Recursive Least-squares Estimation Research Articles

Detection of Data Integrity Attack Using Model and Data-Driven-Based Approach in CPPS

The cyber-physical power system (CPPS) is a modern infrastructure utilising information and communication technology that has become more vulnerable to cyberattacks in recent years. The attack magnitude injected by the adversary is stealthier and it cannot be detected using conventional bad data detection techniques. Protecting sensitive data from data integrity attacks (DIA) is essential for ensuring system security and reliability. A tragic event will occur if the attack goes unreported. Therefore, DIA detection is highly vital for the operator in the control centre to make important decisions. This paper addresses the attack impact on WAC applications and attack detection using the model-based method and data-driven-based methods. On the basis of the validation of performance indicators, various detection approaches are simulated and compared to determine the best detection strategy. Simulation results show that in the model-based anomaly detection method, the recursive polynomial model estimator (RPME) has better detection performance than the recursive least square estimator (RLSE). The convolutional neural network- (CNN-) based data-driven anomaly detection technique outperforms other machine learning (ML) techniques such as support vector machine (SVM), K-nearest neighbour (KNN), and random forest (RF). On the WSCC 3 machine 9-bus system, the efficacy of the suggested methods is evaluated.

Positioning Control Strategy of Hydraulic Support Pushing System in Fully Mechanized Coal Face

At present, the hydraulic support pushing system in coal mines usually uses an electrohydraulic directional valve as the control component. However, the existing control methods based on high-speed on–off valve, servo, and proportional control methods are not suitable for solving such problems because of the nonideal characteristics of the electrohydraulic directional valve, such as discrete input values, low switching frequency, and time delay. This paper proposes a positioning control scheme based on online predictive feedback for the control of hydraulic cylinders by electrohydraulic directional valves. In this scheme, the recursive least-squares estimation algorithm with genetic factors is used to identify the required prediction model in real time, and an improved radial basis function network based on generalized growth and shear is used to realize the online fitting of the target trajectory function. The online learning algorithm provides accurate prediction information for the switching control method, and finally, the hydraulic cylinder can be positioned near the target position using the optimal control method. By using the above methods, a well-designed model can be accurately identified, fundamentally solving the problem of control difficulties caused by the nonideal characteristics of the electrohydraulic directional valve. Finally, the effectiveness of the control scheme is verified through simulation analysis and physical experiment research, which proves that the control strategy can realize accurate and fast positioning control for the hydraulic support pushing system of a fully mechanized mining face.

Lane Change–Intention Inference and Trajectory Prediction of Surrounding Vehicles on Highways

The behavior prediction of the surrounding vehicles is crucial when planning a minimal-risk path when realizing a collision-avoidance system. Herein, we propose a multiple model–based adaptive estimator (MMAE) that infers the lane-change intention of the surrounding vehicles and then predicts their trajectories. Specifically, first, a path is generated in the form of a cubic spline curve using the Frenet coordinate system, which is robust to changes in road curvatures. Linearized recursive least-squares estimation (LRLSE) method is used to adaptively predict a future trajectory based on the past trajectory of the target vehicle. Preview time is defined as a time-varying parameter that determines the final point of the path, and LRLSE updates it in real time. The MMAE applies LRLSEs to multiple paths and obtains the mode probability for each path, then the lane-change intention is inferred using the mode probability and preview time. The predicted future trajectory is the cubic spline curve determined based on the preview time. Further, we verify the performance of our approach using highD, a naturalistic dataset of vehicle trajectories, and compare it with those of existing methods. The proposed method does not require a large amount of data for training and has a low computational burden and high real-time performance.

A Self-Tuning Adaptive Control Scheme for a Grid-Connected Three-Phase PV System

This article presents a new self-tuning sinusoidal recursive controller (STSRC) for handling the uncertainties and disturbances in a three-phase grid-connected photovoltaic system (GCPVS). The performance of a GCPVS is greatly influenced by the uncertainties, such as intermittency in solar irradiation, change in capacitance and equivalent series resistance (ESR) of dc-link capacitor, and variation of impedance between the inverter and the grid. This STSRC comprises improved linear sinusoidal tracer-based recursive least-square estimation (IRLS) to achieve robust performances, despite the parametric uncertainties through real-time estimation of its parameters, and updation of its gains. The efficacy of the proposed STSRC is verified through simulation using MATLAB/Simulink and experimental studies pursued on a 2.5-kW prototype. It is observed that STSRC exhibits superior tracking of PV voltage with reduced ripple and improved grid current with reduced total harmonic distortion (THD) of 1.66%. The estimation accuracy is found above 92%.

