Recursive Least-squares Method Research Articles

Vehicle State Estimation by Integrating the Recursive Least Squares Method with a Variable Forgetting Factor with an Adaptive Iterative Extended Kalman Filter

The sideslip angle and the yaw rate are the key state parameters for vehicle handling and stability control. To improve the accuracy of the input parameters and the time-varying characteristics of noise covariance in state estimation, a combined method of recursive least squares with a variable forgetting factor and adaptive iterative extended Kalman filtering is proposed for estimation. Based on the established three-degrees-of-freedom nonlinear model of the vehicle, the variable forgetting factor recursive least squares method is used to identify the tire cornering stiffness and serves as an input for vehicle state estimation. An innovative algorithm is used to optimise the uncertain noise covariance in the iterative extended Kalman filter (IEKF) process. Finally, with the help of the joint simulation of CarSim2019 and Matlab/Simulink R2022a, a distributed drive electric vehicle state parameter estimation model is established, and a simulation analysis of typical working conditions is carried out. Furthermore, an experiment is conducted with the pix moving vehicle and the integrated navigation system. The simulation and experimental results show that, compared to the traditional extended Kalman filter algorithm, the proposed algorithm improves the estimation accuracy of the yaw rate, sideslip angle, and longitudinal speed by 58.17%, 57.2%, and 76.47%, respectively, which shows that the algorithm has a higher estimation accuracy and a stronger applicability to provide accurate state information for vehicle handling and stability control.

Online Identification of Nonlinear Systems With Separable Structure.

Separable nonlinear models (SNLMs) are of great importance in system modeling, signal processing, and machine learning because of their flexible structure and excellent description of nonlinear behaviors. The online identification of such models is quite challenging, and previous related work usually ignores the special structure where the estimated parameters can be partitioned into a linear and a nonlinear part. In this brief, we propose an efficient first-order recursive algorithm for SNLMs by introducing the variable projection (VP) step. The proposed algorithm utilizes the recursive least-squares method to eliminate the linear parameters, resulting in a reduced function. Then, the stochastic gradient descent (SGD) algorithm is employed to update the parameters of the reduced function. By considering the tight coupling relationship between linear parameters and nonlinear parameters, the proposed first-order VP algorithm is more efficient and robust than the traditional SGD algorithm and alternating optimization algorithm. More importantly, since the proposed algorithm just uses the first-order information, it is easier to apply it to large-scale models. Numerical results on examples of different sizes confirm the effectiveness and efficiency of the proposed algorithm.

Lithium-ion point-of-care ultrasound battery joint state of charge estimation

With recent advances in ultrasound technology, including accessibility and portability, point-of-care ultrasound systems (POCUS) are becoming ubiquitous in urban and rural health services. The efficient use of POCUS battery power is necessary due to the limited access to electricity in rural locations. Accurate estimation of the state-of-charge (SOC) of the onboard lithium-ion battery is crucial in ensuring the safe, efficient, and reliable operation of the battery management system (BMS). This research suggests a novel approach for striking a reasonable balance between the POCUS battery management systems computation time and SOC estimate accuracy. Given that the lithium-ion battery is a non-linear and time-varying system, it is modelled by a second-order RC equivalent circuit model (2-RC ECM). Real-time parametric identification is carried out using the method of recursive least squares with respect to an adaptive forgetting factor (AFFRLS). The joint SOC evaluation technique, ordering the results of real-time identification and the Extended Kalman Filter (EKF) recommended for estimating battery SOC at temperatures between 0 and 45 °C. Simulations were carried out using experimental data from the DST (Dynamic Stress Test), incremental current and, the Federal Urban Driving Program (FUDS) of the CALCE research group to evaluate the proposed approach. Based on the monitoring of dynamic changes in model parameters and the computational complexity of existing algorithms, the results reveal that the joint AFFRLS-EKF estimation proposed for the SOC strategy achieves good accuracy, high adaptability and rapid convergence of SOC estimation.

