Recursive Least Squares Research Articles

Diagnosis of solar panels using Fuzzy logic with a recursive method

The article presents an innovative methodology for diagnosing faults in solar panels using an approach that combines fuzzy logic and recursive least squares (RLS). The main objective of the study is to develop a robust and accurate diagnostic system capable of detecting and locating faults in solar panels. The proposed method uses fuzzy logic to model the complex relationships between the parameters of the solar panel, such as brightness, temperature, voltage, current, and the operating state of the solar panel. Recursive least squares (RLS) are integrated into the diagnostic system to dynamically update the fuzzy parameters of the model based on new observations and real data from the solar panel. This approach allows continuous adaptation of the diagnostic model to changes in environmental conditions and the operation of the solar panel. The results demonstrate the effectiveness and accuracy of the proposed diagnostic system, with a high capability to detect and locate different types of faults in solar panels.

State of Charge Estimation of Lithium Battery Utilizing Strong Tracking H-Infinity Filtering Algorithm

The ability to quickly and accurately estimate the state of charge (SOC) of lithium batteries is a key function of the battery management system (BMS). To enhance the accuracy of SOC estimation for lithium batteries, we propose a method that combines the dynamic factor recursive least squares (DFFRLS) algorithm and the strong tracking H-infinity filtering (STF-HIF) algorithm. To address the issue of fixed forgetting factors in recursive least squares (RLS) that struggle to maintain both fast convergence and stability in battery parameter identification, we introduce dynamic forgetting factors. This approach adjusts the forgetting factor based on the residuals between the model’s estimated and actual values. To improve the H-infinity filtering (HIF) algorithm’s poor performance in tracking sudden state changes, we propose a combined STF-HIF algorithm, integrating HIF with strong tracking filtering (STF). Simulation experiments indicate that, compared to the HIF algorithm, the STF-HIF algorithm achieves a maximum absolute SOC estimation error (MaxAE) of 0.69%, 0.72%, and 1.22%, with mean absolute errors (MAE) of 0.27%, 0.25%, and 0.38%, and root mean square errors (RMSE) of 0.33%, 0.30%, and 0.46% under dynamic stress testing (DST), federal urban driving schedules (FUDS), and Beijing dynamic stress testing (BJDST) conditions, respectively.

Adaptive Path-Tracking Control Algorithm for Autonomous Mobility Based on Recursive Least Squares with External Condition and Covariance Self-Tuning

This paper introduces an adaptive path-tracking control algorithm for autonomous mobility based on recursive least squares (RLS) with external conditions and covariance self-tuning. The advancement and commercialization of autonomous driving necessitate universal path-tracking control technologies. In this study, we propose a path-tracking control algorithm that does not rely on vehicle parameters and leverages RLS with self-tuning mechanisms for external conditions and covariance. We designed an integrated error for effective path tracking that combines the lateral preview distance and yaw angle errors. The controller design employs a first-order derivative error dynamics model with the coefficients of the error dynamics estimated through the RLS using a forgetting factor. To ensure stability, we applied the Lyapunov direct method with injection terms and finite convergence conditions. Each regression process incorporates external conditions, and the self-tuning of the injection terms utilizes residuals. The performance of the proposed control algorithm was evaluated using MATLAB®/Simulink® and CarMaker under various path-tracking scenarios. The evaluation demonstrated that the algorithm effectively controlled the front steering angle for autonomous path tracking without vehicle-specific parameters. This controller is expected to provide a versatile and robust path-tracking solution in diverse autonomous driving applications.

A proportional fusion adaptation algorithm to reduce noise in sEMG signals of the lower limb

