State Estimation Method Research Articles

Machine Learning Applied to Lithium‐Ion Battery State Estimation for Electric Vehicles: Method Theoretical, Technological Status, and Future Development

ABSTRACTLithium‐ion batteries (LIBs) are extensively utilized in electric vehicles due to their high energy density and cost‐effectiveness. LIBs exhibit dynamic and nonlinear characteristics, which raise significant safety concerns for electric vehicles. Accurate and real‐time battery state estimation can enhance safety performance and prolong battery lifespan. With the rapid advancement of big data, machine learning (ML) holds substantial promise for state estimation. This paper systematically reviews several common ML algorithms, detailing the basic principles of each and illustrating their structures with flowcharts. We compare the advantages and disadvantages of various methods. Subsequently, we discuss feature extraction techniques employed in recent studies for estimating state of charge (SOC), state of health (SOH), state of power (SOP), and remaining useful life (RUL), as well as the application of these ML methods in state estimation. Finally, we discuss the challenges associated with using ML methods for state estimation and outline future development trends.

Data-driven parallel optimization method for sensor placement and state estimation based on generative adversarial principle in unobservable systems

Abstract Data-Driven State Estimation (DDSE) is characterized by low measurement requirements and high estimation accuracy, which provides the possibility of stable and efficient estimation for unobservable distribution systems with low measurement quantities. However, the lack of an efficient and flexible sensor placement method with DDSE at this stage hinders the development and application of DDSE in distribution networks. To address this issue, a data-driven parallel optimization method for sensor placement and state estimation based on the generative adversarial principle in unobservable systems is proposed in this paper. This method transforms sensor placement and state estimation into an adversarial learning model, solvable through gradient descent. The sensor placement optimization strategy generates a cost-effective placement scheme, while DDSE evaluates the sensor scheme, provides improvement suggestions, and enhances its estimation accuracy. Through adversarial training, the proposed scheme yields a significantly reduced number of sensor placement schemes compared to traditional methods, while maintaining high precision of DDSE. Simulation results on the IEEE-33 node system validate the effectiveness of the proposed approach.

Differential neural network based adaptive average output feedback control design for dosage determination on cancer based immunotherapy treatment

Immunotherapy involves natural and synthetic substances to stimulate the body’s immune response. This treatment approach is practical not only for addressing immune deficiencies but also for combating malignancies. This paper describes a non-parametric approximated adaptive control process for managing cancer dynamics under immunotherapy treatment, utilizing a combination of a differential neural network (DNN) observer and nonlinear control techniques such as sliding mode and local optimal strategies. By employing the state estimation and control methods, close tracking between the estimated states provided by the neural network and the cancer model dynamics is possible. Internal model reconstruction and an observer provided by a variable structure model are essential for controlling unknown plants. Furthermore, the control design has successfully reduced tumor cells despite uncertainties and external perturbations affecting cancer dynamics. This robustness enhances the reliability of the proposed design. A virtual real-time scheme was developed to demonstrate this controller’s feasibility in real clinical scenarios. In this scheme, a simulated patient generates variables of immunotherapy dynamics as electrical signals, which are then analyzed by a real-time project.

Distribution network topology identification method based on state estimation with mixed integer programming and structural equation model

Distribution network topology identification (DNTI) is an important prerequisite for distribution system operation. Frequent topology changes and limited measurement equipment make identifying the correct topology unavoidably challenging. To this end, this paper proposes a state estimation method for distribution network topology identification using a small amount of phasor measurement unit (PMU) measurement data. Firstly, this paper introduces the application of the structural equation model (SEM) in distribution networks and explains the relationship between branch currents and topology. Then, auxiliary variables are introduced for the feasible domain problem present in the algorithm, which improves the solvability of the algorithm. In addition, this paper reconsiders the operation mode constraints in terms of nodes from the perspective of distribution network operation mode. The Structural Equation Modeling-based Mixed Integer Programming (SEM-MIP) method proposed in this paper can be solved using existing commercial solvers, and its effectiveness has been verified by simulation in IEEE 33-node test system and IEEE 123-node test system.