Resilient Optimal Defensive Strategy of Micro-Grids System via Distributed Deep Reinforcement Learning Approach Against FDI Attack.

The ever-increasing false data injection (FDI) attack on the demand side brings great challenges to the energy management of interconnected microgrids. To address those aspects, this article proposes a resilient optimal defensive strategy with the distributed deep reinforcement learning (DRL) approach. To evaluate the FDI attack on demand response (DR), an online evaluation approach with the recursive least-square (RLS) method is proposed to evaluate the extent of supply security or voltage stability of the microgrids system is affected by the FDI attack. On the basis of evaluated security confidence, a distributed actor network learning approach is proposed to deduce optimal network weight, which can generate an optimal defensive scheme to ensure the economic and security issue of the microgrids system. From the methodology's view, it can also enhance the autonomy of each microgrid as well as accelerate DRL efficiency. According to those simulation results, it can reveal that the proposed method can evaluate FDI attack impact well and an improved distributed DRL approach can be a viable and promising way for the optimal defense of microgrids against the FDI attack on the demand side.

Identification of time-varying inertia tensor parameters of a space solar power satellite based on a robust weighted recursive algorithm under impulsive disturbance

Considering changes in the structural size and mass caused by the on-orbit assembly process in a planar space solar power satellite, this study proposes an improved robust recursive algorithm to identify the time-varying inertia tensor parameters of the system. In this algorithm, to decrease the effect of impulsive disturbance on inertial parameter identification during the on-orbit assembly and improve computational accuracy, robust weighted factor and multi-innovation theory are involved. Then, the time-varying inertia tensor parameters of this large flexible structure are identified based on the distributed measurement results of multiple attitude sensors. The simulation results indicate that the proposed algorithm improves the identification accuracy and has better robustness than the original method under the impulsive disturbance. The relative values of the average relative error caused by the impulsive disturbance under the proposed algorithm are approximately 27.8–73.0% less than those under the original method. Additionally, the results also demonstrate that the proposed algorithm has higher noise immunity than the classical recursive least-squares method in a time-varying system. When the impulsive disturbance and zero-mean Gaussian white noise are applied to the system, compared with the conventional recursive least-squares method, the proposed algorithm yields lower absolute and relative values of the average relative error by approximately 4.2% and 44.9%, respectively.

Bidirectional EMD-RLS: Performance analysis for denoising in speech signal

Empirical Mode Decomposition (EMD) is an alternative decomposition method that allows the analysis of non-stationary and non-linear signals, decomposing them into components called Intrinsic Mode Functions (IMFs). In this paper, we introduce the bidirectional combination between EMD and the Recursive Least Squares (RLS) adaptive filter and compare it to Least Mean Square (LMS), EMD-LMS and RLS methods. The hybrid algorithm relies on the determination of vertical (IMFs indexes) and horizontal (temporal indexes) weighting coefficients. We evaluated the effectiveness of the methods by filtering sets of speech signals artificially corrupted by white Gaussian noise. To find the method that provides the greatest noise reduction and the best speech quality, we took into account the Signal-to-Noise Ratio and the Perceptual Evaluation of Speech Quality (PESQ) score. The analyzed cases showed that EMD-RLS can provide results as good as the other methods, but with a shorter learning curve than LMS and EMD-LMS, despite the higher computational cost. For a single training iteration, the methods presented PESQ scores on average equivalent to each other. However, they showed a significant difference in performance regarding noise reduction, with the best result obtained by RLS, followed by EMD-RLS, EMD-LMS and LMS.

