Kalman Estimator Research Articles

Gust load alleviation of a flexible flying wing with linear parameter-varying modeling and model predictive control

This paper presents a practical model predictive control (MPC) framework for gust load alleviation of a flexible flying wing. Both the controller solving and state estimation are based on a reduced-order model, which features a linear parameter-varying (LPV) form, avoiding online linearization and reducing the scale of the corresponding quadratic programming problem. An improved modeling and model reduction process is used to enhance modeling efficiency and ensure that the reduced-order model can accurately capture the rigid-flexible coupled characteristics of the flexible flying wing under arbitrary gusts. By reconstructing the output of the control-oriented model to include both rigid-body motion and flexible vibrations, the rigid-flexible coupled multi-objective control is established as an MPC problem for reference tracking. The online optimization is formulated in a sparse fashion and combined with an iterative algorithm based on predicted trajectories, describing the variation of model dynamics within the prediction horizon more accurately. With a time-varying Kalman estimator for state updating, the closed-loop simulations are performed for gust alleviation performance validation. Additionally, the real-time potential of the proposed MPC framework is demonstrated through Monte Carlo simulations.

Publisher Correction: A two-state Kalman estimator for atomic gravimetry

Publisher Correction: A two-state Kalman estimator for atomic gravimetry

A Real-Valued Kalman Estimation Method for Harmonic Signal Analysis in Biomedical Applications

This work presents a methodology for obtaining the harmonic estimation of biomedical signals such as electrocardiogram, cardiorespiratory and blood pressure signals. The proposed methodology is achieved using polynomial approximation and the Kalman filter. As advantage, the technique includes instant estimations of signal harmonics and its derivatives using a real-valued model. Furthermore, a comparison of the results is conducted with the Savitzky-Gola, nonlinear tracking differentiator methods, extended state observer and digital differentiator base on Taylor series. The results suggest that the proposed method has the potential to enhance the quality of signal measurements, especially in the presence of noise.

Design of robust active suspension system for performance improvement and vibration control of railway vehicles: An H∞andμ-synthesis perspective

The ride comfort of a high-speed railway vehicle is a significant factor in assessing its performance. Despite having sound suspension systems and efficient control algorithms, the suspension system performance deteriorates with time. Hence, in this paper, a robust active vibration control system used in railway vehicles has been proposed. For analysis, a 27-degree of freedom (DOF) model consisting of structured and unstructured uncertainties has been considered. Two different robust control techniques, [Formula: see text] and [Formula: see text]-synthesis integrated with the Kalman estimator, have been adopted. The robust stability and the robust performance of the proposed control strategies have been evaluated using the structured singular values. The time and frequency domains of the closed loop perturbed responses to random track disturbances are shown. The root mean square (RMS) values of the accelerations of the car bodies are used to compare the suggested control schemes to the passive system. The primary focus of this study is to examine the level of ride comfort provided by the railway vehicle. To achieve this, simulated findings are compared and verified against experimental data collected and reported by the Research Designs and Standards Organization (RDSO). The observational data demonstrates that the results obtained from the suggested control methods are in close agreement with the experimental findings, with a minimal disparity ranging from 2.36% to 8.81% for lateral motion and 2.84% to 6.30% for vertical motion. Also, the % improvement of RMS values with [Formula: see text]-synthesis controller confirms the enhancement of the ride comfort as compared to other techniques.

Modeling of a six-degree-of-freedom magnetic levitation platform actuated by noncontact Lorentz forces

In this study, the modeling of a six-degree-of-freedom (DOF) magnetic levitation platform actuated by noncontact Lorentz forces was analyzed. First, an analytic model of the actuator forces was studied, and the magnetic flux density in the working gap of the actuators was established using the Image Method, Ampere molecular hypothesis, and Biot–Savart law. The dynamics model of the floater actuated by the actuators was then built using the Newton–Euler method. Moreover, the double-pendulum chaotic nonlinear system of the hoisted floater was simplified as a single-DOF system, in which the interaction effects between two DOFs were considered. Furthermore, modeling of the platform control system was performed, which included an acceleration measuring unit with six uniaxial accelerometers, a position measuring unit with three two-dimensional PSDs, and a control unit that decouples the six-DOF control. Finally, an experimental setup was built to perform ground tests on the platform. The results verified the platform modeling; translational and rotational positioning accuracies were approximately 5 μm and 40 μrad at the six DOFs, respectively, and the vibrational suppression efficiencies were greater than 90% for low frequency disturbances. Moreover, Kalman estimators and disturbance observers were introduced into the controller to estimate the movement of the floater and observe the direct disturbance. Simulation testing demonstrated a significant improvement in the vibration-suppression performance of the platform.