Abstract To address issues related to unknown noise pollution and the inadequate performance of single adaptive noise reduction algorithms in measuring lower limb surface electromyography (sEMG) signals, this paper proposes an algorithm that combines the fast convergence speed and strong noise reduction capability of recursive least-squares (RLS) with the low computational complexity of the normalized least-mean-square (NLMS) and improved proportionate NLMS (IPNLMS). Through the proportional fusion of RLS with NLMS and RLS with IPNLMS, the proposed algorithm greatly improves convergence speed, stability, and noise reduction performance while effectively reducing computational complexity. Moreover, considering the influence of the initial value of weights on the noise reduction performance during the updating process of the adaptive noise reduction algorithm, a weight initial value setting (WIS) module is proposed to optimize the initial value of the weights by the known amount of data. Based on 50 independent experiments, an adaptive noise reduction algorithm and WIS module were used to reduce the unknown noise in the lower limb sEMG signals, which was generated by white Gaussian noise, power line interference, or hybrid noise interfered by an unknown environment. The noise reduction performance was evaluated by using the average value of the signal-to-noise ratio (SNR), the root-mean-square error, and R-square. Compared with the RLS, NLMS, and IPNLMS algorithms for noise reduction of vastus lateralis, rectus femoris, and biceps femoris signals containing unknown noise, the SNR of RLS-NLMS, RLS-IPNLMS, WIS-RLS-NLMS, and WIS-RLS-IPNLMS is improved by an average of [7.92%, 55.54%, 55.63%], [7.45%, 54.90%, 54.99%], [19.70%, 72.38%, 72.71%], [19.32%, 71.84%, 72.19%]. The simulation results verify that the proportional fusion adaptive noise reduction algorithm and the WIS module effectively accelerate the convergence speed, enhance the noise reduction capability, and reduce the computational complexity.

ADAPTIVE METHOD OF FORMING COMPLEX SIGNALS ENSEMBLES BASED ON MULTI-LEVEL RECURRENT TIME-FREQUENCY SEGMENT MODELING

The article investigates the implementation of an adaptive method for forming ensembles of complex signals based on multilevel recurrent time-frequency segmentation. It addresses the key challenges faced by cognitive wireless networks operating in dynamic radio frequency environments with high levels of interference, necessitating rapid adaptation to changes in the spectral characteristics of signals. The study substantiates the need for adaptive filters and specific transformations to enhance signal processing quality, particularly in environments with high variability in frequency characteristics and significant noise interference. The proposed method of multilevel recurrent time-frequency segmentation allows for the modification of time segment durations and the use of segments of varying lengths, providing flexibility in signal processing and adaptation to current conditions. This adaptability enables optimal signal processing for each individual case, taking into account short-term impulses, long-term fluctuations, and various types of noise and distortions. This approach effectively separates frequency components and reduces interference between them, which is crucial for maintaining high signal quality and communication stability in cognitive networks. It has been proven that the use of adaptive filters such as LMS (Least Mean Squares) and RLS (Recursive Least Squares), as well as fast Fourier Transform (STFT), wavelet, and Hilbert transforms at different stages of multilevel time-frequency segmentation, significantly enhances signal interference resistance and energy efficiency. Comparative analysis of signal metrics before and after filtering and transformation shows an increase in signal quality by 14,3–24,5% and a reduction in noise levels by 21,7–29,6%. The wavelet transform, in particular, proved to be highly effective, allowing for precise extraction of useful frequency components from the noise background and improving signal parameters through dynamic adjustment to specific radio environment conditions. Experimental results confirm the effectiveness of the proposed method, demonstrating its ability to ensure consistently high-quality processing of complex signal ensembles even in dynamic cognitive radio environments.

Convolutional Long Short-Term Memory Predictor for Collaborative Remotely Operated Vehicle Trajectory Tracking in a Leader–Follower Formation Subject to Communication and Sensor Latency in the Presence of External Disturbances

Nowadays, collaborative operations between Remotely Operated Vehicles (ROVs) face considerable challenges, particularly in leader–follower schemes. The underwater environment imposes limitations on acoustic modems, leading to reduced transmission speeds and increased latency in ROV position and speed transmission. This complicates effective communication between the ROVs. Traditional methods, such as Recursive Least Squares (RLS) predictors and the Kalman filter, have been employed to address these issues. However, these approaches have limitations in handling non-linear patterns and disturbances in underwater environments. This paper introduces a Convolutional Long Short-Term Memory (ConvLSTM) predictor designed to enhance communication and trajectory tracking between ROVs in a leader–follower scheme. The proposed ConvLSTM aims to address the shortcomings of previous methods by adapting effectively to varying conditions, including ocean currents, communication delays, and signal interruptions. Simulations were conducted to evaluate ConvLSTM’s performance and compare it with other advanced predictors, such as Multilayer Perceptron (MLP) and Long Short-Term Memory (LSTM), under different conditions. The results demonstrated that ConvLSTM achieved a 13.9% improvement in trajectory tracking, surpassing other predictors in scenarios that replicate real underwater conditions and multi-vehicle communication. These results highlight ConvLSTM’s potential to significantly enhance the performance and stability of collaborative ROV operations in dynamic underwater environments.

