Traditional Estimation Methods Research Articles

An Adaptive Combined Method for Lithium‐Ion Battery State of Charge Estimation Using Long Short‐Term Memory Network and Unscented Kalman Filter Considering Battery Aging

AbstractThe accurate estimation of battery state of charge (SOC) enables the reliable and safe operation of lithium‐ion batteries. Data‐driven SOC estimation is considered an emerging and effective solution. However, existing data‐driven SOC estimation methods typically involve direct estimation and lack effective feedback correction. Moreover, battery degradation poses additional challenges to accurate SOC estimation. Therefore, this study proposes an adaptive combined method for battery SOC estimation based on a long short‐term memory (LSTM) network and unscented Kalman filter (UKF) algorithm considering battery aging status. First, an LSTM model is constructed to characterize the battery's dynamic performance instead of traditional battery models. Then, the UKF algorithm is employed to perform SOC estimation through the feedback of terminal voltage prediction. To enhance estimation accuracy under different aging statuses, a proportional‐integral‐derivative controller is employed to correct the capacity fading during the SOC estimation process. Validation results indicate that the terminal voltage prediction model demonstrates exceptional robustness against interference from current and voltage noise. Compared to the traditional estimation method combining the deep learning model and Kalman filter algorithm, the proposed method demonstrates superior estimation accuracy under various complex operating conditions. Furthermore, the proposed method outperforms the traditional method in estimation performance during battery aging.

Visual analysis of postmortem interval estimation trends and collaborative networks: a 15-year study (2006-2020).

Utilizing a visual analysis of the literature on postmortem interval (PMI) estimation indexed by Web of Science (WOS), this study investigates developmental trends and research hot points across each 5-year period from 2006 to 2020. Additionally, collaborative efforts among authors, countries, and institutions were examined. Research hot points, high-frequency keywords, authors, countries and institutions in relevant papers were analyzed using CiteSpace.5.7.R2 information visualization analysis software over the past 15 years. The literature related to PMI estimation has witnessed consistent growth over time. In the keyword co-occurrence network, several impactful terms stand out, including blowfly, mitochondrial DNA, and emerging concepts like virtual autopsy. Technological advancements, such as RNA stability analysis and virtual autopsy tools, have played a pivotal role in shaping the direction of PMI research. Scientific research institutions dominate the high-frequency affiliations within the institutional cooperative network. Additionally, the country cooperative network exhibits a trend of co-occurrence and multi-clustering. As science and technology continue to advance, traditional PMI estimation methods mature while novel interdisciplinary approaches drive innovation. By identifying emerging trends and research hotspots, this study provides a roadmap for future investigations, guiding researchers toward new opportunities in PMI estimation.

Multi-innovation adaptive Kalman filter algorithm for estimating the SOC of lithium-ion batteries based on singular value decomposition and Schmidt orthogonal transformation

The state of charge (SOC) of lithium battery is a key parameter for effective management of battery management systems (BMS). To address the problems of low precision, complex computation and poor robustness of traditional charging state estimation methods, an enhanced algorithm based on Unscented Kalman filter (UKF) is proposed. The singular value decomposition (SVD) method is adopted to ensure the normal operation of the Unscented Kalman Filter (UKF) algorithm even when the matrix P lacks positive semi-definiteness from a mathematical perspective. This enhancement significantly improves the theoretical robustness of UKF. Schmidt orthogonal transformation is concurrently used to reduce the computational complexity in the sampling point selection process, and the multi-innovation theory is combined with adaptive noise control to further improve the accuracy of SOC estimation. The algorithm is validated using the Urban Dynamometer Driving Schedule (UDDS) condition. The simulation results are excited using Singular value decomposition-multi-innovation adaptive Schmidt orthogonal unscented Kalman filter method (SVD-MIASOUKF). 0.95 % and 1.29 % of maximum errors are obtained at 25 °C and −10 °C, while the maximum errors are 2.46 %–2.99 % using SVD-UKF and UKF. The proposed approach shows faster convergence speed and higher estimation accuracy in comparison to traditional algorithms.

Deep optimal experimental design for parameter estimation problems

Abstract Optimal experimental design is a well studied field in applied science and engineering. Techniques for estimating such a design are commonly used within the framework of parameter estimation. Nonetheless, in recent years parameter estimation techniques are changing rapidly with the introduction of deep learning techniques to replace traditional estimation methods. This in turn requires the adaptation of optimal experimental design that is associated with these new techniques. In this paper we investigate a new experimental design methodology that uses deep learning. We show that the training of a network as a Likelihood Free Estimator can be used to significantly simplify the design process and circumvent the need for the computationally expensive bi-level optimization problem that is inherent in optimal experimental design for non-linear systems. Furthermore, deep design improves the quality of the recovery process for parameter estimation problems. As proof of concept we apply our methodology to two different systems of Ordinary Differential Equations.