Vibration suppression of base-excited rotors supported by active magnetic bearings based on an augmented Kalman compensator

Rotor systems supported by active magnetic bearings (AMBs) on a moving base, such as ships and vehicles, usually experience increased vibration due to the additional excitations, known as base excitations. In this paper, an augmented Kalman estimator (AKE) based compensator is proposed to suppress the base-excited vibration of an AMBs-rotor system. In the design, the AKE is employed to optimize the gain vectors online with an inaccurate model and noisy response. The optimized gain vectors are subsequently multiplied by the corresponding base-excited parameters to calculate the compensation current for suppressing the base-excited vibration. As a result, the compensation current in phase with the base excitation results in great suppression of the base-excited vibration. Meanwhile, the elimination of the necessity for precise modeling makes the proposed compensators highly robust. In order to provide useful guidance for the selection of the covariance matrices, the influences of the covariance matrices on the compensator performance are thoroughly analyzed. Finally, through the numerical and experimental results under base translation and base swing, the effectiveness and robustness of the proposed compensator are demonstrated.

Illumination pattern optimization in tomography based on the Kalman estimation filter and optimal experiment design

Tomography is widely used in medical imaging or industrial non-destructive testing applications. One costly and time consuming operation in any form of tomography is the process of data acquisition where a large number of measurements are made and collected data is used for image reconstruction. Data acquisition can slow down tomography to the point that the scanner cannot catch up with the speed of changes in the medium under test. By optimizing the information content of each measurement, we can reduce the number of measurements needed to achieve the target precision. Development of algorithms to optimize the information content of tomography measurements is the main goal of this article. Here, the dynamics of the medium and tomography measurements are formulated in the form of a Kalman estimation filter. A mathematical algorithm is developed to compute the optimal measurement matrix which minimizes the uncertainty left in the estimation of the distribution the tomography scanner is reconstructing. Results, as presented in the paper, show noticeable improvement is the quality of generated images when the medium is scanned by optimal measurements instead of traditional raster or random scanning protocols.

Intention inference‐based interacting multiple model estimator in photoelectric tracking

AbstractAiming to improve the estimation and prediction accuracy of a target's position, this paper proposes a state estimation method for photoelectric tracking systems, based on the evaluation of the tracked target's motion intention. Traditional photoelectric tracking systems utilize external physical quantities such as the position, velocity, and acceleration of the target as the estimated states. While this method can output good results for pre‐modelled target positions, it struggles to maintain the accuracy when facing manoeuvering targets or complex motion patterns targets. Here, the relevant parameters of the tracked target's motion intention are directly estimated innovatively, like estimating the circling point position rather than the circular flying target's position and velocity. This approach enables recognizing the target's motion intention and leads to precise estimation, which specifically consists of an interacting multiple model approach, multiple unscented Kalman estimators, and a robust estimator. The effectiveness and stability of this estimator are validated through software simulations and experiments on a dual‐reflection mirror platform.

Augmented Kalman Estimator and Equivalent Replacement Based Taylor Series-LQG Control for a Magnetorheological Semi-Active Suspension

This research presents an augmented Kalman estimator and an equivalent replacement-based Taylor series (ERBTS)-linear quadratic Gaussian (LQG) control strategy to cope with the control accuracy and response delay of magnetorheological (MR) dampers for vehicle semi-active suspensions. The parameters in the MR model are identified from experimental measurements. Then, two main sources of control error, namely, modelling error and real-time variety of the MR damper output force, are defined as an integrated compound real-time variety. Subsequently, they are written into a differential equation with characteristics of the minimum system to augment the state equation of the semi-active suspension system. The augmented Kalman estimator is constructed to estimate the abovementioned compound real-time variety. To calculate an acceptable time-delay compensation predictive control force, an equivalent operation is implemented beforehand in the suspension comprehensive performance index by replacing a part of the squared time-delay control force with the corresponding predictive control force. Simulation results verify the effectiveness of the proposed augmented Kalman estimator, and the newly developed ERBTS-LQG controller almost achieves control effectiveness of the ideal time delay free semi-active suspension.