Adolescent Identity Search Algorithm Based on Fast Search and Balance Optimization for Numerical and Engineering Design Problems.

This paper proposed a fast convergence and balanced adolescent identity search algorithm (FCBAISA) for numerical and engineering design problems. The main contributions are as follows. Firstly, a hierarchical optimization strategy is proposed to balance the exploration and exploitation better. Secondly, a fast search strategy is proposed to avoid the local optimization and improve the accuracy of the algorithm; that is, the current optimal solution combines with the random disturbance of Brownian motion to guide other adolescents. Thirdly, the Chebyshev functional-link network (CFLN) is improved by recursive least squares estimation (RSLE), so as to find the optimal solution more effectively. Fourthly, the terminal bounce strategy is designed to avoid the algorithm falling into local optimization in the later stage of iteration. Fifthly, FCBAISA and comparison algorithms are tested by CEC2017 and CEC2022 benchmark functions, and the practical engineering problems are solved by algorithms above. The results show that FCBAISA is superior to other algorithms in all aspects and has high precision, fast convergence speed, and excellent performance.

Adaptive real-time grid operation via Online Feedback Optimization with sensitivity estimation

In this paper we propose an approach based on an Online Feedback Optimization (OFO) controller with grid input–output sensitivity estimation for real-time grid operation, e.g., at subsecond time scales. The OFO controller uses grid measurements as feedback to update the value of the controllable elements in the grid, and track the solution of a time-varying AC Optimal Power Flow (AC-OPF). Instead of relying on a full grid model, e.g., grid admittance matrix, OFO only requires the steady-state sensitivity relating a change in the controllable inputs, e.g., power injections set-points, to a change in the measured outputs, e.g., voltage magnitudes. Since an inaccurate sensitivity may lead to a model-mismatch and jeopardize the performance, we propose a recursive least-squares estimation that enables OFO to learn the sensitivity from measurements during real-time operation, turning OFO into a model-free approach. We analytically certify the convergence of the proposed OFO with sensitivity estimation, and validate its performance on a simulation using the IEEE 123-bus test feeder, and comparing it against a state-of-the-art OFO with constant sensitivity.

Voltage Sag Compensation Through Dynamic Voltage Restorer Under Non-Sinusoidal Electrical Grid Condition

This work presents a method of voltage insertion into the grid with harmonic distortions through a dynamic voltage restorer (DVR) for protection of sensitive loads to short-term voltage sags. The aim is to recover the nominal voltage level at the load by restoring only the fundamental frequency component without compensating the harmonic contents. Corrections carried out in this manner are justified as the DVR is a device dedicated to restore the amplitude of the sensitive load to its rated value, based on rapid variations from the power grid. The correction of distortions is not suitable for this equipment as harmonics are permanent problems and originate from nonlinearities of electrical loads. Therefore, the batteries that supply the DVR do not support the correction of permanent problems, only for rapid variations. Thus, it allows an extension in the lifespan of the batteries (needed in this type of compensator). Collaterally, restoring only the fundamental decreases the total harmonic distortion of the load, thus allowing this method to make a double contribution to improving the system’s power quality. For this purpose, a recursive least-square estimation is developed, suitable for voltages with harmonic content, here called HRLS. The construction of the reference voltage to be produced by the DC–AC converter also considers the synchronism with the fundamental component of the grid, which allows an optimization of the voltage level used on the DC-link. Correction scenarios only inserting the fundamental, as well as with harmonic content, are tested in simulation to compare performance in the use of the compensator power. The same scenarios are also tested on an experimental platform developed in the laboratory to confirm the proposal.

Generalized recursive least squares: Stability, robustness, and excitation

We study a class of recursive least-squares estimators in an errors-in-variables setting where disturbances affect both the regressor and the regressand variables. We prove the existence and stability of an optimal steady state and robustness with respect to the disturbances in form of input-to-state and input–output stability relative to the unperturbed steady-state trajectories. Depending on the choice of some design parameters, different specific estimators can be realized within the considered class, each of which is associated with a different underlying optimization problem and with different excitation requirements for the unperturbed regressor. As expected, we find that persistence of excitation is associated with uniform, in fact exponential, convergence. In addition, we also show that choices of the design parameters are possible for which convergence and robustness hold without persistence of excitation and with the same asymptotic gain, the only difference being a loss of uniformity in the convergence rate.