A low-complexity error-feedback lattice-equalizer with phase tracking for underwater acoustic communications.

Recursive least squares (RLS)-based equalizers are hindered by their high complexity in underwater acoustic (UWA) communications. This article proposes an adaptive equalizer with a phase tracking method for the UWA communication, named the error-feedback lattice-equalizer (EFLE). First, we derive the algorithm for recursively solving the least squares problem from EFLE, introducing a lattice structure using time and order updates, thereby reducing the complexity to be linearly related to its length. The error-feedback mechanism used in computing reflection coefficients ensures the numerical stability of the algorithm. By focusing on the rapid tap rotation in time-varying channels, we design phase tracking in EFLE to further improve equalization performance. To verify the bit error rate (BER) performance of the proposed EFLE, we study the UWA communication system and conduct UWA simulations and at-sea experiments. Comparisons include linear complexity equalizers such as least mean square (LMS), leaky LMS, least mean mixed-norm, and ϵ-normalized LMS equalizers, and quadratic complexity RLS equalizers. At-sea experiment results show that the BER performance of EFLE significantly outperforms its counterparts.

Research on random dynamic cylinder deactivation control strategy of engine based on nonlinear model prediction

In the process of cycle cylinder deactivation, the different proportion of cylinder deactivation between adjacent working cycles will cause the problem of uneven operation of each cylinder. In this paper, a random dynamic cylinder deactivation (RD-CDA) control method based on nonlinear model prediction is proposed. The RBF neural network model of the RD-CDA system is built. The K-means algorithm is applied to the offline training of the center position c of the hidden layer node. The P-nearest algorithm is used to train the hidden layer node width σ offline. The recursive least squares (RLS) algorithm is applied to train the output layer weight vector w online. The online adaptive change of the model is realized, and the model verification is carried out. Then, the nonlinear model predictive control system structures with the minimum torque fluctuation and brake specific fuel consumption rate (BSFC) are built respectively. Under different working conditions, the average torque fluctuation per cycle is improved by about 9% to 18.75%, and the average BSFC is improved by about 2 % -3.9 %, which verifies the effectiveness of this strategy in reducing the dynamic fluctuation of random dynamic cylinder deactivation torque and improving fuel economy.

Porównanie metod sterowania adaptacyjnego dla stołu balansującego kulą

The purpose of this paper is to present and compare adaptive control algorithms: Model Identification Adaptive Control (MIAC) and Model Reference Adaptive Control (MRAC), with their modifications that allow to improve quality of control in specific cases. The ball balancing (BBT) table physical stand, which is an example of a ball on plate system, was used, and the balancing problem that occurs could potentially lead to work on stabilizing a boat or a drone. This paper presents a non-linear model of the object and its linear approximation in the vicinity of the operating point, additionally demonstrating the process of parameters identification with the Recursive Least Square (RLS) method. The quality of the adaptive control algorithms was compared during transients and in steady state. The research showed the possibilities of both indirect and direct adaptation of the controller parameters, depending on the selected method. Quality indices, such as the cost of control and the integral of absolute error, were utilized for the comparative analysis. The advantages of the compared algorithms and their modifications, that can enhance the system performance in special cases, were also demonstrated. The tested adaptive control algorithms made the system robust to modeling errors (lack of knowledge of parameters) or other internal disturbances.

Design and application of interval type-2 fuzzy neural network systems optimized with hybrid algorithms

Interval type-2 fuzzy neural network systems (IT2 FNNSs) own the advantages of IT2 fuzzy logic systems (FLSs) and NN. The paper designs a kind of IT2 FNNSs for permanent magnetic drive (PMD) forecasting. For each rules of IT2 FNNSs, whose antecedents, consequents and input measurements are chosen as Gaussian IT2 membership functions (MFs). The proposed hybrid backpropagation (BP) algorithms and recursive least square (RLS) algorithms are adopted to tune all the parameters simultaneously. Simulation instances on the basis of data of permanent magnetic drive (PMD) torque and revolutions per minute (rpm) are adopted for testing the performances of proposed hybrid optimized IT2 FNNSs for forecasting. Convergence analysis illustrates that the IT2 FNNSs have excellent generalization capability compared with both singleton and non-singleton T1 FNNSs.

