Recursive Least-squares Algorithm Research Articles

Distributed Quantization-Aware RLS Learning With Bias Compensation and Coarsely Quantized Signals

In this work, we present an energy-efficient distributed learning framework using coarsely quantized signals for Internet of Things (IoT) networks. In particular, we develop a distributed quantization-aware recursive least-squares (DQA-RLS) algorithm that can learn parameters in an energy-efficient fashion using signals quantized with few bits while requiring a low computational cost. Moreover, we develop a bias compensation strategy to further improve the performance of the proposed DQA-RLS algorithm. We carry out a statistical analysis of the proposed DQA-RLS algorithm and derive analytical expressions for predicting the mean-square deviation. A computational complexity evaluation and a study of the power consumption of the proposed and existing techniques are then presented. Numerical results assess the DQA-RLS algorithm against existing techniques for a distributed parameter estimation task in a scenario where IoT devices operate in peer-to-peer mode.

Tukey’s Biweight M-Estimate With Conjugate Gradient Adaptive Learning

We propose a novel M-estimate conjugate gradient (CG) algorithm, termed Tukey’s biweight M-estimate CG (TbMCG), for system identification in impulsive noise environments. In particular, the TbMCG algorithm can achieve a faster convergence while retaining a reduced computational complexity as compared to the recursive least-squares (RLS) algorithm. Specifically, the Tukey’s biweight M-estimate incorporates a constraint into the CG filter to tackle impulsive noise environments. Moreover, the convergence behavior of the TbMCG algorithm is analyzed. Simulation results confirm the excellent performance of the proposed TbMCG algorithm for system identification and active noise control applications.

Enhancement of Tracking and Disturbance Suppression Performance via Adaptive Parameter Tuning of Two-degree-of-freedom Control System Using On-line FRIT

In general, the characteristics of the control object changes over time due to aging, breakdowns, and changes in operating conditions and environment. In such cases, tracking and disturbance suppression performance of the entire closed-loop system may deteriorate. Based on a data-driven approach (online FRIT), we propose a method for simultaneously and sequentially tuning the control parameters of the feedforward and feedback controller of a two-degree-of-freedom control system in real time. We set two reference models as indicators of control performance: a target response model and a sensitivity characteristic model. The adaptive computation mechanism of the proposed method is based on the RLS (recursive least-squares) algorithm with a forgetting factor which can appropriately reflect changes in the characteristics of the controlled object. The proposed method enhances target tracking and disturbance suppression performance for time-varying systems without control system shutdown in real time. Finally, the effectiveness of the proposed method is demonstrated through simulation on benchmark process system.

State of Energy Estimation for Lithium-Ion Battery Pack via Prediction in Electric Vehicle Applications

Accurate state of energy (SOE) estimation of the battery pack is very important for the electric vehicle's driving range estimation, which is still a very challenging problem under actual vehicle application conditions at present. This paper proposes a method for estimating the SOE of the battery pack based on prediction, taking into account the future voltage and temperature changes of the battery pack. Firstly, a novel definition of the battery pack SOE is proposed, which considers the inconsistency of the battery pack. Secondly, the thermo-electric lumped parameter equivalent circuit model of a single cell in the battery pack is applied. The electrical parameters are identified using the forgetting factor recursive least-squares algorithm, and the extended Kalman filter is used to estimate the SOC of each cell. Finally, the future current, voltage and temperature response of the cell in the battery pack are accurately predicted and iterative calculations are performed to get SOE under the condition that the future output power of the battery pack is predicted by the Markov chain model method. The effectiveness of the proposed method is verified under dynamic conditions at different temperatures. The results show that the above method has high precision and good robustness, and can meet the needs of actual vehicle applications.

Accurate estimation of modern power system harmonics using a novel LSA hybridized recursive least square technique

Abstract This paper purposes a new type of hybrid technique depends on lightning search algorithm (LSA) and recursive least square (RLS) named as LSA-RLS to overcome the harmonic estimation issues in time varying modern power system signals buried with noises. LSA is based on a natural phenomenon of lightning. It consists of three types of projectiles: transition, space and lead projectiles. Transition projectiles create population, space projectiles do the exploration and the lead projectiles do the work of exploitation and find the optimal solution. The basic LSA algorithm is mixed with RLS algorithm in an adaptive way to estimate the states of the harmonic signals. Simulation and validation are made with real time data obtained from a converter fed D.C motor drive. The efficacy of the proposed algorithm is verified by comparing the simulation results of recently reported algorithms such as particle swarm optimization (PSO), differential evolution (DE), bacteria foraging optimization (BFO), gravity search algorithm hybridized recursive least square method (GSA-RLS). It is verified that proposed (LSA-RLS) technique is the best in terms of computational time, convergence, accuracy.

