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In state-of-charge (SOC) estimation approaches which rely on electric circuit models, the accuracy of the model’s parameters is influenced by factors such as battery aging and temperature, leading to SOC estimation errors. To tackle this issue effectively, a constant update of battery parameters is proposed. Our novel approach introduces the variable recursive least squares (VRLSs) algorithm, specifically designed to upgrade the parameters of a 2-capacitor–resistor network and accurately evaluate the terminal voltage of the battery. To assess the effectiveness of the VRLS algorithm, we conducted a comparison with two other methods: recursive least squares (RLS) and adaptive forgetting factor RLS (AFFRLS) algorithms. We employed experimental data from the CALCE Battery Research Group, with the Samsung and the A123 lithium-ion cells for testing. The results of the tests revealed that VRLS outperformed both AFFRLS and RLS methods. Notably, VRLS demonstrated significantly lower distribution in high error range and exhibited superior predictive performance indicators, including root-mean-square error, mean absolute error, and mean absolute percentage error across all tests.

For the unforced dynamical non-linear statespace model, a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article. The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems. With the help of an ortho-normal triangularization method, which relies on numerically stable givens rotation, matrix inversion causes a computational burden, is reduced. Matrix computation possesses many excellent numerical properties such as singularity, symmetry, skew symmetry, and triangularity is achieved by using this algorithm. The proposed method is validated for the prediction of stationary and non-stationary MackeyGlass Time Series, along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness. By the learning curves regarding mean square error (MSE) are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS. This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays, which is efficient in developing very-large-scale integration (VLSI) applications with non-linear input data. Multiple experiments are carried out to validate the reliability, effectiveness, and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares (EKRLS) algorithm.

The model predictive control (MPC) technique is widely employed in process industries as a control scheme. The quality of the model used greatly influences the performance of the MPC. In time-varying systems, the plant model plays a critical role in determining the controller’s performance, as the controller’s control action relies on an adaptive model. Therefore, updating the system parameters rapidly and symmetrically in time-varying systems becomes necessary. To address this need, in the proposed work, a non-minimal state space model of a time-varying system is utilized for parameter estimation, and these parameters are updated at every sampling instant using a multi-innovation recursive least squares (MIRLS) scheme, which enables the timely updates of system parameters. We have explored various extensions of the recursive least square (RLS) scheme, such as the multi-innovation recursive least squares (MIRLS) method. This extension aims to achieve a higher convergence rate for parameter estimation. Furthermore, we have focused on the parameter estimation of a non-minimal state space time-varying system, where the system parameters change at each time interval. Additionally, we have incorporated a time-varying objective function into the MPC formulations, which enables adaptability to change the system dynamics. To demonstrate the applicability of our proposed approach, we have conducted simulation experiments using a benchmark time-varying model. These experiments showcase the effectiveness and benefits of our proposed methodology in dealing with time-varying systems.

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.

Filtering noises/artifacts from the electrocardiogram (ECG) can sustain the efficient clinical decision making. Comparative analysis of several filtering techniques is proposed: two adaptive noise cancellation techniques, Least Mean Square (LMS), Recursive Least Square (RLS); Savitzky-Golay (SG) smoothing filter and Discrete Wavelet Transform (DWT). These methods are implemented on 60 Hz Power-Line Interference (PLI), ECG signals of FANTASIA database and MIT-BIH Arrhythmia Database. Here, Short-Term Fourier Transforms (STFT) and Continuous Wavelet Transform (CWT) is introduced as a graphical tool to measure the noise level in the filtered ECG signals and also to validate the filtering performances of the proposed techniques. Statistical evaluation is also performed calculating the Signal to Noise Ratio (SNR), Mean Square Error (MSE), the Root Mean Square Error (RMSE), Peak Signal to Noise Ratio (PSNR) and Peak to Peak Amplitude (P2P) change before and after filtering of the ECG signals. The graphical results (frequency domain analysis using STFT and CWT) and statistical observation suggest that the noise cancellation performance of DWT is better, over other techniques.