Variable Recursive Least Square Algorithm for Lithium-ion Battery Equivalent Circuit Model Parameters Identification

For SOC (state of charge) assessment techniques based on electrical circuit models, the parameters of the model are strongly biased by: battery aging, temperature, causing some errors in the estimation of the SOC. One approach to solve this problem is to update the model parameters constantly. We suggest a new algorithm VRLS (variable recursive least squares) to update the parameters of a 2-resistor-capacitor (RC) network and to estimate the output battery voltage. VRLS is compared to the recursive least squares (RLS) and the adaptive forgetting factor recursive least squares (AFFRLS) algorithms. For algorithm assessment, we utilized real experimental data conducted on the Samsung 18650-20R lithium-ion cell. The tests indicate that compared to RLS and AFFRLS methods, VRLS recorded a low distribution in the high error range, in addition to small predictive performance indicators (RMSE, MAE, and MAPE) in all tests, which implies that VRLS has a good parameter identification ability.

Robot-Assisted Teleoperation Ultrasound System Based on Fusion of Augmented Reality and Predictive Force

This study presents a novel method to realize an augmented reality (AR) and haptic feedback teleoperation ultrasound system, which can reduce the influence of time delay on the operator. The physician uses a haptic device to send commands to a remote site while observing the AR environment. In the virtual environment, the organ model is projected onto the corresponding position according to the human pose, and the UR robot model can respond to the physician's action in advance. Based on force data, the dynamic environmental model is updated by the recursive least-squares method, allowing real-time force feedback. The contact force is computed from the identified parameters together with the position and velocity of the master site. An experimental platform has been built, where experiments have been conducted to evaluate the overall architecture, highlighting the role of AR and contact-force prediction models, and including clinical validation. Results show that the system can correctly perform remote ultrasound scanning tasks and ensure authenticity and synchronization.

Receding Horizon D-Optimal Input Design for Identification of Wireless Power Transfer Systems

This paper develops a method of input design for the identification of wireless power transfer (WPT) systems based on receding horizon D-optimization. The dynamic behavior of the system is characterized by a discrete-time, Single-Input, Single-Output (SISO) model, and the associated model parameters are estimated by a recursive least-squares method. To improve the quality of the parameter estimates, the excitation signal of the system is designed based on receding horizon D-optimization. To improve the convergence and efficiency of the input design process, the Sequential Quadratic Programming (SQP) method is employed to solve the receding horizon D-optimization. Numerical and experimental results are presented to demonstrate the effectiveness of the proposed method.

Research on Harmonic Mitigation Strategy of Static VAR Generator Based on Frequency Adaptation

Offshore wind farms are integrated into the power grid via AC submarine cables, which may cause severe harmonic problems and reduce the power quality of the grid. To address the problem of excessive harmonics in offshore wind power plants (WPPs), this paper proposes a method applying the static var generator (SVG) with frequency adaptive harmonic mitigation function to the offshore WPPs. Firstly, the SVG model and the mechanism of harmonic mitigation are investigated. Secondly, the proportional and resonant control strategy is proposed according to the internal model theorem and applied to the voltage control loop of SVG. The harmonic suppression performance of SVG is studied through the Bode diagram. Thirdly, to adapt to the uncertainty of harmonic frequencies, the recursive least-squares method is introduced to realize the real-time tracking of harmonic frequencies. And the harmonic compensation bandwidth of the SVG is broadened by adjusting the parameters of the controller. Finally, the offshore WPPs in Jiangsu are built based on the Matlab/Simulink platform to verify the effectiveness of the mitigation strategy. Compared with the LC filter, the improved method can effectively mitigate (inter-) harmonics and has strong robustness and adaptability.

Identification of Differential Drive Robot Dynamic Model Parameters.

The paper presents the identification process of the mathematical model parameters of a differential-drive two-wheeled mobile robot. The values of the unknown parameters of the dynamics model were determined by carrying out their identification offline with the Levenberg-Marguardt method and identification online with the Recursive least-squares method. The authors compared the parameters identified by offline and online methods and proposed to support the recursive least squares method with the results obtained by offline identification. The correctness of the identification process of the robot dynamics model parameters, and the operation of the control system was verified by comparing the desired trajectories and those obtained through simulation studies and laboratory tests. Then an analysis of errors defined as the difference between the values of reference position, orientation and velocity, and those obtained from simulations and laboratory tests was carried out. On itd basis, the quality of regulation in the proposed algorithm was determined.