Driveline Modeling With Transmission Loss and Robust Torque Observer Design for Dual Clutch Transmission

This paper presents a design of driveline torque observer with dual clutch transmission (DCT). A goal of this study is to improve estimation performance of the observer. To increase the observer’s performance, it is important to make an accurate driveline model and a robust observer. First, to increase the accuracy of the model, we propose lumped driveline efficiency which is a parameter that expresses driveline transmission loss. In addition, a recursive least square estimation (RLSE) algorithm is proposed to estimate the parameter using driving data. Then, the model is updated using the estimated parameter value. Second, a reduced order observer is proposed to estimate transmitted torques of driveline in both driving and gear shifting process. Moreover, the observer, which is robust against measurement noise and disturbance, is designed through frequency domain analysis. For frequency domain analysis, an eigenstructure assignment method is applied to tune observer gains. Performance of the proposed RLSE algorithm and the observer are verified through simulation and testbench experiments.

Multi-Layered Recursive Least Squares for Time-Varying System Identification

Traditional recursive least squares (RLS) adaptive filtering is widely used to estimate the impulse responses (IR) of an unknown system. Nevertheless, the RLS estimator shows poor performance when tracking rapidly time-varying systems. In this paper, we propose a multi-layered RLS (m-RLS) estimator to address this concern. The m-RLS estimator is composed of multiple RLS estimators, each of which is employed to estimate and eliminate the misadjustment of the previous layer. It is shown that the mean squared error (MSE) of the m-RLS estimate can be minimized by selecting the optimum number of layers. We provide a method to determine the optimum number of layers. A low-complexity implementation of m-RLS is discussed and it is indicated that the complexity order of the proposed estimator can be reduced to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal O}(M)$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> is the IR length. Through simulations, we show that m-RLS outperforms the classic RLS and the RLS methods with a variable forgetting factor.

Sequential Fusion Based Approach for Estimating Range Gate Pull-Off Parameter in a Networked Radar System: An ECCM Algorithm

Networked radar is an emerging and effective alternative to traditional radar systems to provide improved performance by fusing information from multiple radars. Further, networked radar systems (NRS) have found numerous deployments in military and civilian infrastructures in recent years. Electronic countermeasures (ECM) like jamming, Range Gate Pull-Off (RGPO), and Velocity Gate Pull-Off (VGPO) generally pose a high risk to the radar systems by injecting intentional interference. This paper proposes networked radar to detect the RGPO ECM attack and estimate the range gate deception parameter of the deceived local track in an NRS. Each radar comprises a local tracker to provide the local estimates (updated state and updated covariance), and these estimates are then sent to the fusion node. Thereafter, a track-to-track association (T2TA) is formulated at the fusion node to detect the deceived tracks using all the available local tracks. For the deceived track, the pseudo-measurements are created using the inverse Kalman filter-based tracklets. All the local tracks except deceived track are compensated and sequentially fused to create a reference measurement. After that, the deception parameter of the deceived track is estimated by using pseudo-measurement and the reference measurement by employing the recursive least square estimator (RLSE). In addition, the proposed algorithm is analyzed for single and multiple RGPO based ECM scenarios. Further, the Cramer Rao Lower Bound (CRLB) for the proposed methodology is derived. The results are quantified with a Position Root Mean Square Error (PRMSE), CRLB, innovation test, normalized estimation error squared (NEES) test, and confidence interval. The simulation results demonstrate that the proposed estimation technique provides good performance in the presence of all the local tracks are being attacked by RGPO ECM. Besides, it is evident from the results that estimator efficiency is falling below the 5% tail probability of the chi-square distribution.

A Recursive Least-Squares Approach with Memorizing Factor for Deriving Dynamic Equivalents of Power Systems

In this research, a two-stage identification-based approach is proposed to obtain a two-machine equivalent (TME) system of an interconnected power system for transient stability studies. To estimate the parameters of the equivalent system, a three-phase fault is applied near and/or at the bus of a local machine in the original multimachine system. The electrical parameters of the equivalent system are calculated in the first stage by equating the active and reactive powers of the local machine in both the original and the predefined equivalent systems. The mechanical parameters are estimated in the second stage by using a recursive least-squares estimation (RLSE) technique with a factor called “memorizing factor”. The approach is demonstrated on New England 10-machine 39-bus system, and its accuracy and efficiency are verified by computer simulation in MATLAB software. The results obtained from the TME system agree well with those obtained from the original multimachine system.