Mixture quantized error entropy for recursive least squares adaptive filtering

Error entropy is a well-known learning criterion in information theoretic learning (ITL), and it has been successfully applied in robust signal processing and machine learning. To date, many robust learning algorithms have been devised based on the minimum error entropy (MEE) criterion, and the Gaussian kernel function is always utilized as the default kernel function in these algorithms, which is not always the best option. To further improve learning performance, two concepts using a mixture of two Gaussian functions as kernel functions, called mixture error entropy and mixture quantized error entropy, are proposed in this paper. We further propose two new recursive least-squares algorithms based on mixture minimum error entropy (MMEE) and mixture quantized minimum error entropy (MQMEE) optimization criteria. The convergence analysis, steady-state mean-square performance, and computational complexity of the two proposed algorithms are investigated. In addition, the reason why the mixture mechanism (mixture correntropy and mixture error entropy) can improve the performance of adaptive filtering algorithms is explained. Simulation results show that the proposed new recursive least-squares algorithms outperform other RLS-type algorithms, and the practicality of the proposed algorithms is verified by the electro-encephalography application.

Proportionate RLS with l1 norm regularization: Performance analysis and fast implementation

Sparse recursive least squares (RLS) adaptive filter algorithms achieve faster convergence and better performance than the standard RLS algorithm under sparse systems. Existing methods are designed by either incorporating a sparse regularization term, e.g., l1-norm, into the standard RLS cost function or introducing a proportionate matrix into the updating equation. As the principles behind the two designs are complementary, we propose in this paper to combine them together and develop an enhanced method named the l1-proportionate RLS (l1-PRLS). Theoretical performance analysis of the proposed l1-PRLS is carried out in terms of the first-order and second-order transient property, and steady-state property. Based on the analysis, guidances for the selection of adaptive parameters are obtained. With proper choices of relevant parameters, the l1-PRLS is guaranteed to be stable and achieve better performance than existing methods. To improve the applicability of the l1-PRLS, a fast implementation named the l1-proportionate stable fast transversal filter (l1-PSFTF) is also derived. Simulation results from sparse system identifications support the theoretical analysis.

Estimation of state-of-power capability for lithium-ion battery considering limiting conditions recalibration

ABSTRACT As one of the most significant deciding factors for energy management systems (EMSs) and battery management systems (BMSs) in electrified vehicles, battery state-of-power (SOP) estimation is an area of interest in battery research. Battery model parameters change obviously under the limiting working condition of SOP, and the available maximum current and state-of-charge (SOC) have to be updated for accurate SOP estimation. This paper tries to contribute to the existing literature as follows: Based on Thevenin model, recursive least-square (RLS) and H-infinity filter algorithm are adopted for parameter identification and SOC estimation for a recalibration purpose to improve the prediction of battery SOP under variable degradation. Multi-constraints are firstly adopted to calculate the limiting current, and the response function of capacity loss-temperature-discharge rate is brought back to correct the actual capacity at this current for the revised limiting current with consideration of weight distribution ratio. Finally, the experiment verifies that the final maximum charging-discharging current modifies the initial calculation value by 5% and 4%, and realizes the more accurate online SOP estimation. This method provides a more accurate and reliable SOP estimation method for electric vehicles.

Orthogonal Imbalance Compensation Method of Φ-OTDR System Based on RLS Algorithm

Aiming at the quadrature unbalance phenomenon in the phase-sensitive optical time domain reflectometry ( $\Phi $ -OTDR) system, a method of quadrature unbalance compensation for the $\Phi $ -OTDR system based on the recursive least square (RLS) algorithm is studied and demonstrated to improve the accuracy of the demodulated phase waveform. Firstly, the DC residual term of the quadrature imbalance is eliminated by calculating the mean value of the envelope. Further, the cyclic symmetry of the AC orthogonal unbalance is tracked to complete parameter estimation, and then the orthogonal unbalance correction is completed through an adaptive filtering method. The experimental results show that under the condition of the detection light pulse with a repetition frequency of 5 KHz and a pulse width of 100 ns, the RLS compensation algorithm greatly improves the demodulation characteristics of the system and suppresses the quadrature imbalance. It is of great significance to the practical process of the $\Phi $ -OTDR system.

Adaptive Turbo Equalization for Nonlinearity Compensation in WDM Systems

In this paper, the performance of adaptive turbo equalization for nonlinearity compensation (NLC) is investigated. A turbo equalization scheme is proposed where a recursive least-squares (RLS) algorithm is used as an adaptive channel estimator to track the time-varying intersymbol interference (ISI) coefficients associated with inter-channel nonlinear interference (NLI) model. The estimated channel coefficients are used by a MIMO $2\times 2$ soft-input soft-output (SISO) linear minimum mean square error (LMMSE) equalizer to compensate for the time-varying ISI. The SISO LMMSE equalizer and the SISO forward error correction (FEC) decoder exchange extrinsic information in every turbo iteration, allowing the receiver to improve the performance of the channel estimation and the equalization, achieving lower bit-error-rate (BER) values. The proposed scheme is investigated for polarization multiplexed 64QAM and 256QAM, although it applies to any proper modulation format. Extensive numerical results are presented. It is shown that the scheme allows up to 0.7 dB extra gain in effectively received signal-to-noise ratio (SNR) and up to 0.2 bits/symbol/pol in generalized mutual information (GMI), on top of the gain provided by single-channel digital backpropagation.

