Extended Kalman Filter Observer Research Articles

Learning-Based Vehicle State Estimation Using Gaussian Process Regression Combined with Extended Kalman Filter

In order to address the challenge of accurate vehicle state estimation, especially in highly nonlinear and complex operating conditions, this paper proposes a learning-based method for vehicle state estimation. To achieve this, a novel theoretical framework is constructed that combines the model-based Extended Kalman Filter (EKF) with Gaussian process regression (GPR). By establishing a dynamic model of the vehicle and describing the errors using machine learning techniques, the sources of state estimation errors are analyzed. Furthermore, by considering the model uncertainty, an error prediction model is developed through GPR learning from real-world vehicle data. Combined with EKF, the proposed method enables high-precision online estimation of vehicle state. To validate the proposed method, tests are performed on a real vehicle test platform equipped with high-precision sensors and data acquisition equipment, under two different operating conditions: emergency and normal. The results are compared with those obtained using EKF and State Observer, which demonstrates a more accurate and adaptable vehicle state estimation, and provides a method for quantitatively describing the confidence interval of vehicle state estimation result.

Estimation of Lateral Velocity and Cornering Stiffness in Vehicle Dynamics Based on Multi-Source Information Fusion

<div>To address the challenge of directly measuring essential dynamic parameters of vehicles, this article introduces a multi-source information fusion estimation method. Using the intelligent front camera (IFC) sensor to analyze lane line polynomial information and a kinematic model, the vehicle’s lateral velocity and sideslip angle can be determined without extra sensor expenses. After evaluating the strengths and weaknesses of the two aforementioned lateral velocity estimation techniques, a fusion estimation approach for lateral velocity is proposed. This approach extracts the vehicle’s lateral dynamic characteristics to calculate the fusion allocation coefficient. Subsequently, the outcomes from the two lateral velocity estimation techniques are merged, ensuring rapid convergence under steady-state conditions and precise tracking in dynamic scenarios. In addition, we introduce a tire parameter online adaptive module (TPOAM) to continually update essential tire parameters such as cornering stiffnesses, with its effectiveness demonstrated through DLC and slalom simulation tests. Using a dual extended Kalman filter (DEKF) observer, the article allows for joint estimation of vehicle states and tire parameters. Ultimately, we offer a cost-effective estimation method of vital dynamic vehicle parameters to support the motion control module in autonomous driving.</div>

Nonlinear Time-Delayed Quorum Sensing System: State Estimation Via a Robust Observer

This paper proposes an innovative method to estimate the states in a nonlinear time-delayed quorum sensing (QS) model using an extended Kalman filter (EKF) observer. By addressing the inherent time delays in QS system which arise as a delayed response of bacteria to population fluctuations, the study introduces variable structure dynamical estimators, specifically the EKF, to approximate missing states based on available measurements. The EKF observer is applied to estimate four out of five internal non-measurable nonlinear states in a time-delayed QS model. This is the first attempt to utilize the EKF state estimation in nonlinear time delay QS models. The research contributes to the understanding of QS systems, provides insights into the communication dynamics inside biological systems, and offers a practical solution for estimating states in realistic scenarios.

Sensor Fusion for Power Line Sensitive Monitoring and Load State Estimation.

This paper deals with a specific approach to fault detection in transformer systems using the extended Kalman filter (EKF). Specific faults are investigated in power lines where a transformer is connected and only the primary electrical quantities, input voltage, and current are measured. Faults can occur in either the primary or secondary winding of the transformer. Two EKFs are proposed for fault detection. The first EKF estimates the voltage, current, and electrical load resistance of the secondary winding using measurements of the primary winding. The model of the transformer used is known as mutual inductance. For a short circuit in the secondary winding, the observer generates a signal indicating a fault. The second EKF is designed for harmonic detection and estimates the amplitude and frequency of the primary winding voltage. This contribution focuses on mathematical methods useful for galvanic decoupled soft sensing and fault detection. Moreover, the contribution emphasizes how EKF observers play a key role in the context of sensor fusion, which is characterized by merging multiple lines of information in an accurate conceptualization of data and their reconciliation with the measurements. Simulations demonstrate the efficiency of the fault detection using EKF observers.