Optimal Subsampling for Functional Quasi-Mode Regression with Big Data

We propose investigating optimal subsampling for functional regression with massive datasets based on the mode value, which is referred to as functional quasi-mode regression, to reduce data volume and alleviate computational burden. Using data-adaptive weights derived from regression residuals, the suggested regression offers enhanced robustness against nonnormal errors compared to traditional least squares or maximum likelihood estimation methods. To estimate the model, we employ B-spline basis functions to approximate the functional coefficient and include a penalty term in the objective function for enforcing smoothness in the resulting estimator. We adopt a computationally efficient mode-expectation-maximization algorithm, augmented by a Gaussian kernel, for numerical estimation. Under mild regularity conditions, we derive the asymptotic distributions of both full data and subsample quasi-mode estimators. The optimal subsampling probabilities by minimizing the asymptotic variance-covariance matrix under A- and L-optimality criteria are identified. These optimal probabilities rely on the full data estimate, prompting the development of a two-step algorithm to approximate the optimal subsampling procedure. The resultant algorithm is processing-efficient and can significantly reduce computational time compared to the full data approach. We also establish the asymptotic normality of the quasi-mode estimator obtained through this two-step algorithm. To assess finite sample performance, we conduct Monte Carlo simulations and analyze air quality data, showcasing the effectiveness of the developed estimator. Supplemental materials for this article are available online.

Bad data identification method considering the on-load tap changer model

With the connection and integration of renewable energy, the on-load tap-changer (OLTC) has become an important device for regulating voltage in distribution networks. However, due to non-smooth and non-linear characteristics of OLTC, traditional bad data identification and state estimation methods for transmission network are limited when applied to the distribution network. Therefore, the nonlinearity and droop control constraints of the OLTC model are considered in this paper. At the same time, the quadratic penalty function is introduced to realize the fast normalization of the tap position. It proposes a two-stage bad data identification method based on mixed-integer linear programming. In the first stage, suspicious measurements are identified using projection statistics and maximum normalized residual methods for preprocessing the measurement data. In the second stage, a linearization approach utilizing hyhrid data-physical driven is applied to handle nonlinear constraints, leading to the development of a bad data identification model based on mixed-integer linear programming. Finally, the proposed methodology is validated using a modified IEEE-33 node test feeder example, demonstrating the accuracy and efficiency of bad data identification.

Introduction and evaluation of size-specific DLP for radiation dose estimation in CT examinations.

The increased utilization of computed tomography (CT) has raised concerns about patient radiation exposure. Effective dose (ED), which requires precise estimation, is crucial for assessing and managing these risks. Traditional ED estimation methods, which are based on the dose-length product (DLP), often lack accuracy due to variations in patient size and anatomy. This study aims to evaluate the efficacy of size-specific DLP (SS-DLP), a novel metric that combines the size-specific dose estimate (SSDE) with scan length, to provide a more accurate estimation of radiation exposure from CT examinations. Focusing on adult chest-abdomen-pelvis (CAP) scans, we calculated SSDE and SS-DLP and utilized two simulation tools, Radimetrics and WAZA-ARI, for a detailed analysis. Our findings indicate that SS-DLP is highly correlated with EDs from Monte Carlo simulations, suggesting its reliability. Additionally, SS-DLP showed a moderate reduction in errors based on patient sex and body mass index compared to traditional DLP-based methods. Thus, SS-DLP offers a more accurate and personalized radiation exposure estimate, potentially enhancing patient safety.