Data-Driven Modeling and Open-Circuit Voltage Estimation of Lithium-Ion Batteries

This article presents a data-driven methodology for modeling lithium-ion batteries, which includes the estimation of the open-circuit voltage and state of charge. Using the proposed methodology, the dynamics of a battery cell can be captured without the need for explicit theoretical models. This approach only requires the acquisition of two easily measurable variables: the discharge current and the terminal voltage. The acquired data are used to build a linear differential system, which is algebraically manipulated to form a space-state representation of the battery cell. The resulting model was tested and compared against real discharging curves. Preliminary results showed that the battery’s state of charge can be computed with limited precision using a model that considers a constant open-circuit voltage. To improve the accuracy of the identified model, a modified recursive least-squares algorithm is implemented inside the data-driven method to estimate the battery’s open-circuit voltage. These last results showed a very precise tracking of the real battery discharging dynamics, including the terminal voltage and state of charge. The proposed data-driven methodology could simplify the implementation of adaptive control strategies in larger-scale solutions and battery management systems with the interconnection of multiple battery cells.

Particle Filtering for Enhanced Parameter Estimation in Bilinear Systems Under Colored Noise

This paper addresses the challenging problem of parameter estimation in bilinear systems under colored noise. A novel approach, termed B-PF-RLS, is proposed, combining a particle filter (PF) with a recursive least squares (RLS) estimator. The B-PF-RLS algorithm tackles the complexities arising from system nonlinearities and colored noise by effectively estimating unknown system states using the particle filter, which are then integrated into the RLS parameter estimation process. Furthermore, the paper introduces an enhanced particle filter that eliminates the need for explicit knowledge of the measurement noise variance, enhancing the method's practicality for real-world applications. Numerical examples demonstrate the B-PF-RLS algorithm's superior performance in accurately estimating both system parameters and states, even under uncertain noise conditions. This work offers a robust and effective solution for system identification in various engineering applications involving bilinear models subject to complex noise environments.

A new voltage sensitivity-based distributed feedback online optimization for voltage control in active distribution networks

Rising sustainability, environmental, and decarbonization considerations have prompted a recent increase in the integration of inverter-based distributed energy resources (DER), such as photovoltaics (PV), into the power grid. This trend raises concerns about potential voltage violations within distribution systems, emphasizing the growing relevance of effective voltage regulation. Utilizing smart inverters for active and reactive power control proves highly efficient in addressing voltage rise issues within active distribution networks (ADN). This work proposes a distributed feedback online optimization (FOO) strategy for voltage regulation in ADNs. The FOO strategy utilizes online recursive least squares (RLS) sensitivity-based feedback, relying on local measurements to iteratively compute optimal reactive power set points for DERs, ensuring bus voltage regulation to within acceptable limits. The distributed control algorithm employs a primal-dual update approach, enabling coordinated information exchange between neighboring controllers. This online feedback-based control offers a promising solution for real-time coordinated voltage control in distribution grids, particularly with the increasing integration of inverter-based DERs at the grid's edge. The approach demonstrates robustness under varying conditions, communication dynamics, and topology changes, validated using real distribution feeders with actual solar PV production and consumption data. Advancements in sensing, communication systems, and smart grid tools further enhance the feasibility and scalability of this strategy for evolving power systems.

Learning and Controlling Multiscale Dynamics in Spiking Neural Networks Using Recursive Least Square Modifications.