FPGA Implementation of RLSE Algorithm for Multichannel Brain Imaging

This paper describes the implementation of a computationally efficient embedded system on an Field Programmable Gate Array (FPGA) platform for real-time brain activity estimation with multiple channels. The brain signals from multiple channels are considered as output of independent linear systems with unknown parameters representing the brain activity in corresponding channels. Multiple adaptive Recursive Least-Squares Estimation (RLSE) cores are implemented in FPGA to independently estimate the brain activity in each channel concurrently. The proposed RLSE-FPGA system provides dedicated (no time or resource sharing) and parallel processing environment. The universal asynchronous receiver transmitter core is also developed to communicate the measured and estimated parameters supported by storage facility programmed as shared memory. The computational precision is guaranteed by deploying a 32-bit floating point core for all the variables. The validation carried out by real Functional Near-Infrared Spectroscopy dataset and comparative analysis with the previously reported result, demonstrates the effectiveness of the proposed system. The computational cost endorses the effectiveness of concurrent processing of multiple channelsꞌ data in a sample before the arrival of the next sample. The proposed methodology has potential in real-time medical, military and industrial applications.

Adaptive robust precision motion control of single PAM actuated servo systems with non-local memory hysteresis force compensation

An adaptive robust controller with non-local memory hysteresis force compensation is investigated for the precision tracking control of pneumatic artificial muscle (PAM). The proposed controller presents a two-layer cascade structure, and each layer has an adaptive law part and a robust control law part. A modified operator based Prandtl–Ishlinskii (PI) model is employed in the development of the robust control algorithm with the hysteresis feedback linearization compensation. Moreover, in the robust control law part, the problem of unbounded uncertain nonlinearities introduced by the hysteresis force term is addressed by applying an on-line monitoring method. In the adaptive law part, model parameters including weights of the modified operator are updated online by the recursive least squares estimation (RLSE) method, and then the effect of the hysteresis non-local memory characteristic is further attenuated. The tracking error is guaranteed to converge to a small residual set. Comparative experimental results demonstrate the significance of the non-local memory hysteresis force compensation, then, a desired precision can be guaranteed.

Stealthy Cyberattacks on Loads and Distributed Generation Aimed at Multi-Transmission Line Congestions in Smart Grids

Developing attack models is the first step to understand cyberattacks in smart grids and develop countermeasures. In this article, a three-level nonlinear programming formulation is proposed for false data injection (FDI) cyberattacks that could result in multiple transmission line congestions without being detected by conventional bad data detection (BDD) algorithms. The model is then converted to a mixed integer linear programming (MILP) formulation to guarantee a global optimum exists. A detection framework based on recursive least-square estimation (RLSE) is developed that can successfully detect the stealthy FDIs. The developed model with the detection framework is validated through various case studies in IEEE 118-bus benchmark.

Autoregressive exogenous input modelling for lipase catalysed esterification process

One of the effective ways to enhance the productivity of esters is by controlling the process at its optimum conditions. The crucial task of model based control is the development of an appropriate process model. Model requires to be less complex but with adequately accurate. The development of a suitable empirical model is imperative to ensure the best control performance for model based controller. In this works, a linear Autoregressive with Exogenous input (ARX) and a Nonlinear Autoregressive with exogenous input (NARX) models were developed and compared for lipase catalysed esterification batch process. The identification and validation data for the ARX and NARX models were generated from the first principle model. The inputs data included were jacket flowrate, air flowrate and jacket temperature. Meanwhile, the outputs data considered were temperature and water activity. The empirical model developed was determined by varying the number of inputs/outputs model order and the model parameters involved were estimated using the Kalman filter method in the Recursive Least Squares Estimation (RLSE) function block in MATLAB®/Simulink. The accuracy of the model was the main indicator for selection. The values of R2for the ARX and the NARX models for the reactor temperature were 70.80% and 98.06%, respectively, while for the water activity the values of R2for the best ARX and NARX models were 63.46% and 99.04%, respectively. The results show that the NARX with low order models fit the real data very well if compared to the ARX models.