An improved two-phase robust distributed Kalman filter

To enhance the efficacy of the distributed filter in mitigating heavy-tailed non-Gaussian noise and accommodating intricate environments, this study investigates the utilization of absolute and relative measurement information for the realization of multi-target cooperative positioning and proposes an improved robust distributed Kalman filter in this paper. The method is divided into two phases. Firstly, absolute measurement information undergoes processing via the standard Kalman filter, yielding the Kalman estimation value for the first phase, subsequently serving as the time update value for the second phase. Next, a robust Kalman filter based on Student’s t distribution is used to process relative measurement information for measurement updates, resulting in more accurate estimates. Simulation results demonstrate that the proposed approach effectively approximates the posterior probability distribution, leading to enhanced stability and accuracy in positioning within environments characterized by both Gaussian and heavy-tailed non-Gaussian noise.

Robust sequential fusion Kalman estimators with asymptotic equivalence and stability for networked uncertain sensor systems

For networked uncertain sensor systems (NUSSs) with an improved unified sensor model with “hard” and “soft” sensors including five uncertainties plus two-step random measurement delays and colored measurement noises, applying the block matrix inversion formula, a new sequential inverse covariance fusion (SICF) approach is presented. It can sequentially compute the global inverse covariance according to the time order of the received data, but need not wait until all data are received. The corresponding minimax robust time-varying and steady-state sequential fusion (SF) Kalman estimators (predictor, filter, and smoother) are presented in the sense that their actual error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. They have lower computation complexities and higher accuracies equivalent to ones of the robust optimal batch-fusion (BF) Kalman estimators, and are suitable for real-time applications. Their asymptotic equivalence, absolute asymptotic stability, and accuracy relations are proved. Their strict complexity analysis is given. They constitute a novel universal robust SF estimation, convergence and stability theory for NUSSs. One simulation example applied to the uncertain ARMA signal processing verifies the effectiveness of the proposed approach and theory.

Image-based visual servoing with Kalman filter and swarm intelligence optimisation algorithm

The article proposes a new Kalman depth estimation and an improved swarm intelligence optimisation algorithm for adaptive tuning of servo gain for image-based visual servo control. First, a Kalman depth estimation model is established from the principle of image-based visual servoing, and two state equations are designed for depth estimation based on the number of state quantities. Second, the improved sparrow search algorithm is proposed to tune the servo gain adaptively to improve the convergence speed and stability. To verify the effectiveness of the proposed method, the conventional image-based visual servoing and conventional Kalman estimation are reproduced and compared with the proposed method, and the simulation is completed on the Simulink simulation platform for verification. Finally, the experiments are completed in the robotic arm experimental platform. Both the simulation and experimental results show the effectiveness of the proposed method, which reduces the redundancy of the camera and shortens the convergence time.

Continuous Kalman Estimation Method for Finger Kinematics Tracking from Surface Electromyography.

Deciphering hand motion intention from surface electromyography (sEMG) encounters challenges posed by the requisites of multiple degrees of freedom (DOFs) and adaptability. Unlike discrete action classification grounded in pattern recognition, the pursuit of continuous kinematics estimation is appreciated for its inherent naturalness and intuitiveness. However, prevailing estimation techniques contend with accuracy limitations and substantial computational demands. Kalman estimation technology, celebrated for its ease of implementation and real-time adaptability, finds extensive application across diverse domains. This study introduces a continuous Kalman estimation method, leveraging a system model with sEMG and joint angles as inputs and outputs. Facilitated by model parameter training methods, the approach deduces multiple DOF finger kinematics simultaneously. The method's efficacy is validated using a publicly accessible database, yielding a correlation coefficient (CC) of 0.73. With over 45,000 windows for training Kalman model parameters, the average computation time remains under 0.01 s. This pilot study amplifies its potential for further exploration and application within the realm of continuous finger motion estimation technology.