Estimation of aboveground biomass of Alfalfa using field robotics

Alfalfa is a high-yielding forage crop that is widely grown in the United States for grazing, hay and silage making. A proper maintenance of these grasslands is necessary to ensure optimum productivity and profits. The pre-harvest estimation of biomass yield helps in quantifying the profits and optimizing the forage allocation in advance. Most traditional methods of forage estimation are relatively laborious and time-consuming. Recent developments in contact and remote sensing technologies opened numerous paths for performing aboveground biomass estimation tasks with flexibility and easiness. This study focused on the development of crop height measurement systems for estimating the aboveground biomass yield of Alfalfa (Medicago sativa L.). Five different systems for measuring crop height were evaluated on their ability to estimate aboveground wet and dry biomass. The crop height measurement systems used in this study were Structure-from-Motion, Ultrasound Sensor and Ski, Inertial Measurement Unit and Ski, Inertial Measurement Units and Roller, and a Depth Camera. The results indicated that the system using the Inertial Measurement Unit sensor and ski (IMU-Ski) performed the best among ground-based methods (R2= 0.79; SeY= 3166 kg-wet/ha). The Structure-from-Motion (SfM) method using UAV also provided satisfactory results for biomass predictions (R2= 0.74; SeY= 2543 kg-wet/ha). The models based on IMU-Ski and UAV-based SfM methods were facilitated with vegetation coverage as an additional independent variable to evaluate their effect on biomass predictions. The results indicated that the vegetation coverage did not improve the predictions in any of these systems. Thus, the models based on only the crop height (IMU-Ski and UAV-SfM) were the recommended approaches for Alfalfa biomass estimations. The addition of data points for wide ranges of crop height and vegetation coverage is recommended for future studies to improve the results and ensure the adaptability of these systems in varying environmental conditions.

Advanced concept for noise monitoring in smart cities through wireless sensor units with AI classification technologies

The rapid urbanization in the cities has indicated the importance of sustainable development for creating smart cities with high quality of life. Environmental noise as one of the main concerns has to be addressed according to International Directives and Legislation. Traditional noise estimation methods are costly and time-consuming, but the emerging technologies like low-cost wireless sensor units (WSUs) offer more granular data collection and analysis. Requirements for more accurate assessment of the noise pollution by detecting the dominant noise sources impose the need to apply novel approaches in the technical systems for noise monitoring. To this aim, this paper investigates the advanced methods for noise monitoring through WSUs with AI classification technologies. The proposed concept of the device not only quantitively describes the noise pollution, but also tends to recognize the class of the disturbing sound events. The accuracy of the WSUs are configured by comparing the results with professional hand-held analyzer, showing powerful and affordable low-cost units able to publish results through cloud and fog computing based on the IoT and smart city technologies. The paper discusses the challenges for merging noise measurement technology and the AI algorithms to classify and quantify the different classes of sound events.

Comparative analysis of deep learning and machine learning-based models for simultaneous prediction of minerals in perilla (Perilla frutescens L.) seeds using near-infrared reflectance spectroscopy

Perilla seeds contain a rich array of essential minerals, thus having the potential to address multiple micronutrient deficiencies at a time. However, traditional methods of mineral estimation are complex, time-consuming, expensive, and require technical expertise. This study includes the development of Near-Infrared Reflectance Spectroscopy (NIRS)-based prediction models for predicting five important minerals (Calcium, Copper, Magnesium, Manganese, and Phosphorus) using machine learning and deep learning techniques. Four models, including 1D Convolutional Neural Networks (1D CNNs), Artificial Neural Networks (ANNs), Random Forests (RFs), and Support Vector Regression (SVR), were developed and evaluated. The developed 1D CNN model outperformed other considered models in predicting calcium, magnesium, and phosphorus content with RPD (Residual Prediction Deviation) values of 1.75, 1.83, and 2.96, respectively. Whereas, SVR performed best in predicting copper and manganese with an RPD of 1.82 and 2.2, respectively. The 1D CNN model demonstrated R2 (Coefficient of determination) values above 0.65 for all minerals, with a maximum of 0.88 for phosphorus. In addition, the developed models performed superior as compared to the Partial Least Square Regression method (R2= 0.32). The developed models provide efficient tools for rapidly screening perilla germplasm available in global repositories, thus aiding in the selection of mineral-rich genotypes to mitigate micronutrient deficiencies.

Pore Size Classification and Prediction Based on Distribution of Reservoir Fluid Volumes Utilizing Well Logs and Deep Learning Algorithm in a Complex Lithology