Cooperative constrained parameter estimation by ADMM-RLS

With recent advances in cloud computing, resources with customizable computational power and memory can be exploited to store and analyze data collected from large sets of devices. Although one can exploit the connection to the cloud to perform all the desired tasks on the cloud itself, in many applications it is also desirable to retrieve and process information locally. In this paper, we present a collection of cloud-aided consensus-based Recursive Least-Squares (RLS) estimators. The approaches are tailored to handle linear and nonlinear consensus constraints and limitations on parameter ranges. All the methods are designed so that raw measurements collected at the device level are processed by the device itself, requiring minimal changes to (possibly pre-existing) RLS estimators. The local estimates are then recursively refined and fused on the cloud to reach consensus among the devices.

Distributed Multisensor Multitarget Tracking Algorithm with Time-Offset Registration

In multisensor systems, the signal processing delay, measurement acquisition delay, and other factors will lead to imprecisely time-stamped measurements, namely, the problem of time-offset. To deal with the measurement time offsets in distributed multisensor systems, a distributed multisensor multitarget tracking algorithm with time-offset registration is proposed. The local processors track multiple targets in the presence of false alarms and missed detections based on the joint probabilistic data association (JPDA) algorithm and the extended Kalman filter (EKF), providing the time-biased local tracks. In the global processor, in allusion to the global track accuracy degradation introduced by the time offsets of local tracks, the equivalent measurements are firstly constructed based on local tracks by using the inverse Kalman filter. The pseudo-measurement equation of time offset for constant velocity targets is derived and the pseudo-measurement calculation method is presented. Then, the pseudo-measurement based relative time-offset estimation algorithm is presented, by using the recursive least squares estimation (RLSE) and the Kalman filter (KF) to jointly estimate the state in space and time domains, respectively. Finally, a framework of distributed multisensor multitarget tracking with time-offset registration is presented, where the time-varying relative time-offset estimation and compensation, 'equivalent measurement to global track' association, and global track update are included. Simulations for multisensor multitarget tracking in the presence of false alarms and missed detections are conducted, demonstrating that the present algorithm effectively improves the accuracy of fused global tracks.

Role of the RLS-VCE-estimated stochastic model for improvement of accuracy and convergence time in multi-GNSS precise point positioning

• We solve the PPP problem using RLS. • The VCE method used to estimate the appropriate stochastic model. • The use of the RLS-VCE method for stochastic model estimation has a significant impact on PPP performance. • The improvement of the PPP performance is investigated by increasing accuracy and reducing convergence time. • The combination of multi-GNSS observations has an impact on PPP positioning performance. We present a method for PPP adjustment based on Recursive Least Square Estimation (RLSE). This method estimates the stochastic model of GPS, GLONASS, Galileo and BeiDou observations by using RLS-Variance Components Estimation (RLS-VCE). The accuracy and the convergence time of horizontal, altitudinal and three-dimensional components is compared by using both nominal and RLS-VCE method so that the estimated accuracy for these coordinate components in suggested method is more accurate than nominal method. The accuracy of horizontal, altitudinal and three-dimensional components in this method are 1.3, 1.25 and 1.8 cm respectively in comparison to nominal method with 4, 3.8 and 5.6 cm. By considering 15 cm as the convergence condition, convergence time is estimated 3 and 5.3 min for suggested and nominal methods respectively. The obtained RMSE after convergence time in proposed and nominal methods are 7.1 and 9.2 cm respectively. According to the presented results, when Multi-GNSS observations are combined, the lowest RMSE are estimated for the coordinate components. As time passes, the stochastic model becomes more stable, therefore, the presented method will be more accurate.

A two-stage observer for the compensation of actuator-induced disturbances in tool-force sensors

In this paper, a novel two-stage observer strategy for improving the measurement of tool forces is presented. The mass-spring-damper system which inevitably occurs when a tool and a (compliant) force sensor are combined is studied and its adverse influence on the measurement signal is analyzed. The proposed observer consists of two stages. The first stage captures the input-output characteristics from the control input to the tool force by a recursive least-squares estimation algorithm. The estimated tool characteristics are used in a second stage to suppress the oscillations in the measurement signal, which mainly occur due to the mass-spring-damper nature of the tool-sensor combination. In a tailored experimental test rig, which mimics the conditions in magnetic levitation, magnetic bearings, or magnetic strip positioning devices in hot-dip galvanizing lines, the efficacy and the high estimation accuracy of the developed observer strategy are demonstrated.