PREDICTION MODEL OF PITCH ANGLE OF GREENHOUSE ELECTRIC TRACTORS BASED ON TIME SERIES ANALYSIS

The pitch angle of greenhouse tractors changes when operating on rough soil pavement. As a result, the feedback signal lags behind the tractor motion attitude signal, thereby affecting the real-time control of tilling depth. In this study, a pitch angle prediction model of greenhouse electric tractor was proposed based on extended Kalman filter (EKF) and time series analysis to improve the dynamic response speed of tilling depth regulation by providing predictive information for advance control. EKF was used to track the tilling depth of greenhouse electric tractor in real time, and an auto-regressive moving average model (ARMA) was established for the obtained time series data. ARMA (2, 1) was designed as the pitch angle prediction model of greenhouse electric tractors by constructing a simulation model. Inertia measurement unit (IMU) of tractor was used to construct the extended Kalman estimation model of the pitch angle. Actual vehicle tests were carried out under different working conditions. Results show that the estimated values obtained under two operating conditions have a high correlation with the measured values, with correlation coefficients(R) of 0.9504 and 0.9734, root mean square error (RMSE) of 0.2355 and 0.2173, and maximum absolute error (MAE) of 0.1929 and 0.1703, respectively. And ,the MAE and the RMSE of the predicted and measured values of ARMA (2,1) model approximately have the same value under the two conditions, with with the R of 0.9665 and 0.9755, the RMSE of 0.2002 and 0.1812, and the MAE of 0.1578 and 0.1387, respectively. The effectiveness of ARMA (2, 1) as the pitch angle estimation and prediction model of greenhouse electric tractors is verified. This study provides theoretical reference for designing the control law of tilling depth stability in subsequent greenhouse operation. Keywords: Time series, prediction, pitch angle,electric tractor

Speed sensorless Adaptive Power Control for photovoltaic-fed water pump using Extended Kalman–Bucy filter

In this study, a speed sensorless control method is proposed for a photovoltaic water-pump system operating under variable atmospheric conditions. The developed system not only continuously determines the maximum power point of the photovoltaic system but also generates a reference speed appropriate for each power value produced. The MATLAB/Simulink model of the driver system incorporates Adaptive Power Control, Direct Torque Control, a 3-phase induction motor, and the power plant. The determination of the maximum power point of the photovoltaic system and the input reference speed information for the Direct Torque Control under varying atmospheric conditions is accomplished through the application of the Adaptive Power Control algorithm. Notably, the control process operates as a closed-loop system without the requirement of a speed sensor. Instead, the Extended Kalman–Bucy estimator is employed for speed estimation. Empirical evaluation of the proposed method was conducted under constant temperature conditions and varying irradiance values. The results clearly illustrate the consistent operation of the motor, with a constant torque production aligned with each identified maximum power point corresponding to distinct irradiance levels. The control system demonstrates robust performance and operational efficiency across the entire range of operating points. The efficacy of the Kalman estimator in monitoring the reference speed, the utilization of a single solar radiation sensor, and the successful implementation of sensorless operation are significant advantages of the developed adaptive approach. The demonstrated performance of the proposed system showcases its potential for enhancing the efficient and reliable control of photovoltaic water-pump systems in real-world applications.

Heat exchanger networks: A predictive control approach

This work demonstrates the development of a practical predictive control approach to regulate the outputs of a network of heat exchangers. The full nonlinear continuous-time dynamic of the network is introduced to simulate the real process. Whereas a discrete linear and simpler version of this dynamic is employed to construct the predictive controller as well as an extended Kalman estimator. The presented algorithm is a time-varying model predictive control (MPC) where the simplified model is successively linearized on-line around the current available measurements. For the closed-stability of the introduced MPC scheme, a modified method is suggested to design terminal stabilizing weights where reference tracking problem, external disturbance dynamics, as well as the proper dynamics of a heat exchanger with bypass are all considered. The on-line updated extended Kalman estimator is utilized to estimate both the process states and unknown disturbances. Thanks to the successive linearization technique, the introduced predictive controller benefits from efficient online computations and online adaptations in operation points. Nonetheless, an accurate model of the heat exchanger is essential. Compared with a typical linear MPC, it is concluded that the presented predictive algorithm produces satisfactory results for disturbance rejection and switched operation points circumstances.