Pore size analysis plays a pivotal role in unraveling reservoir behavior and its intricate relationship with confined fluids. Traditional methods for predicting pore size distribution (PSD), relying on drilling cores or thin sections, face limitations associated with depth specificity. In this study, we introduce an innovative framework that leverages nuclear magnetic resonance (NMR) log data, encompassing clay-bound water (CBW), bound volume irreducible (BVI), and free fluid volume (FFV), to determine three PSDs (micropores, mesopores, and macropores). Moreover, we establish a robust pore size classification (PSC) system utilizing ternary plots, derived from the PSDs.Within the three studied wells, NMR log data is exclusive to one well (well-A), while conventional well logs are accessible for all three wells (well-A, well-B, and well-C). This distinction enables PSD predictions for the remaining two wells (B and C). To prognosticate NMR outputs (CBW, BVI, FFV) for these wells, a two-step deep learning (DL) algorithm is implemented. Initially, three feature selection algorithms (f-classif, f-regression, and mutual-info-regression) identify the conventional well logs most correlated to NMR outputs in well-A. The three feature selection algorithms utilize statistical computations. These algorithms are utilized to systematically identify and optimize pertinent input features, thereby augmenting model interpretability and predictive efficacy within intricate data-driven endeavors. So, all three feature selection algorithms introduced the number of 4 logs as the most optimal number of inputs to the DL algorithm with different combinations of logs for each of the three desired outputs. Subsequently, the CUDA Deep Neural Network Long Short-Term Memory algorithm(CUDNNLSTM), belonging to the category of DL algorithms and harnessing the computational power of GPUs, is employed for the prediction of CBW, BVI, and FFV logs. This prediction leverages the optimal logs identified in the preceding step. Estimation of NMR outputs was done first in well-A (80% of data as training and 20% as testing). The correlation coefficient (CC) between the actual and estimated data for the three outputs CBW, BVI and FFV are 95%, 94%, and 97%, respectively, as well as root mean square error (RMSE) was obtained 0.0081, 0.098, and 0.0089, respectively. To assess the effectiveness of the proposed algorithm, we compared it with two traditional methods for log estimation: multiple regression and multi-resolution graph-based clustering methods. The results demonstrate the superior accuracy of our algorithm in comparison to these conventional approaches. This DL-driven approach facilitates PSD prediction grounded in fluid saturation for wells B and C.Ternary plots are then employed for PSCs. Seven distinct PSCs within well-A employing actual NMR logs (CBW, BVI, FFV), in conjunction with an equivalent count within wells B and C utilizing three predicted logs, are harmoniously categorized leading to the identification of seven distinct pore size classification facies (PSCF). this research introduces an advanced approach to pore size classification and prediction, fusing NMR logs with deep learning techniques and extending their application to nearby wells without NMR log. The resulting PSCFs offer valuable insights into generating precise and detailed reservoir 3D models.

Advanced Beam Estimation for Antennas Via Patterned Coupling-Line Detection Board in Ka-Band

In this research, we present an innovative method for estimating the beams of array antennas. Traditional beam analysis methods rely on placing receiving antennas in the far-field region, which requires moving or rotating the Tx or Rx, and using radiation pattern measurements. However, such methods often demand vast spatial requirements and the use of high-cost network analyzers. In contrast, the technique proposed in this study utilizes a board patterned with coupling lines strategically placed in the antenna's near-field zone. Signals intercepted by these coupling lines undergo conversion into DC voltage via a power detector situated at the line terminus. Interestingly, this method enables beam estimation solely based on the DC voltage level output of the power detector, thus offering a cost-effective and space-efficient solution that represents a significant advancement from traditional beam estimation methods.

Development of a Machine Learning Framework for Real-Time PMI (Post-Mortem Interval) Estimation in Field Forensics

Accurate estimation of the Post-Mortem Interval (PMI) is critical in forensic investigations, aiding in determining the time of death. However, traditional PMI estimation methods, often reliant on physiological observations and environmental factors, face significant limitations in accuracy and efficiency, especially in field conditions. This paper presents the development of a machine learning (ML) framework designed for real-time PMI estimation, integrating multimodal sensor data to address the challenges encountered in field forensics. Our framework utilizes environmental and physiological features, including body temperature, ambient humidity, and biochemical decomposition markers, to predict PMI with high precision. The ML model, trained on historical forensic data, is deployed on a real-time processing platform, enabling rapid analysis and decision-making in resource- constrained environments. The system is optimized for field operations, incorporating low-power hardware and edge computing capabilities to provide forensic investigators with reliable PMI estimates on-site. Through a series of controlled experiments simulating forensic scenarios, our framework demonstrates a significant improvement in PMI accuracy compared to traditional methods, while maintaining low latency for real-time applications. This research highlights the potential of machine learning to revolutionize forensic practices, offering a scalable and adaptive solution for time-sensitive investigations. Here are some relevant keywords for the development of a machine learning framework for real-time PMI (Post- Mortem Interval) estimation in field forensics: Keywords: Field Forensics, Real-Time Machine Learning, Body Decomposition Stages, Machine Learning in Forensic Science, Artificial Intelligence for PMI Analysis, Sensor Data in PMI Estimation, Deep Learning for PMI Estimation, Automated Forensic Analysis, Data Acquisition in Field Forensics.