Intelligent Deep Learning Estimators of a Lithium-Ion Battery State of Charge Design and MATLAB Implementation—A Case Study

The main objective of this research paper was to develop two intelligent state estimators using shallow neural network (SNN) and NARX architectures from a large class of deep learning models. This research developed a new modelling design approach, namely, an improved hybrid adaptive neural fuzzy inference system (ANFIS) battery model, which is simple, accurate, practical, and well suited for real-time implementations in HEV/EV applications, with this being one of the main contributions of this research. On the basis of this model, we built four state of charge (SOC) estimators of high accuracy, assessed by a percentage error of less than 0.5% in a steady state compared to the 2% reported in the literature in the field. Moreover, these estimators excelled by their robustness to changes in the model parameters values and the initial “guess value” of SOC from 80–90% to 30–40%, performing in the harsh and aggressive realistic conditions of the real world, simulated by three famous driving cycle procedure tests, namely, two European standards, WLTP and NEDC, and an EPA American standard, FTP-75. Furthermore, a mean square error (MSE) of 7.97 × 10−11 for the SOC estimation of the NARX SNN SOC estimator and 5.43 × 10−6 for voltage prediction outperformed the traditional SOC estimators. Their effectiveness was proven by the performance comparison with a traditional extended Kalman filter (EKF) and adaptive nonlinear observer (ANOE) state estimators through extensive MATLAB simulations that reveal a slight superiority of the supervised learning algorithms by accuracy, online real-time implementation capability, in order to solve an extensive palette of HEV/EV applications.

DTC-SVM οf Sensorless Five-phase Induction Machine Using Extended Kalman Filter

This work relates to the study of direct torque control based on space vector modulation applied on five-phase induction machine. It is well established that the conventional direct torque control using hysteresis comparators suffers from high torque ripples and variable switching frequency. The most common solution to those problems is the use of space vector modulation. In the other hand, this paper aims also to design an extended Kalman filter observer for speed/flux estimation, which improves not only the control performances by using a sensorless algorithm but also can lower the cost and increase the reliability of the system. Both theoretical principle and simulation results of the sensorless control method of multiphase drive will be conducted to verify the effectiveness of the proposed control approach.

A Parameter-Free Method for Estimating the Stator Resistance of a Wound Rotor Synchronous Machine

This paper presents a new online method based on low frequency signal injection to estimate the stator resistance of a Wound Rotor Synchronous Machine (WRSM). The proposed estimator provides a parameter-free method for estimating the stator resistance, in which there is no need to know the values of the parameters of the machine model, such as the stator and rotor inductances or the rotor flux linkage. In this method, a low frequency sinusoidal current is injected in the d axis of the stator current to produce a sinusoidal flux in the stator. In this paper, it is shown that the phase difference between the generated sinusoidal flux and the injected sinusoidal current is related to the stator resistance mismatch. Using this phase difference, the stator resistance is estimated. To validate the proposed model-free estimator, simulations were performed with Matlab Simulink and the results were compared with the extended Kalman filter observer. Finally, experimental tests, under different conditions, were performed to estimate the stator resistance of a WRSM.

Coordinated Lateral Stability Control of Autonomous Vehicles Based on State Estimation and Path Tracking

This paper proposes a coordinated control system of autonomous vehicles’ lateral stability based on state estimation and path tracking, which contributes to enhancing path-tracking capability and at the same time maintaining the stability of autonomous vehicles driving in complex and dynamic road conditions. First, an extended Kalman filter observer is designed to estimate the vehicle parameters. Then, based on the single-point preview theory, an adaptive preview time model is built for the accuracy of path tracking. When designing the direct yaw-moment controller, sideslip angle and yaw rate, two critical parameters for lateral dynamic stability control are considered, and the single-wheel braking method is utilized to reasonably distribute the additional yaw moment to a certain wheel. To make full use of active front steering and direct yaw-moment control, the critical steering angle of the front wheel is determined, and a switching function is formulated. Co-simulation shows that the suggested coordinated control system can effectively strengthen maneuvering stability and simultaneously satisfy tracking accuracy.

Digital Twin Model of Electric Drives Empowered by EKF.

