural features from the input design, while incorporating them into traditional nongraph-based models can significantly improve the model accuracy. Such “hybrid” models can improve delay prediction accuracy by 93% compared to simple additive models and provide <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$175\times $ </tex-math></inline-formula> speedup compared to LS. Furthermore, we discuss key insights from our experiments, identifying the influence of different HLS features on model performance.

Improving the accuracy of models to map alpine grassland above‐ground biomass using Google earth engine

AbstractAccurate modelling and mapping of alpine grassland aboveground biomass (AGB) are crucial for pastoral agriculture planning and management on the Qinghai Tibet Plateau (QTP). This study assessed the effectiveness of four popular models (traditional multiple linear regression (MLR), support vector machine (SVM), artificial neural network (ANN), and deep neural network (DNN)) with various input combinations (geospatial variables [GV], vegetation types [VT], field measurements [FM], meteorological variables [MV] and observation time [OT]) for AGB estimation based on a new framework for AGB modelling and mapping using Google Earth Engine. The results showed that the input feature of GV had a poor performance in AGB estimation (0.121 &lt; R2 &lt; 0.591). FM improved the accuracy the most when incorporated with GV (0.815 &lt; R2 &lt; 0.833). Although MV, VT and OT improved the accuracy (R2) only by 0.112–0.216 with an importance rank order of MV &gt; VT &gt; OT for machine learning models, their outputs could be used to map AGB. Grass AGB was less accurately predicted than shrub AGB, but the pooling of both VTs improved estimation accuracy (R2) by 0.171–0.269. The performance of the models followed the ranked order of DNN &gt; ANN &gt; SVM &gt; MLR. DNN had the highest accuracy (R2 = 0.818) using all non‐field measured variables (excluding FM) as the inputs, and it was successfully applied to a new dataset (not associated with the data used in the training and testing) with aR2of 0.676. This study presents an effective and operational framework for modelling and mapping grassland AGB. Accordingly, it provides the scientific foundations to determine of sustainable grazing carrying capacity in alpine grasslands.

Influence of oversimplifying the head anatomy on cerebral blood flow measurements with diffuse correlation spectroscopy.

Diffuse correlation spectroscopy (DCS) is an emerging optical modality for non-invasive assessment of an index of regional cerebral blood flow. By the nature of this noninvasive measurement, light must pass through extracerebral layers (i.e., skull, scalp, and cerebral spinal fluid) before detection at the tissue surface. To minimize the contribution of these extracerebral layers to the measured signal, an analytical model has been developed that treats the head as a series of three parallel and infinitely extending slabs (mimicking scalp, skull, and brain). The three-layer model has been shown to provide a significant improvement in cerebral blood flow estimation over the typically used model that treats the head as a bulk homogenous medium. However, the three-layer model is still a gross oversimplification of the head geometry that ignores head curvature, the presence of cerebrospinal fluid (CSF), and heterogeneity in layer thickness. Determine the influence of oversimplifying the head geometry on cerebral blood flow estimated with the three-layer model. Data were simulated with Monte Carlo in a four-layer slab medium and a three-layer sphere medium to isolate the influence of CSF and curvature, respectively. Additionally, simulations were performed on magnetic resonance imaging (MRI) head templates spanning a wide-range of ages. Simulated data were fit to both the homogenous and three-layer model for CBF. Finally, to mitigate the errors in potential CBF estimation due to the difficulty in defining layer thickness, we investigated an approach to identify an equivalent, "optimized" thickness via a pressure modulation. Both head curvature and failing to account for CSF lead to significant errors in the estimation of CBF. However, the effect of curvature and CSF on relative changes in CBF is minimal. Further, we found that CBF was underestimated in all MRI-templates, although the magnitude of these underestimations was highly influenced by small variations in the source and detector optode positioning. The optimized thickness obtained from pressure modulation did not improve estimation accuracy of CBF, although it did significantly improve the estimation accuracy of relative changes in CBF. In sum, these findings suggest that the three-layer model holds promise for improving estimation of relative changes in cerebral blood flow; however, estimations of absolute cerebral blood flow with the approach should be viewed with caution given that it is difficult to account for appreciable sources of error, such as curvature and CSF.