Power Quality State Estimation for Distribution Grids Based on Physics-Aware Neural Networks—Harmonic State Estimation

In the transition from traditional electrical energy generation with mainly linear sources to increasing inverter-based distributed generation, electrical power systems’ power quality requires new monitoring methods. Integrating a high penetration of distributed generation, which is typically located in medium- or low-voltage grids, shifts the monitoring tasks from the transmission to distribution layers. Compared to high-voltage grids, distribution grids feature a higher level of complexity. Monitoring all relevant nodes is operationally infeasible and costly. State estimation methods provide knowledge about unmeasured locations by learning a physical system’s non-linear relationships. This article examines a new flexible, close-to-real-time concept of harmonic state estimation using synchronized measurements processed in a neural network. A physics-aware approach enhances a data-driven model, taking into account the structure of the electrical network. An OpenDSS simulation generates data for model training and validation. Different load profiles for both training and testing were utilized to increase the variance in the data. The results of the presented concept demonstrate high accuracy compared to other methods for harmonic orders 1 to 20.

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.

A State Estimation Method for Rectangular Singular Systems Based on State Decomposition

This paper proposes a state estimation method of linear discrete rectangular singular systems. The system is observable and regular, and the system matrix is rectangular without full column rank. To give the estimation of the state, the state is decomposed into two parts based on QR factorization, and the weighted least squares method is used to obtain the prediction of one part of the state. Then, the partial measurement equation is used to obtain the prediction of the other part of the state, and the projection theorem is used to obtain the state estimation value. Combined with the data-driven idea, a Kalman filtering algorithm based on historical data modeling is established. Finally, the feasibility and effectiveness of our approach is discussed and verified through performance analysis and numerical simulation perspectives.

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.

Bias and multiscale correction methods for variational state estimation

Data assimilation performance can be significantly impacted by biased noise in observations, altering the signal magnitude and introducing fast oscillations or discontinuities when the system lacks smoothness. To mitigate these issues, this paper employs variational state estimation using the so-called parametrized-background data-weak method. This approach relies on a background manifold parametrized by a set of constraints, enabling the state estimation by solving a minimization problem on a reduced-order background model, subject to constraints imposed by the input measurements. The proposed formulation incorporates a novel bias correction mechanism and a manifold decomposition that handles rapid oscillations by treating them as slow-decaying modes based on a two-scale splitting of the classical reconstruction algorithm. The method is validated in different examples, including the assimilation of biased synthetic data, discontinuous signals, and Doppler ultrasound data obtained from experimental measurements.

Study on Second-order RC Model Charge State Estimation Method for Lithium Battery Based on EKF Algorithm

In order to improve the estimation accuracy of the state of charge (SOC) of lithium-ion batteries, this paper proposes a SOC estimation method based on the second-order RC equivalent circuit model and the extended Kalman filter (EKF) algorithm. Firstly, the second-order RC equivalent circuit model is selected as the research object in this paper, and the parameters of the second-order RC model are identified by combining the hybrid pulse charging and discharging test and the 1stopt software, and then the extended Kalman filtering algorithm is applied under the MATLAB environment to estimate the SOC based on the second-order RC equivalent circuit model. The simulation results show that the adopted estimation method can accurately track the SOC trend of the battery compared with the actual state-of-charge (SOC) reference value. Through experimental analysis, the estimation results of the EKF algorithm combined with the second-order RC equivalent circuit model have a small error with the actual value, and the estimation accuracy is high and ideal.

Fast Motion State Estimation Based on Point Cloud by Combing Deep Learning and Spatio-Temporal Constraints

Moving objects in the environment have a higher priority and more challenges in growing domains like unmanned vehicles and intelligent robotics. Estimating the motion state of objects based on point clouds in outdoor scenarios is currently a challenging area of research. This is due to factors such as limited temporal information, large volumes of data, extended network processing times, and the ego-motion. The number of points in a point cloud frame is typically 60,000–120,000 points, but most current motion state estimation methods for point clouds only downsample to a few thousand points for fast processing. The downsampling step will lead to the loss of scene information, which means these methods are far from being used in practical applications. Thus, this paper proposes a motion state estimation method that combines spatio-temporal constraints and deep learning. It starts by estimating and compensating the ego-motion of multi-frame point cloud data and mapping multi-frame data to a unified coordinate system; then the point cloud motion segmentation model on the multi-frame point cloud is proposed for motion object segmentation. Finally, spatio-temporal constraints are utilized to correlate the moving object at different moments and estimate the motion vectors. Experiments on KITTI, nuScenes, and real captured data show that the proposed method has good results, with an average vector deviation of only 0.036 m and 0.043 m in KITTI and nuScenes under a processing time of about 80 ms. The EPE3D error under the KITTI data is only 0.076 m, which proves the effectiveness of the method.

Quantized State Estimation for Linear Dynamical Systems.