New Energy Power System Static Security and Stability Region Calculation Research Based on IPSO-RLS Hybrid Algorithm

With the rapid expansion of new energy in China, the large-scale grid connection of new energy is increasing, and the operating safety of the new energy power system is being put to the test. The static security and stability region (SSSR) with hyper-plane expression is an effective instrument for situational awareness and the stability-constrained operation of power systems. This paper proposes a hybrid improved particle swarm optimization (IPSO) and recursive least square (RLS) approach for rapidly approximating the SSSR boundary. Initially, the operating point data in the high-dimensional nodal injection space is examined using the IPSO algorithm to find the key generators, equivalent search space, and crucial points, which have a relatively large impact on static stability. The RLS method is ultimately utilized to fit the SSSR border that best suits the crucial spots. Consequently, the adopted algorithm technique was used to rapidly approximate the SSSR border in power injection spaces. Finally, the suggested algorithm is confirmed by simulating three kinds of generators of the new energy 118 bus system using the DIgSILENT/Power Factory. As a result, this method accurately characterized the stability border of the new energy power system and created the visualization space of the SSSR. Using the SSSR, a rapid state analysis could be undertaken on a variety of parameters, such as security evaluation with diverse energy supply capacities. This study’s findings confirmed the accuracy and efficacy of the suggested modeling for the considered system and may thus give technical support for the new energy power system’s stability.

Extended real-time voltage instability identification method based on synchronized phasor measurements

This paper presents an extended adaptive approach designed to accurately estimate the Thévenin equivalent parameters using phasor measurements at a given bus for measurements lying in any of four quadrants of the PQ-plane. The improvement is achieved by using a new condition to properly update the estimated parameters after an initial guess. Based on an adaptive philosophy, the proposed approach can correctly account for the intrinsic nonlinearities of a power system, can provide a real-time estimation of Thévenin parameters, and does not require network topology knowledge. The method is validated using the Kundur 2-area system, showing estimation improvements compared to the current adaptive approach and the classical recursive least-squares method. The proposed approach is able to estimate both sides of the system with respect to the measurement bus. In addition, a data-driven voltage stability index is developed. To illustrate the performance of the proposed approach in a larger power system, a voltage stability assessment is carried out on the IEEE 39-bus system, considering the action of overexcitation limiters of generators and nonlinear loads. The proposed approach is suitable for applications that require an accurate Thévenin equivalent estimation in real-time, such as for voltage stability assessment. The new approach provides a reliable tool for the system operators to make proper and timely decisions.

Research on Tire–Road Parameters Estimation Algorithm for Skid-Steered Wheeled Unmanned Ground Vehicle

Skid-steered wheeled vehicles can be applied in military, agricultural, and other fields because of their flexible layout structure and strong passability. The research and application of vehicles are developing towards the direction of “intelligent” and “unmanned”. As essential parts of unmanned vehicles, the motion planning and control systems are increasingly demanding for model and road parameters. In this paper, an estimation method for tire and road parameters is proposed by combining offline and online identification. Firstly, a 3-DOF nonlinear dynamic model is established, and the interaction between tire and road is described by the Brush nonlinear tire model. Then, the horizontal and longitudinal stiffness of the tire is identified offline using the particle swarm optimization (PSO) algorithm with adaptive inertia weight. Referring to the Burckhardt adhesion coefficient formula, the extended forgetting factor recursive least-squares (EFRLS) method is applied to identify the road adhesion coefficient online. Finally, the validity of the proposed identification algorithm is verified by TruckSim simulation and real vehicle tests. Results show that the relative error of the proposed algorithm can be well controlled within 5%.