Kalman tracking and parameter estimation of continuous gravitational waves with a pulsar timing array

Abstract Continuous nanohertz gravitational waves from individual supermassive black hole binaries may be detectable with pulsar timing arrays. A novel search strategy is developed, wherein intrinsic achromatic spin wandering is tracked simultaneously with the modulation induced by a single gravitational wave source in the pulse times of arrival. A two-step inference procedure is applied within a state-space framework, such that the modulation is tracked with a Kalman filter, which then provides a likelihood for nested sampling. The procedure estimates the static parameters in the problem, such as the sky position of the source, without fitting for ensemble-averaged statistics such as the power spectral density of the timing noise, and therefore complements traditional parameter estimation methods. It also returns the Bayes factor relating a model with a single gravitational wave source to one without, complementing traditional detection methods. It is shown via astrophysically representative software injections in Gaussian measurement noise that the procedure distinguishes a gravitational wave from pure noise down to a characteristic wave strain of h0 ≈ 2 × 10−15. Full posterior distributions of model parameters are recovered and tested for accuracy. There is a bias of ≈0.3 rad in the marginalised one-dimensional posterior for the orbital inclination ι, introduced by dropping the so-called ‘pulsar terms’. Smaller biases $\lesssim 10~{{\%}}$ are also observed in other static parameters.

Enhanced‐Resolution Learning‐Based Direction of Arrival Estimation by Programmable Metasurface

AbstractDue to its growing importance and wide range of applications, direction‐of‐arrival (DOA) estimation has become a major research topic, particularly in the field of communication systems. While traditional DOA estimation methods rely on antenna arrays and complex algorithms, recent progress achieved in the design and implementation of metasurfaces has proved their effectiveness as promising alternatives. This study presents a distinct approach for DOA estimation that combines the use of a programmable metasurface with deep learning. The programmable metasurface together with a radio‐frequency power detector placed at the focal point, acts as a parabolic reflector antenna with an adjustable pointing direction, which scans the azimuth plane in 5° increments to receive the power level of incoming signals. The collected data is then fed into a pre‐trained multilayer neural network to enable DOA estimation with a resolution of lower than 1° without requiring fine‐tuning of the scanning procedure. This approach ensures accurate and fast estimations, paving the way for advanced solutions in detection and localization for various applications.

Maximum likelihood estimators for colony-forming units.

Measuring the abundance of microbes in a sample is a common procedure with a long history, but best practices are not well-conserved across microbiological fields. Serial dilution methods are commonly used to dilute bacterial cultures to produce countable numbers of colonies, and from these counts, to infer bacterial concentrations measured in colony-forming units (CFUs). The most common methods to generate data for CFU point estimates involve plating bacteria on (or in) a solid growth medium and counting their resulting colonies or counting the number of tubes at a given dilution that have growth. Traditionally, these types of data have been analyzed separately using different analytic methods. Here, we build a direct correspondence between these approaches, which allows one to extend the use of the most probable number method from the liquid tubes experiments, for which it was developed, to the growth plates by viewing colony-sized patches of a plate as equivalent to individual tubes. We also discuss how to combine measurements taken at different dilutions, and we review several ways of analyzing colony counts, including the Poisson and truncated Poisson methods. We test all point estimate methods computationally using simulated data. For all methods, we discuss their relevant error bounds, assumptions, strengths, and weaknesses. We provide an online calculator for these estimators.Estimation of the number of microbes in a sample is an important problem with a long history. Yet common practices, such as combining results from different measurements, remain sub-optimal. We provide a comparison of methods for estimating abundance of microbes and detail a mapping between different methods, which allows to extend their range of applicability. This mapping enables higher precision estimates of colony-forming units (CFUs) using the same data already collected for traditional CFU estimation methods. Furthermore, we provide recommendations for how to combine measurements of colony counts taken across dilutions, correcting several misconceptions in the literature.

Channel estimation of massive MIMO FSO communication system using deep attention residual U-Net

Channel estimation in massive-MIMO FSO systems is critical for ensuring reliable data transmission. However, conventional estimators offer limited benefits due to the computational difficulty of accurately estimating the channel. This paper presents a novel approach to estimate channels using an attention residual U-Net (ARU-Net) architecture which utilizes the advantages of both attention and residual connection. In the simulation, the channel matrix has been represented as a 2D image. The proposed model significantly outperforms traditional channel estimation methods and other deep learning models in terms of MSE (10−5 at 25 dB SNR), especially in atmospheric turbulence and other noises.