Digital twins, a product of new-generation information technology development, allows the physical world to be transformed into a virtual digital space and provide technical support for creating a Metaverse. A key factor in the success of Industry 4.0, the fourth industrial revolution, is the integration of cyber-physical systems into machinery to enable connectivity. The digital twin is a promising solution for addressing the challenges of digitally implementing models and smart manufacturing, as it has been successfully applied for many different infrastructures. Using a digital twin for future electric drive applications can help analyze the interaction and effects between the fast-switching inverter and the electric machine, as well as the system's overall behavior. In this respect, this paper proposes using an Extended Kalman Filter (EKF) digital twin model to accurately estimate the states of a speed sensorless rotor field-oriented controlled induction motor (IM) drive. The accuracy of the state estimation using the EKF depends heavily on the input voltages, which are typically supplied by the inverter. In contrast to previous research that used a low-precision ideal inverter model, this study employs a high-performance EKF observer based on a practical model of the inverter that takes into account the dead-time effects and voltage drops of switching devices. To demonstrate the effectiveness of the EKF digital twinning on the IM drive system, simulations were run using the MATLAB/Simulink software (R2022a), and results are compared with a set of actual data coming from a 4 kW three-phase IM as a physical entity.

Concentration Estimation for Fuel Cells: Design of Experiments, Nonlinear Identification, and Observer Design With Experimental Validation

Fuel cells (FCs) are promising eco-friendly power sources. Nevertheless, there are challenges to overcome if they are to be widely deployed in areas such as degradation avoidance and control, where the knowledge of the unavailable concentrations is crucial. In this respect, observers can provide unavailable quantities based on an estimation algorithm and available measurements. This paper presents an FC concentration observer design workflow, covering the model-based design of experiments (DOE), their execution, systematic nonlinear identification, and measurement-based validation. The model-based DOE and the validation with a mass spectrometer, including dynamic operation, are unique for PEMFC observers. The workflow is demonstrated with a constrained extended Kalman filter observer on a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {30 \text {k} \text {W} }$ </tex-math></inline-formula> polymer electrolyte membrane FC (PEMFC) test stand. A control-oriented model serves as the workflow basis, and the DOE is based on optimizing the parameter sensitivity. The test stand delivers the measurements, the parametrization comprises a sensitivity analysis, and the experimentally validated observer yields outstanding concentration estimation performance.

Design of extended Kalman filter observer coupled to ammonia cross-sensitivity model for an SCR system

Commercial diesel vehicles that comply the China/EURO VI emission regulations are generally equipped with selective catalytic reduction (SCR) systems for reducing [Formula: see text] emission and [Formula: see text] sensors at its downstream for accurate closed-loop control. However, [Formula: see text] sensors have significant ammonia cross-sensitivity pushing up their readings. Moreover, for the closed-loop control of SCR systems effectively estimating the critical states from the [Formula: see text] sensor readings remains a further challenge. In this paper, an ammonia cross-sensitivity model with segmented sin and quadratic composite functions describing high frequency characteristics is established by analyzing the experimental data of an SCR system. A control-oriented three-states model of an SCR system is established, and based on it an extended Kalman filter (EKF) observer coupled to the ammonia cross-sensitivity model is proposed. The simulation results show that from the [Formula: see text] sensor readings the EKF observer can effectively estimate the deterioration trend of the [Formula: see text] and [Formula: see text] emissions, and describe the dynamic change process of the ammonia coverage rate. The experimental results under the four non-excitation cycles show that the EKF observer can effectively estimate the deterioration trend, that the average estimated accuracy of [Formula: see text] and [Formula: see text] during their deterioration stage can respectively reach 86.16% and 54.87%, and that the observer has better robustness to disturbances from the operating conditions.

A Position Sensorless Closed-Loop Control Mode of a Three-Phase Hybrid Stepper Motor

The demand for the high-performance and low-cost position control actuators in many applications promotes the development of three-phase hybrid stepper motors. The torque ripple, loss, and pullout torque of the motor are the key factors to be considered in the motor application. In order to solve the problems of the open-loop control mode, this paper proposes a new “sensorless closed-loop” control mode to significantly improve the performance of three-phase hybrid stepper motors. This control mode is developed by estimating the rotor position with the Extended Kalman filter observer, thereby realizing the closed-loop control of the motor with sensorless technology. This paper illustrates the effects of this control mode by analyzing motor noise, losses, and pullout-torque. The results show that the use of the “sensorless closed-loop” control mode presented can effectively improve the performance of the stepper motor while maintaining the advantages of the motor in terms of cost and size. These results have positive significance for the development, application, and promotion of high-performance three-phase hybrid stepper motor systems.