Online Distributed ADMM Algorithm With RLS-Based Multitask Graph Filter Models

This article establishes a multitask graph filter model based on the recursive least square (RLS) method and proposes an online distributed alternating direction method of multipliers (ODADMM) algorithm. We are interested in the time-varying graph signal, i.e., the graph filter is estimated from streaming data. Considering that current popular graph shift operators' energy can not be preserved, which will lead to slow estimation speed, so the RLS method is adopted in graph filters (GFs) to improve the convergence rate. Besides, a multitask GFs model is proposed for node-variant GFs, where each vertex cooperates with neighbours to improve the estimation performance by utilizing the correlation of tasks. Then, according to our model, a distributed alternating direction method of multipliers (DADMM) algorithm is designed, while it has enormous computational complexity. To address this drawback, an ODADMM algorithm is further developed, and the algorithm can converge to an optimal point that is validated. Numerical results verify that the proposed algorithm is more competitive in convergence speed and performance than other related algorithms, and two real scenes are tested to verify the effectiveness of the algorithm.

РАЗРАБОТКА ЭНЕРГЕТИЧЕСКИ ЭФФЕКТИВНОЙ СИСТЕМЫ СВЯЗИ В ТРОПОСФЕРНОМ РАДИОКАНАЛЕ НА БАЗЕ OFDM-СИГНАЛОВ

It is known that inter-symbol interference may occur during data transmission in radio relayand tropospheric communication systems. The presence of multipath propagation and frequencyselectivefading in the tropospheric, radio relay channel significantly reduces the energy efficiencyof the communication system as a whole. The aim of the work was to increase the efficiency ofusing the channel for radio relay and tropospheric communication by using OFDM (orthogonalfrequency-division multiplexing using the methods of reducing the peak factor of the OFDM signaland increasing the linearity of the transmission path. To evaluate digital predistortion algorithmsin the Matlab/Simulink environment, a model was developed for the LMS, NLMS, RLS, RPEMmethods and a power amplifier model with real characteristics. Based on the results of modelingalgorithms, RLS was chosen. In addition, in this work, a modified version of the adaptation algorithmbased on the recursive least squares method (RLSm) was developed. The main result of themodification is: a decrease in the number of arithmetic operations per iteration (more than5 times), an increase in the stability of adaptation algorithms, due to the introduction of regularizationmethods, a decrease in the convergence time, due to the introduction of an exponential dependence.Various algorithms for reducing the peak factor of an OFDM signal were investigated,the best result was achieved by combining Tone reservation (TR) and Active constellation extension(ACE). Simulation in the Matlab/Simulink environment showed that the combination of TRand ACE algorithms reduces the peak factor of OFDM signals by ~5dB for BPSK data stream and~4.5dB for 8-PSK, QAM-16, QAM-64, QAM-128 and QAM- 256. To increase the linearity of thetransmission path, the RLSm digital pre-distortion algorithm was selected and upgraded, it madeit possible to reduce the magnitude of the error vector modulus (EVM) by 13.5dB, and also increasethe modulation/error ratio (MER) by 13.6dB.

Predicting greenhouse daily light integral using photosynthetic photon flux density and finite difference method

In the state-of-the-art agricultural technology using greenhouses, it is useful to estimate a dynamic model of internal environmental changes according to external environmental changes. In this article, we propose a method to predict the change in the daily light integral inside the greenhouse according to the change in the daily light integral outside the greenhouse. Since daily light integral corresponds to the integral value of photosynthetic photon flux density, it is necessary to obtain a model of change in photosynthetic photon flux density inside the greenhouse according to the change in photosynthetic photon flux density outside the greenhouse to improve the prediction accuracy. The greenhouse was considered a nonlinear first-order system with a time lag for the photosynthetic photon flux density, and the system parameters were identified using the recursive least-squares method. Here, the photosynthetic photon flux density data measured outside the greenhouse is used as the input to the system, and the photosynthetic photon flux density data measured inside the greenhouse is used as the output of the system. Next, we obtain the daily light integral prediction model. The daily light integral prediction model is estimated from the photosynthetic photon flux density model using the finite difference method. The performance of the proposed method has been evaluated through extensive experimental studies. In Korea, since the weather changes in summer and winter are great, it must compare the daily light integral prediction performance in summer and winter to more accurately verify the proposed method. In this study, the experimental results are presented, respectively, for summer in August 2021 and winter in January 2022. The error performance of the human empirical prediction method and the proposed data-driven prediction method are compared for two seasons, and the robustness of the rapid weather changes of the proposed method is discussed.