Hybrid Intelligent Model for Estimating the Cost of Huizhou Replica Traditional Vernacular Dwellings

Amidst the backdrop of rural revitalization and cultural renaissance, there is a surge in the construction demand for replica traditional vernacular dwellings. Traditional cost estimation methods struggle to meet the need for rapid and precise estimation due to the complexity inherent in their construction. To address this challenge, this study aims to enhance the accuracy and efficiency of cost estimation by innovatively developing an Adaptive Self-Explanatory Convolutional Neural Network (ASCNN) model, tailored to meet the specific cost estimation needs of replica traditional vernacular dwellings in the Huizhou region. The ASCNN model employs a Random Forest model to filter key features, inputs these into the CNN for cost estimation, and utilizes Particle Swarm Optimization (PSO) to optimize parameters, thereby improving predictive accuracy. The decision-making process of the model is thoroughly interpreted through SHAP value analysis, ensuring credibility and transparency. During the construction of the ASCNN model, this study collected and analyzed bidding control price data from 98 replica traditional vernacular dwellings. The empirical results demonstrate that the ASCNN model exhibits outstanding predictive performance on the test set, with a Root Mean Square Error (RMSE) of 9828.06 yuan, a Mean Absolute Percentage Error (MAPE) of 0.6%, and a Coefficient of Determination (R2) as high as 0.989, confirming the model’s high predictive accuracy and strong generalization capability. Through SHAP value analysis, this study further identifies key factors such as floor plan layout, roof area, and column material coefficient that are central to cost prediction. The ASCNN model proposed in this study not only significantly improves the accuracy of cost estimation for Huizhou replica traditional vernacular dwellings, but also enhances its transparency and credibility through model interpretation methods, providing a reliable basis for related investment decisions. The findings of this study also offer valuable references and insights for rapid and precise cost estimation of replica buildings in other regions worldwide.

Data-Driven Channel Modeling for End-to-End Visible Light DCO-OFDM Communication System Based on Experimental Data

End-to-end systems have been introduced to address the issue of independent signal processing module design in traditional communication systems, which prevents achieving global system optimization. However, research on indoor end-to-end Visible Light Communication (VLC) systems remains limited, especially regarding the channel modeling of high-speed, high-capacity Direct Current-biased Optical Orthogonal Frequency Division Multiplexing (DCO-OFDM) systems. This paper proposes three channel modeling methods for end-to-end DCO-OFDM VLC systems. The accuracy of the proposed methods is demonstrated through R-Square model fitting performance and data distribution analysis. The effectiveness of the proposed channel modeling methods is further validated by comparing the bit error rate (BER) performance of traditional receivers and existing deep learning (DL)-based receivers. The results show that the proposed methods can effectively mitigate both linear and nonlinear distortions. By employing these channel modeling methods, communication systems can reduce the spectral occupancy of pilot signals, thereby significantly lowering the complexity of traditional channel estimation methods. Thus, these methods are suitable for use in end-to-end VLC communication systems.

A Subspace-Based Frequency Synchronization Algorithm for Multicarrier Communication Systems

We present a subspace-based polynomial rooting algorithm to estimate the frequency bias (FB) of generalized frequency division multiplexing (GFDM) systems employing null subcarriers and repetitive sub-symbols. The estimation process is classified into fractional FB (FFB) and integer FB (IFB) estimation. The use of repetitive sub-symbols creates a quasi-periodic structure in the FB-distorted received signal, allowing the proposed algorithm to estimate the FFB using the root-MUSIC algorithm. Based on this, the proposed algorithm compensates for the FFB in the received signal and then estimates the null subcarrier pattern (NSP) in the frequency domain. As a result, the IFB estimate can be obtained in a maximum likelihood (ML) manner. Before the NSP estimation, this study uses a sub-symbol combiner to enhance signal strength of the FFB-aligned signal, ensuring the reliability of the IFB estimate. Computer simulations show that the proposed subspace-based algorithm has several advantages over traditional FB estimation methods: 1. Unlike some existing algorithms that use a training sequence to estimate FB, the proposed approach is a semi-blind algorithm because it can deliver information through repeated sub-symbols while estimating FB; 2. The proposed algorithm demonstrates excellent estimation accuracy compared to most traditional FB estimation algorithms; and 3. The proposed algorithm is computationally efficient, making it applicable to real-time applications in future communication systems.