DOA-Based 3D Tracking With Factor Graph Technique for a Multi-Sensor System

In this paper, a direction-of-arrival (DOA)-based factor graph (FG) technique is proposed for three-dimensional (3D) tracking. Multiple sensors are utilized in this system, which could measure both azimuth and elevation DOAs emitted from an anonymous target. To realize non-linear tracking, a modified extended Kalman filter (EKF) is proposed. Specifically, on the one hand, the proposed EKF observer is no longer independent of the EKF predictor, but instead takes the predicted target location into its operation. With this technique, the accuracy of detection is improved while the computational complexity is dramatically reduced. On the other hand, the variance of the EKF observer error is estimated in real time, based on the predicted Cramer-Rao bound (PCRB). Therefore, the robustness of detection can be guaranteed even with an unstable sensing environment. In this sense, the EKF observer and the EKF predictor are operated in an integrated FG framework. The advantages of the proposed technique are verified by both complexity analyses and simulation results.

Robust dichotomy solution-based model predictive control for the grid-connected inverters with disturbance observer

This paper proposes a robust dichotomy-based model predictive control (DS-MPC) with a fixed switching frequency for the grid-connected inverter (GCI). The proposed fast dichotomy algorithm can select and deduce the optimal voltage vector dynamically through the space vector plane. Therefore, the proposed DS-MPC strategy could ensure dynamic performance and steady-state performance as well. Also, the current control robustness can be improved through DS-MPC with disturbance observer (DO) based on the extended Kalman filter (EKF). The novelty of this control is that the current control with fast dynamic response can be realized in the weak grid, even if the grid voltages are greatly distorted. Simulation and hardware experiments on the weak grid validate the effectiveness of the proposed DS-MPC with the EKF observer approach.

Optimum Design of Fractional Order PIᵅ Speed Controller for Predictive Direct Torque Control of a Sensorless Five-Phase Permanent Magnet Synchronous Machine (PMSM)

In both direct torque control (DTC) and predictive direct torque control (PDTC) strategies, just single voltage vector is applied. The question arose, is this applied vector the optimumin terms of minimizing torque and stator flux ripples? In DTC, it may not be the optimum one. However, in case of PDTC, there is a possibility to evaluate the performance of different voltage vectors, where a cost function is proposed to determine the appropriate voltage vector that brings the lowest torque and stator flux ripple within one cycle. On the other hand, PI controller provides a good performance but if the parameters change, the system may lose its performance. With the aim of enhancing the robustness of the PDTC scheme, a fractional order PI controller is proposed that can be considered as a generalization of the classical PI controller, and to set its parameters, a Grey Wolf Optimization algorithm is employed. Furthermore, omitting the sensor increases reliability and decrease the size and cost of the drive system. For these reasons, an extended Kalman filter observer is adopted, where the rotor speed and rotor position as well as the load torque are estimated. In this work, a fractional order PI controller tuned by GWO for PDTC of a five-phase permanent magnet synchronous machine (PMSM) based on EKF observer is presented. Analysis of simulation results exhibit clearly the efficiency and robustness of the suggested control compared to conventional DTC based on classical PI controller.

EKF-Based Actuator Fault Detection and Diagnosis Method for Tilt-Rotor Unmanned Aerial Vehicles

Flight safety is of vital importance for tilt-rotor unmanned aerial vehicles (UAVs), which can take off and land vertically as well as cruise at high speed, especially in different kinds of complex environment. As being the executor of the flight control, the actuator failure will directly affect the controllability of the tilt-rotor UAV, and it has high probability of causing fatal personal injury and financial loss. However, due to the limitation of weight and cost, small UAVs cannot be equipped with redundant actuators. Therefore, there is an urgent need of fault detection and diagnosis method for the actuators. In this paper, an actuator fault detection and diagnosis (FDD) method based on the extended Kalman filter (EKF) and multiple-model adaptive estimation (MMAE) is proposed. The actuator deflections are added to the state vector and estimated using EKF. The fault diagnosis algorithm of MMAE could assign a conditional probability to each faulty actuator according to the residual of EKF and diagnose the fault. This paper is structured as follows: first, the structure and model of tilt-rotor UAV actuator are established. Then, EKF observers are introduced to estimate the state vector and to calculate residual sequences caused by different faulty actuators. The residuals from EKFs are used by fault diagnosis algorithm to assign a conditional probability to each failure condition, and fault type can be diagnosed according to the probabilities. The FDD method is verified by simulations, and the results demonstrate that the FDD algorithm could accurately and efficiently diagnose actuator fault without any additional sensor.