Sliding Mode Control for Sensorless Speed Tracking of PMSM with Whale Optimization Algorithm and Extended Kalman Filter

This paper proposes a sensorless speed control strategy for a permanent magnet synchronous motor system. Sliding mode control with a whale optimization algorithm was developed for robustness and chattering reduction. To estimate the position and speed of the rotor, an extended Kalman filter using Gaussian process regression was designed. In this controller, the whale optimization method adjusts the switching gain to minimize the tracking error. However, it provides chattering reduction and robustness, owing to the adaptive gain. The extended Kalman estimator calculates the rotor speed by using the current and voltage of the motor as an observer. The observer ensures the high reliability and low cost of the controller. The noise covariance and weight matrices that validated the performance of the estimation were optimized using a regression algorithm. The Gaussian process regression was trained to approximate the best covariance and matrices from the results of the motor controller execution. The performance of the proposed method was demonstrated through simulations under several conditions of tracking speed and load torque changes.

Robust Fusion Kalman Estimator of the Multi-Sensor Descriptor System with Multiple Types of Noises and Packet Loss.

Under the influence of multiple types of noises, missing measurement, one-step measurement delay and packet loss, the robust Kalman estimation problem is studied for the multi-sensor descriptor system (MSDS) in this paper. Moreover, the established MSDS model describes uncertain-variance noises, multiplicative noises, time delay and packet loss phenomena. Different types of noises and packet loss make it more difficult to build the estimators of MSDS. Firstly, MSDS is transformed to the new system model by applying the singular value decomposition (SVD) method, augmented state and fictitious noise approach. Furthermore, the robust Kalman estimator is constructed for the newly deduced augmented system based on the min-max robust estimation principle and Kalman filter theory. In addition, the given estimator consists of four parts, which are the usual Kalman filter, predictor, smoother and white noise deconvolution estimator. Then, the robust fusion Kalman estimator is obtained for MSDS according to the relation of augmented state and the original system state. Simultaneously, the robustness is demonstrated for the actual Kalman estimator of MSDS by using the mathematical induction method and Lyapunov's equation. Furthermore, the error variance of the obtained Kalman estimator is guaranteed to the upper bound for all admissible uncertain noise variance. Finally, the simulation example of a circuit system is examined to illustrate the performance and effectiveness of the robust estimators.

Evaluation of RAOs of a semi-submersible platform using field measurements: A full-scale model in Caspian sea environmental conditions

The present research investigates the motion response of a semi-submersible platform using measured field data. The Iran-Amirkabir semi-submersible platform (SSP) was considered as full-scale model in operation conditions. First, 14 accelerometer sensors were installed on the platform's hull, and measurements were made in 5 different scenarios in the Caspian Sea environmental conditions. Then, the Response Amplitude Operators (RAOs) for six degrees of motion were extracted using measured accelerator data. The Surge, Sway, and Heave RAOs processed by the Kalman estimation filter, Pitch, Roll, and Yaw RAOs were calculated from the Sensor Array method. Moreover, the boundary element method in ANSYS/AQWA software for the Iran-Amirkabir semi-submersible model was developed, and the RAO results were validated against the extracted field measurements. The obtained results from the Sensor Array method and the Kalman estimation filter are compared with the numerical simulations, which show Root Mean Square Errors of less than 3% and 4%, respectively for rotational and translational movements. The Mean Square Errors between both methods were also close to zero. Therefore, the proposed methods predicted activities of the studied SSP with relatively good accuracy by field data collected in the Caspian Sea.

Control Algorithms, Kalman Estimation and Near Actual Simulation for UAVs: State of Art Perspective

The pervasive use of unmanned aerial vehicles for both commercial and military operations has undergone rapid development in the recent past. When designing unmanned aerial vehicles, it is highly desirable for them to be able to complete their missions with minimal human intervention. Reaching full autonomy requires a reliable and efficient control algorithm that can handle all flight conditions. Due to the confidential nature of UAV design and development, there is a lack of comprehensive literature on the subject. When it comes to the practical application of the ideas presented in the literature, the situation is even bleaker. This research not only examines the flight phases in which controllers and estimators are used for UAVs but also provides an in-depth analysis of the most recent and state-of-the-art control and estimate techniques for UAVs. Research opportunities and challenges specific to UAVs were also examined in this study in an effort to raise the bar for UAV design as a whole and smooth the way for researchers to go from simulation-based research to practical applications. This review paper establishes a foundation that not only investigates the inherent flight dynamics, control architecture, and Kalman estimators utilized in the development of UAVs but also points out the shortcomings that currently exist in research. A number of design considerations for realistic applications and potential studies are presented in the conclusion.