Online structural damage state identification of concrete arch dams under dynamic loads using a recursive TVARX approach

Concrete arch dams have been widely constructed worldwide, and many of these dams are located in areas with high seismic activity. However, strong seismic loading poses a severe threat to concrete arch dams, and dams have the risk of suffering damage and the possibility of an ensuing dam break. In past decades, seismic and structural health monitoring has undergone rapid growth in the context of arch dams to track the operation state of arch dams under strong seismic loading. In fact, arch dams with damage caused by seismic loading normally exhibit nonlinear dynamic behaviors and time-variable dynamic properties. To effectively identify the structural damage state development of arch dams under seismic loading, an online damage identification method using a novel recursive time-variable autoregressive with exogenous (TVARX) input model was presented in this paper. To improve the tracking capability for the time-variable coefficients of the TVARX model, an adaptive adjustment algorithm of variable weighting factors was incorporated into the recursive least-squares method. In the proposed method, the predicted model residual, a damage index named the fit ratio (FR), the difference between fit ratios (DF), and a damage index based on the change in ARX model parameters (CH) were proposed to identify the presence of damage, damage area, and relative damage extent for arch dams. Eventually, the proposed approach was used for the online damage state identification of arch dams in a numerical simulation example and a shaking table test, and the identification results demonstrated the effectiveness of the proposed approach.

Comparison of Adaptive Equalization Methods for Improving Indoor Optical Wireless Communications Employing Few-Mode Based Uniform Beam Shaping

Few-mode based uniform beam shaping exploiting the use of different spatial modes has been recently shown to improve the system resistance against pointing errors and link outage in indoor optical wireless communications. However, the inter-symbol interference arising from transmission of different spatial modes following different paths and mode crosstalk during the transmission becomes another important challenge. In this paper, we theoretically investigate and experimentally compare the performance of two popular adaptive equalization methods, namely least mean square and recursive least-square in both multi-equalizer and single-equalizer configurations, to improve the performance of indoor optical wireless communication system employing few-mode based uniform beam shaping. For both equalization methods, the multi-equalizer scheme achieves better equalization performance and higher convergence speed than the single-equalizer scheme for a similar cost of required computational complexity for each iteration. Moreover, recursive least-square method has a higher convergence speed than least mean square equalization while least mean square method has a lower computational complexity than recursive least-square method under the same desired equalization performance. More importantly, for a fixed reference BER threshold (KP4 FEC limit), the least mean square based single-equalizer scheme with a step size of 0.0035 and a tap number of 61 has the lowest computational complexity among the four types of equalization schemes. This kind of equalizer with relatively low computational complexity can provide guidelines for selecting an applicable adaptive equalization scheme in optical wireless communications with few-mode based beam shaping based on the comprehensive requirements of BER performance and computational complexity.

Recursive Least Squares Based Refinement Network for Vehicle Trajectory Prediction

Trajectory prediction of surrounding objects plays a pivotal role in the field of autonomous driving vehicles. In the current rollout process, it suffers from an accumulation of errors, which has a negative impact on prediction accuracy. This paper proposes a parametric-learning recursive least-squares (RLS) method integrated with an encoder–decoder framework for trajectory prediction, named the recursive least-squares-based refinement network (RRN). Through the generation of several anchors in the future trajectory, RRN can capture both local and global motion patterns. We conducted experiments on the prevalent NGSIM and INTERACTION datasets, which contain various scenarios such as highways, intersections and roundabouts. The promising results indicate that RRN could improve the performance of the rollout trajectory prediction effectively.