Mode-switch model predictive controller with “pre-contact” method for alleviating driveline vibration of electric vehicles considering backlash

The backlash between engaging components in a driveline is inevitable and contributes to the nonlinearity of the driveline. The existing motor controllers of an electric vehicle usually ignore the backlash, which often brings impacts and vibration. This paper proposes an active driveline vibration controller for electric vehicles. A nonlinear driveline model considering backlash and wheel slip ratio is established in MATLAB/Simulink, and the results of bench test proved that the model could effectively reflect the transient dynamics of the electric driveline. Based on this model, a dual extended Kalman filter observer is designed to estimate both the system state variables and vehicle mass, which are essential information for the controller design. Then, a mode-switch model predictive controller based on two linearized models is proposed to alleviate the impacts and vibration caused by the transient change of motor torque. The proposed controller would identify whether the driveline is operating in “contact mode” or “backlash mode” and thus generates an optimal motor torque by solving a Quadratic Programing. Note that the control targets and model structures in two modes are different. Furthermore, a “pre-contact” method is proposed as an additional part to handle the condition when motor command torque is zero. Simulation results demonstrate that the proposed controller can effectively alleviate the impacts and vibration in the electric driveline while keeping the torque delay negligible. Moreover, the robustness of the proposed controller against estimation errors and system noises are discussed.

Blockage Detection in Pipeline Based on the Extended Kalman Filter Observer

Currently numerous approaches with various applicability have been generated in order to detect damage in pipe networks. Pipeline faults such as leaks and partial or complete blockages usually create serious problems for engineers. The model-based leak, as well as block detection methods for the pipeline systems gets more and more attention. Among these model-based methods, the state observer and state feedback based methods are usually used. While the observability, as well as controllability, are taken to be the prerequisites for utilizing these techniques. In this work, a new technique based on the extended Kalman filter observer is proposed in order to detect and locate the blockage in the pipeline. Furthermore, the analysis of observability and controllability in the pipe networks is investigated. Important theorems are given for testing the observability as well as controllability of the pipeline system.

An EKF-Based Fast Tube MPC Scheme for Moving Target Tracking of a Redundant Underwater Vehicle-Manipulator System

This paper presents a control scheme for addressing the moving target grabbing problem by a kinematically constrained redundant underwater vehicle-manipulator system (UVMS) in the presence of unmodeled uncertainties, sensory detecting noises, and time-varying external disturbances. Our proposed control scheme is designed by a robust fast tube model predictive controller (FTMPC) with an extended Kalman filter (EKF) target observer. The proposed robust FTMPC consists of an online fast nominal MPC and an online ancillary nonlinear controller to overcome the uncertainties and disturbances of the UVMS. The problem of the UVMS kinematic redundancy and mechanical/physical constraints is translated into a part of online optimization of FTMPC. The feasibility and stability of the FTMPC are proved. The proposed EKF observer is used to estimate the moving target trajectory and overcome the sensory measurement (system) noises, which can eliminate the assumption that most prior existing research works need to know the tracking reference trajectory precisely. Finally, the effectiveness of the proposed control scheme is verified through a series of UWSim simulations by the 6-degree-of-freedom (DoF) vehicle and 5-DoF manipulator GIRONA500 UVMS.

State estimation and damping control for unmanned ground vehicles with semi-active suspension system

The new type of transportation based on intelligent driverless vehicles will bring great changes to people’s travel modes and put forward higher requirements for the ride comfortability of vehicles. This paper presents a new observing algorithm to estimate the suspension states in real time and cooperate with sliding mode controller to improve the ride comfortability. First, the nonlinear model of an air suspension system equipped with a continuously controllable damper is described in detail. Then, this nonlinear suspension model is linearized precisely based on the differential geometry theory; a linear Kalman filter observer is implemented for this linearized model; through the coordinate reverse transformation, the designed linear observer is transformed into a nonlinear one, which will be suitable for the original nonlinear system, so that, the proposed state observer can estimate all the states of the nonlinear quarter car suspension system. Then, in this nonlinear suspension system, a model reference sliding mode controller is designed to continuously control the damping force to improve the ride comfortability. Finally, the effectiveness and advantage of the proposed feedback linearization Kalman observer is illustrated by comparing with a traditional extended Kalman filter observer. The simulation research shows that the proposed feedback linearization observer enjoys a better estimation accuracy, higher operation efficiency, and greater control performance while cooperating with the sliding mode controller in ride comfortability control.