This paper investigates state estimation methods for dynamical systems when model evaluations are performed on resource-constrained embedded systems with finite precision compute elements. Minimum mean square estimation algorithms are reformulated to incorporate finite-precision numerical errors in states, inputs, and measurements. Quantized versions of least squares batch estimation, sequential Kalman, and square-root filtering algorithms are proposed for fixed-point implementations. Numerical simulations are used to demonstrate performance improvements over standard filter formulations. Steady-state covariance analysis is employed to capture the performance trade-offs with numerical precision, providing insights into the best possible filter accuracy achievable for a given numerical representation. A low-latency fixed-point acceleration state estimation architecture for optomechanical sensing applications is realized on Field Programmable Gate Array System on Chip (FPGA-SoC) hardware. The hardware implementation results of the estimator are compared with double-precision MATLAB implementation, and the performance metrics are reported. Simulations and the experimental results underscore the significance of modeling quantization errors into state estimation pipelines for fixed-point embedded implementations.

Large-scale magnetic target state estimation using model parameter optimization

Abstract Aiming at the problem of non-negligible target scale in the state estimation of magnetic targets, a state estimation method that requires only the measurement data of a single three-axis magnetic sensor and is insensitive to the initial value is proposed. Firstly, the state estimation model of a single three-component magnetic sensor is established based on a magnetic dipole array. A signal preprocessing method is designed to reject useless signals and keep the waveform intact. Five swarm intelligent optimization algorithms such as Particle Swarm Optimization (PSO), Artificial Hummingbird Algorithm (AHA), Artificial Rabbits Optimization (ARO), Grey Wolf Optimizer (GWO), and Improved GWO (IGWO) are introduced to perform state optimization, and two methods, such as Conjugate Gradient Least Squares (CGLS), and Stepwise Regression (SR), are introduced to calculate the magnetic moment parameters, and PSO-CGLS, AHA-CGLS, AHA-CGLS, ARO-CGLS, ARO-CGLS, ARO-CGLS, ARO-CGLS, ARO-CGLS, ARO-CGLS, ARO-CGLS, ARO-CGLS, and ARO-CGLS are designed in combination. CGLS, ARO-CGLS, GWO-CGLS, IGWO-SR, IGWO-CGLS, and six state estimation methods. In order to address the problem that the parameter optimization range is too large, the state to be estimated is adjusted from the initial state to the state at the moment of the maximum value of the magnetic field modulus, and the method of positive transverse distance estimation is used to narrow the range of positive transverse position optimization. Finally, numerical simulation tests and ship model tests are used for verification, and the results show that the proposed methods are accurate and can meet the needs of precise target state estimation.

Harmonic voltage phasor reconstruction and harmonic state estimation based on the measurement data of a capacitive voltage transformer

AbstractHarmonic state estimation, which highly depends on accurate synchronised phasors, is a crucial basis for the location, traceability, and governance of harmonics in power systems. However, most existing synchronous phasor measurement units (PMUs) provide power frequency phasors rather than harmonic phasors. In addition, as the dominant voltage signal provider for PMUs in power systems, capacitive voltage transformers (CVTs) have complex frequency responses and cannot be directly used for harmonic measurement. Therefore, accurate harmonic state estimation is difficult to achieve in applications. A method for harmonic voltage phasor reconstruction and harmonic state estimation based on the measurement data of a CVT is proposed. First, the reasons for harmonic voltage measurement errors were analysed. Second, the scattering parameter method was used to measure the wideband voltage transfer characteristics of CVT. Third, a voltage reconstruction method was proposed to improve the measurement accuracy and expand the frequency range of synchronous phasor measurement. Fourth, this method was applied to harmonic state estimation, and the performance of harmonic state estimation before and after voltage reconstruction was quantitatively compared. Results showed that the proposed method can remarkably improve the accuracy of harmonic state estimation. Finally, some factors, such as state observability, complex error disturbances, CVT structure, and harmonic order, influencing the performance of the proposed method were investigated. Results further demonstrated that the method has high accuracy, strong anti‐interference, and adaptability, and can provide basic information for harmonic localisation and traceability.

Dynamic state estimation of distribution network under Markov DOS attack

AbstractEnergy information is vulnerable to malicious denial of service (DoS) attacks due to the diversity and openness of the smart grid environment. In order to cope with the above challenges, this paper first proposes to adopt Markov hopping model to describe the random packet loss of measurement due to DoS attacks. Then, based on Holt two‐parameter exponential smoothing and untraced Kalman filtering techniques, a one‐step predictive value compensation method for measurement data loss is proposed, and an improved dynamic untraced particle filtering algorithm based on data fusion compensation strategy is designed. Finally, an IEEE‐30 bus system is used to simulate the proposed dynamic state estimation method, which proves that the proposed method can effectively resist DoS attack.