Gaussian kernel quadrature Kalman filter

The solution to practical nonlinear filtering problems broadly relies on Gaussian filtering. The Gaussian filtering involves intractable integrals that are numerically approximated during the filtering. The literature witnesses various Gaussian filters with varying accuracy and computational demand, which are developed using different numerical approximation methods. Among them, the quadrature rule based Gaussian filters are known for offering the best accuracy. They apply the univariate Gauss-Hermite quadrature rule for approximating the intractable integrals. For the practical multivariate filtering problems, they additionally apply a univariate-to-multivariate conversion rule. This paper develops a new quadrature rule based Gaussian filter, named Gaussian kernel quadrature Kalman filter (GKQKF). The proposed GKQKF replaces the univariate Gauss-Hermite quadrature rule with the univariate Gaussian kernel quadrature rule and uses the product rule for extending the univariate quadrature rule in the multivariate domain. The Gaussian kernel quadrature rule improves the numerical approximation accuracy, which results in improved estimation accuracy of the proposed GKQKF over the existing quadrature rule based Gaussian filters. As the quadrature rule based Gaussian filters are the most accurate existing Gaussian filters, the proposed GKQKF outperforms the other existing Gaussian filters as well. The improved accuracy of the proposed GKQKF is validated for three different simulation problems.

Collaborative estimations of state of energy and maximum available energy of lithium-ion batteries with optimized time windows considering instantaneous energy efficiencies

The state of energy (SOE) of the lithium-ion battery indicates the driving range of electric vehicles, which is affected by its maximum available energy (MAEgy). Meanwhile, the energy efficiency is of great significance to improve the estimation accuracy. In this paper, a collaborative estimation method of the SOE and MAEgy with optimized time windows considering energy efficiency is proposed. Firstly, based on the Thevenin model of the battery, the forgetting factor recursive least squares is used to identify its parameters. The state space equations of the SOE and MAEgy are established respectively and two extended Kalman filters are leveraged to estimate them with different time windows. To reduce calculations and improve estimation accuracy, the multi-objective genetic algorithm is applied to optimize the time windows for the transient scheme and steady scheme, respectively. Then the optimal time windows of the initial and convergence phase are derived from these two schemes by the entropy weight method. Finally, the instantaneous energy efficiency is deduced, and the influences of four different calculation methods on the estimation performances are discussed. The results show that the proposed method has better transient performances and steady-state accuracy under dynamic driving condition and is robust against incorrect initial values.

The vertical velocity field of the Tibetan Plateau and its surrounding areas derived from GPS and surface mass loading models

Obtaining a precise velocity field of the Earth's surface is critical for probing Earth's tectonic movements. In this contribution we construct a precise vertical velocity field with high-spatial resolution for the Tibetan Plateau (TP) and its surrounding areas using both 113 continuous and 969 campaign GPS time series over the period 2008 to 2019. Specifically, we compared the statistical distribution of residual continuous GPS time series to find the optimal regional surface mass loading (SML) models. The optimal modeled nontectonic displacements were used to correct these campaign GPS time series to reduce their scatter and accordingly improve the precision of the uplift rate estimates. The results showed that we could reduce the root mean square (RMS) on the vertical coordinate time series by more than 75% of the campaign GPS stations. We computed and removed vertical deformation due to horizontal strain rates obtained from GPS time series, and discussed dynamic sources (mantle dynamic topography, isostatic adjustment, and flexural loading) that drive the residual vertical tectonic motion. The study presents the most recent surface kinematic constraints for comprehending the dynamic sources of tectonic uplift or subsidence between and within tectonic units.Plain Language Summary: Movements of the Tibetan Plateau (TP) have a profound impact on adjacent areas. We collected all available GPS data to determine a precise vertical velocity field with high-spatial resolution. We make use of optimal surface mass loading (SML) models to improve estimation accuracy of campaign GPS stations, including an estimate of the vertical movement caused by the horizontal tectonic motions. We combine geological and geophysical data with our vertical velocity field to understand the dynamic sources of uplift or subsidence between and within tectonic units of the TP.

State of charge estimation for lithium-ion battery based on whale optimization algorithm and multi-kernel relevance vector machine.

Lithium-ion batteries are key elements of electric vehicles and energy storage systems, and their accurate State of Charge (SOC) estimation is momentous for battery energy management, safe operation, and extended service life. In this paper, the Multi-Kernel Relevance Vector Machine (MKRVM) and Whale Optimization Algorithm (WOA) are used to estimate the SOC of lithium-ion batteries under different operating conditions. In order to better learn and estimate the battery SOC, MKRVM is used to establish a model to estimate lithium-ion battery SOC. WOA is used to automatically adjust and optimize weights and kernel parameters of MKRVM to improve estimation accuracy. The proposed model is validated with three lithium-ion batteries under different operating conditions. In contrast to other optimization algorithms, WOA has a better optimization effect and can estimate the SOC more accurately. In contrast to the single kernel function, the proposed multi-kernel function greatly improves the precision of the SOC estimation model. In contrast to the traditional method, the WOA-MKRVM has a higher precision of SOC estimation.