Invasive brain-computer interfaces (BCIs) have the capability to simultaneously record discrete signals across multiple scales, but how to effectively process and analyze these potentially related signals remains an open challenge. This article introduces an innovative approach that merges modern control theory with spiking neural networks (SNNs) to bridge the gap among multiscale discrete information. Specifically, the macroscopic point-to-point trajectory is formulated as an optimal control problem with fixed terminal time and state, and it is iteratively solved using the direct dynamic programming (DDP) algorithm. Additionally, SNN is utilized to simulate microscale neural activities in the premotor cortex, employing the product of the weighted adjacency matrix and the mesoscale firing rate to approximate the macroscopic trajectory. The error between actual macroscale behavior and the preceding approximation is then used to update the weighted adjacency matrix through the recursive least square (RLS) method. Analysis and simulation of various tasks, including low-dimensional point-to-point tasks, high-dimensional complex Lorenz systems, and center-out-and-back tasks, verify the feasibility and interpretability of our method in processing multiscale signals ranging from spiking neurons to motion trajectory through the integration of SNN and control theory.

Multi-head self-attention mechanism combined with feedforward network for time-varying nonlinear digital self-interference cancellation

In-band full duplex (IBFD) allows simultaneous communication in the same frequency band, thus significantly improving spectral efficiency. However, self-interference (SI) at the local transmitter affects decoding at the receiver, and SI intensity increases when the channel is time-varying. Existing techniques concentrate on dealing with digital self-interference (DSI) in static channels, which are difficult to adapt to time-varying environments. For this purpose, firstly, the recursive least squares (RLS) method is utilized to counteract linear DSI. Secondly, a new feedforward neural network based on the multi-head self-attention mechanism (MHSAM-FFNN) is designed to eliminate dynamically changing nonlinear DSI. RLS can track signals and update linear coefficients. The self-attention mechanism computes the attention between any two signals in a time-varying sequence and aggregates the temporal relations by the obtained attention weights. MHSAM-FFNN utilizes multiple self-attention modules in parallel, which enhances the acquisition of different effective information in the time-varying sequence to better learn the feature relationships between the current signal and other signals. It ultimately reconstructing the nonlinearity and memory effects of DSI. As tested in different time-varying environments, results show that this paper's scheme successfully reduces DSI to the noise floor. In addition, this paper considers two scenarios where both the power amplifier (PA) and the low noise amplifier (LNA) are nonlinear and where PA is nonlinear while LNA is linear. Results demonstrate that our scheme can achieve higher interference cancellation in different nonlinear scenarios.

Nonlinear acoustic echo cancellation using low-complexity low-rank recursive least-squares algorithms

Adaptive exponential functional link networks (AEFLN) are a type of linear-in-the-parameter nonlinear filters, which have shown enhanced modeling capability for nonlinear systems. However, the convergence speed of traditional AEFLN is generally slow for long impulse responses, hence, AEFLN trained using recursive least-squares becomes an attractive choice to achieve faster convergence. Moreover, huge computational burden of RLS makes it unsuitable in practical applications like echo cancellation. While low complexity versions of RLS are widely available in literature, they still suffer from low convergence speed. To address this issue, we propose a nonlinear acoustic echo cancellation (NAEC) system using AEFLN-RLS, based on the nearest Kronecker product (NKP) decomposition and low-rank approximation technique, which not only reduces computational complexity but also achieves improved convergence speed (especially tracking). To further improve the echo cancellation performance in non-stationary conditions, a variable regularization approach based NKP-AEFLN-RLS system is also proposed. To also reduce the computational complexity further, dichotomous coordinate descent (DCD) updates are incorporated into the proposed NKP-AEFLN-RLS NAEC system and its variable regularization version. Experimental results show the effectiveness of the proposed algorithms, with the variable regularized version of the algorithm using DCD iterations showing the best compromise between convergence capability and lower computational complexity.

Adaptive Filtering with Fitted Noise Estimate (AFFiNE): Blink Artifact Correction in Simulated and Real P300 Data.