State-of-charge (SOC) estimation of lithium-ion batteries (LIBs) is the basis of other state estimations. However, its accuracy can be affected by many factors, such as temperature and ageing. To handle this bottleneck issue, we here propose a joint SOC-SOH estimation method considering the influence of the temperature. It combines the Forgetting Factor Recursive Least Squares (FFRLS) algorithm, Total Least Squares (TLS) algorithm, and Unscented Kalman Filter (UKF) algorithm. First, the FFRLS algorithm is used to identify and update the parameters of the equivalent circuit model in real time under different battery ageing degrees. Then, the TLS algorithm is used to estimate the battery SOH to improve the prior estimation accuracy of SOC. Next, the SOC is calculated by the UKF algorithm, and finally, a more accurate SOH can be obtained according to the UKF-based SOC trajectory. The battery-in-the-loop experiments are utilized to verify the proposed algorithm. For the cases of temperature change up to 35 °C and capacity decay up to 10%, our joint estimator can achieve ultra-low errors, bounded by 2%, respectively, for SOH and SOC. The proposed method paves the way for the advancement of battery use in applications, such as electric vehicles and microgrid applications.

This article studies identification problems of multiple linear regression models, which may be described a class of multi-input multi-output systems (i.e. multivariable systems). Based on the coupling identification concept, a novel coupled-least-squares (C-LS) parameter identification algorithm is introduced for the purpose of avoiding the matrix inversion in the multivariable recursive least-squares (RLS) algorithm for estimating the parameters of the multiple linear regression models. The analysis indicates that the C-LS algorithm does not involve the matrix inversion and requires less computationally efforts than the multivariable RLS algorithm, and that the parameter estimates given by the C-LS algorithm converge to their true values. Simulation results confirm the presented convergence theorems.

The solar panel or solar cell is one of the most important components of the solar system that produces electrical energy with high efficiency compatible with electrical loads, but any defect in this cell can cause its efficiency to decrease. The objective of this work is to establish a fault diagnosis method that can be implemented in a real structure. These faults are diagnosed and located by implementing an algorithm based on the measured values ​​of the solar panel using an intelligent recursive least squares approach. Our objective is to contribute to the diagnosis of faults in photovoltaic systems based on fuzzy logic in a recurrent manner. The integration of recursive least squares (RLS) with fuzzy logic are essential to improve system efficiency and reliability. This approach enables rapid identification and resolution of faults, helping to avoid energy losses, reduce downtime and support proactive maintenance. It guarantees the optimal functioning of solar panels, maximizing energy production and improving return on investment. Quantitatively, this method achieves high diagnostic accuracy (over 90%), reduces error rates by up to 30% under dynamic conditions, and provides real-time fault detection with minimal latency. The combination of RLS and fuzzy logic improves fault diagnosis by effectively handling uncertainties and handling ambiguous situations better than traditional methods.

With the popularity of electric vehicles, lithium-ion batteries as a power source are an important part of electric vehicles, and online identification of equivalent circuit model parameters of a lithium-ion battery has gradually become a focus of research. A second-order RC equivalent circuit model of a lithium-ion battery cell is modeled and analyzed in this paper. An adaptive expression of the variable forgetting factor is constructed. An adaptive forgetting factor recursive least square (AFFRLS) method for online identification of equivalent circuit model parameters is proposed. The equivalent circuit model parameters are identified online on the basis of the dynamic stress testing (DST) experiment. The online voltage prediction of the lithium-ion battery is carried out by using the identified circuit parameters. Taking the measurable actual terminal voltage of a single battery cell as a reference, by comparing the predicted battery terminal voltage with the actual measured terminal voltage, it is shown that the proposed AFFRLS algorithm is superior to the existing forgetting factor recursive least square (FFRLS) and variable forgetting factor recursive least square (VFFRLS) algorithms in accuracy and rapidity, which proves the feasibility and correctness of the proposed parameter identification algorithm.

The intelligent vehicle is a complicated nonlinear system, and the design of a path tracking controller is one of the key technologies in intelligent vehicle research. This paper mainly designs a lateral control dynamic model of the intelligent vehicle, which is used for lateral tracking control. Firstly, the vehicle dynamics model (i.e., transfer function) is established according to the vehicle parameters. Secondly, according to the vehicle steering control system and the CARMA (Controlled Auto-Regression and Moving-Average) model, a second-order control system model is built. Using forgetting factor recursive least square estimation (FFRLS), the system parameters are identified. Finally, a neural network PID (Proportion Integral Derivative) controller is established for lateral path tracking control based on the vehicle model and the steering system model. Experimental simulation results show that the proposed model and algorithm have the high real-time and robustness in path tracing control. This provides a certain theoretical basis for intelligent vehicle autonomous navigation tracking control, and lays the foundation for the vertical and lateral coupling control.