State estimation for constant-time labeled automata under dense time

In this paper, we focus on state estimation for constant-time labeled automata in a dense time context, i.e., the time constraints of the automata can be given according to real numbers. Given a sequence of timed observations (i.e., pairs of logical observations with their time stamps) collected from a system within a finite time window, a state estimation method is proposed to find the set of states in which the system might reside by the end of the time window. By using both labeling and timing information as well as the structure of the system, we can express any finite time evolution from one state to another into constraint satisfaction problems (CSPs). This structural analysis is independent of all collected sequences of timed observations and can be achieved offline, although its cost is exponential with respect to the number of states in the system. Consequently, two algorithms are designed to perform state estimation under a single observation and no observation, respectively, by solving a finite number of CSPs generated according to the system’s structural information. Both algorithms can be jointly used in an iterative approach to perform state estimation for any sequence of timed observations. In such a case, the number of generated CSPs in the algorithms increases linearly with respect to the length of the observed sequence.

Joint state and process inputs estimation for state-space models with Student’s t-distribution

This paper proposes a joint state and unknown inputs (UIs) discrete-time estimation method for industrial processes, represented by a state-space model. To cope with the outliers in process data, the measurement noise is characterized by the Student’s t-distribution. The identification of UIs is accomplished through the recursive expectation–maximization (REM) approach. Specifically, in the E-step, a recursively calculated Q-function is formulated by the maximum likelihood criterion, and the states and the variance scale factor are estimated iteratively. In the M-step, UIs are updated analytically together with the degree of freedom is updated approximately. The effectiveness of the proposed algorithm is validated using a quadruple water tank process and a continuous stirred tank reactor. It shows that the proposed method significantly enhances the robustness and estimation accuracy of state and UIs in industrial processes, effectively handling outliers and reducing computational demands for real-time applications.

Identifying traffic-induced bridge excitations using an optimized state estimation method

Identifying traffic-induced bridge excitations using an optimized state estimation method

A new dynamic state estimation method for distribution networks based on modified SVSF considering photovoltaic power prediction

The fluctuations brought by the renewable energy access to the distribution network make it difficult to accurately describe the state space model of the distribution network’s dynamic process, which is the basis of the existing dynamic state estimation methods such as the Kalman filter. The inaccurate state space model directly causes an error of dynamic state estimation results. This paper proposed a new dynamic state estimation method which can mitigates the impact of renewable energy fluctuation by considering PV power prediction in establishing distribution network state space model. Firstly, the proposed method mitigates the impact of renewable energy fluctuation by considering PV power prediction in establishing distribution network state space model. Secondly, SVSF filter is introduced to achieve more accurate estimation under noise. The case study and evaluations are carried out based on MATLAB simulation. The results prove that the smooth variable structure filter with photovoltaic power prediction has a better dynamic state estimation effect under the fluctuation of the distribution network compared with the existing Kalman filter.

Online state estimation in water distribution systems via Extended Kalman Filtering

Operators of water distribution systems (WDSs) need continuous and timely information on pressures and flows to ensure smooth operation and respond quickly to unexpected events. While hydraulic models provide reasonable estimates of pressures and flows in WDSs, updating model predictions with real-time sensor data provides clearer insights into true system behavior and enables more effective real-time response. Despite the growing prevalence of distributed sensing within WDSs, standard hydraulic modeling software like EPANET do not support synchronous data assimilation. This study presents a new method for state estimation in WDSs that combines a fully physically-based model of WDS hydraulics with an Extended Kalman Filter (EKF) to estimate system flows and heads based on sparse sensor measurements. To perform state estimation via EKF, a state-space model of the hydraulic system is first formulated based on the 1-D Saint-Venant equations of conservation of mass and momentum. Results demonstrate that the proposed model closely matches steady-state extended-period models simulated using EPANET. Next, through a holdout analysis it is found that fusing sensor data with EKF produces flow and head estimates that closely match ground truth flows and heads at unmonitored locations, indicating that state estimation successfully infers internal hydraulic states from sparse sensor measurements. These findings pave the way towards real-time operational models of WDSs that will enable online detection and mitigation of hazards like pipe leaks, main bursts, and hydraulic transients.