(1) Background: The electroencephalogram (EEG) is frequently corrupted by ocular artifacts such as saccades and blinks. Methods for correcting these artifacts include independent component analysis (ICA) and recursive-least-squares (RLS) adaptive filtering (-AF). Here, we introduce a new method, AFFiNE, that applies Bayesian adaptive regression spline (BARS) fitting to the adaptive filter's reference noise input to address the known limitations of both ICA and RLS-AF, and then compare the performance of all three methods. (2) Methods: Artifact-corrected P300 morphologies, topographies, and measurements were compared between the three methods, and to known truth conditions, where possible, using real and simulated blink-corrupted event-related potential (ERP) datasets. (3) Results: In both simulated and real datasets, AFFiNE was successful at removing the blink artifact while preserving the underlying P300 signal in all situations where RLS-AF failed. Compared to ICA, AFFiNE resulted in either a practically or an observably comparable error. (4) Conclusions: AFFiNE is an ocular artifact correction technique that is implementable in online analyses; it can adapt to being non-stationarity and is independent of channel density and recording duration. AFFiNE can be utilized for the removal of blink artifacts in situations where ICA may not be practically or theoretically useful.

Temporal Convolutional Neural Network-Based Prediction of Vascular Health in Elderly Women Using Photoplethysmography-Derived Pulse Wave during Exercise.

(1) Background: The objective of this study was to predict the vascular health status of elderly women during exercise using pulse wave data and Temporal Convolutional Neural Networks (TCN); (2) Methods: A total of 492 healthy elderly women aged 60-75 years were recruited for the study. The study utilized a cross-sectional design. Vascular endothelial function was assessed non-invasively using Flow-Mediated Dilation (FMD). Pulse wave characteristics were quantified using photoplethysmography (PPG) sensors, and motion-induced noise in the PPG signals was mitigated through the application of a recursive least squares (RLS) adaptive filtering algorithm. A fixed-load cycling exercise protocol was employed. A TCN was constructed to classify flow-mediated dilation (FMD) into "optimal", "impaired", and "at risk" levels; (3) Results: TCN achieved an average accuracy of 79.3%, 84.8%, and 83.2% in predicting FMD at the "optimal", "impaired", and "at risk" levels, respectively. The results of the analysis of variance (ANOVA) comparison demonstrated that the accuracy of the TCN in predicting FMD at the impaired and at-risk levels was significantly higher than that of Long Short-Term Memory (LSTM) networks and Random Forest algorithms; (4) Conclusions: The use of pulse wave data during exercise combined with the TCN for predicting the vascular health status of elderly women demonstrated high accuracy, particularly in predicting impaired and at-risk FMD levels. This indicates that the integration of exercise pulse wave data with TCN can serve as an effective tool for the assessment and monitoring of the vascular health of elderly women.

A robust PID and RLS controller for TCP/AQM system

Transmission Control Protocol (TCP) controlling congestion by peer-to-peer is challenging to handle communication with numerous concurrent TCP flows and heavy traffic loads. Therefore, TCP requires the active queue management (AQM) to assist in avoiding buffer bloat in intermediate devices. Thus, Some AQM controllers, such as Red, Codel, and Pie, have been proposed to control congestion better. However, these controllers are unable to overcome the drawbacks, including micro-burst streams, unfair competition of flows with different workloads, as well as sluggishly responding to congestion in heavy traffic, which degrade the performance of data transmission. To address these problems, in this paper, we proposed a queueing-delay-based AQM controller for TCP/AQM systems, namely PID-R. PID-R adopts two-level control components, i.e., the Proportional-Integral-Derivative (PID) algorithm and the recursive least squares (RLS) filter, and combines the advantages of the two parts. Meanwhile, we also constructed a new TCP/PID-R fluid model derived from TCP/AQM classical model. According to the model, PID-R parameters are determined to keep the TCP/PID-R system steady. The comprehensive simulation reveals that PID-R outperforms the state-of-the-art AQM controllers.

A solution on parameter fluctuation of integrated on‐board battery chargers based on recursive least square algorithm

SummaryIntegrated on‐board battery chargers (IOBCs) are receiving increasing academic attention due to their low cost and low weight advantages. However, IOBCs suffer from periodic saturation, which causes periodic changes in inductance, which may lead to deterioration in control performance. Model‐free predictive control (MFPC) is a strongly robust control method that is suitable for solving the periodic saturation problem of IOBCs with pulsating magnetic fields. In this paper, a common single‐phase IOBC topology is used as an example, the causes of inductance fluctuations are analyzed, and finite element analysis (FEM) of motor inductance with different motor qualities is carried out. A recursive least squares (RLS)‐based solution method is proposed, and its convergence is analyzed. The feasibility of the proposed control scheme is experimentally verified.