Photonic-based analog and digital RF self-interference cancellation with high spectral efficiency.

A photonic-assisted analog and digital radio frequency (RF) self-interference cancellation (SIC) approach with high spectral efficiency is reported for base stations in in-band full-duplex radio-over-fiber systems on the basis of our previous research. One dual-polarization quadrature phase-shift keying (DP-QPSK) modulator is used as the canceller for one base station. The two dual-parallel Mach-Zehnder modulators of the DP-QPSK modulator are both biased as carrier-suppressed single-sideband modulators and driven by the received signal and reference signal, respectively, to achieve high spectral efficiency while implementing the SIC in the optical domain. The baseband optical signal after SIC is further transmitted to the central station, where the electrical signal is recovered, sampled, and processed to further suppress the residual self-interference in the digital domain by using the recursive least-square (RLS) algorithm. An experiment is then performed. The proposed system is demonstrated by employing two independent channels. The analog cancellation depths of the 200, 500, and 800 Mbaud QPSK-modulated self-interferences are around 24, 20, and 20 dB, respectively; the total cancellation depths are around 29, 28, and 25 dB, respectively, when the analog cancellation and the RLS algorithm digital cancellation are applied. Meanwhile, the fiber distribution has no significant influence on SIC performance.

BEM Adaptive filtering for SI cancellation in full-duplex underwater acoustic systems

Self-interference (SI) cancellation (SIC) is the key technology for achieving full-duplex (FD) communications in underwater acoustic systems. In practice, SI channels are often fast-varying, e.g., due to reflections from surface waves. Classical adaptive filters, such as the recursive least squares (RLS) algorithm, predict the channel impulse response when used for channel estimation. If a tracking delay is acceptable, interpolating estimators capable of providing more accurate estimates of time-varying impulse responses can be used. Interpolating estimators with good tracking performance are normally of high complexity. In this paper, we propose low-complexity interpolating adaptive filters which combine the basis expansion model (BEM) approach with the sliding-window RLS (SRLS) algorithm. Specifically, we use the Legendre polynomials as the basis functions and solve the system of equations using dichotomous coordinate descent (DCD) iterations, thus the name the SRLS-L-DCD adaptive filter. A sparse algorithm (HSRLS-L-DCD) based on homotopy iterations is then proposed to exploit the sparsity in the expansion coefficients. The identification performance of the adaptive filters is investigated by a simulation which mimics an FD lake experiment. Both the simulation and lake experiments show that significant improvement in the SIC performance is achieved with the proposed low-complexity algorithms compared to the classical SRLS algorithm.

Slip-Clutch Torque Estimation via Real-Time Adaptive Lookup Table

Abstract Transfer case clutch is crucial in determining traction torque distribution between front and rear tires for four-wheel-drive (4WD) vehicles. Estimating time-varying clutch surface friction coefficient is critical for traction torque control since it is proportional to the clutch output torque. As a result, this paper proposes a real-time adaptive lookup table strategy to provide the time-varying clutch surface friction coefficient. Specifically, the clutch-parameter-dependent (such as clutch output torque and clutch touchpoint distance) friction coefficient is first estimated with available low-cost vehicle sensors (such as wheel speed and vehicle acceleration); and then a clutch-parameter-independent approach is developed for clutch friction coefficient through a one-dimensional lookup table. The table nodes are adaptively updated based on a fast recursive least-squares (RLS) algorithm. Furthermore, the effectiveness of adaptive lookup table is demonstrated by comparing the estimated clutch torque from adaptive lookup table with that estimated from vehicle dynamics, which achieves 14.8 Nm absolute mean squared error (AMSE) and 2.66% relative mean squared error (RMSE).

Low-Complexity Recursive Least-Squares Adaptive Algorithm Based on Tensorial Forms

Modern solutions for system identification problems employ multilinear forms, which are based on multiple-order tensor decomposition (of rank one). Recently, such a solution was introduced based on the recursive least-squares (RLS) algorithm. Despite their potential for adaptive systems, the classical RLS methods require a prohibitive amount of arithmetic resources and are sometimes prone to numerical stability issues. This paper proposes a new algorithm for multiple-input/single-output (MISO) system identification based on the combination between the exponentially weighted RLS algorithm and the dichotomous descent iterations in order to implement a low-complexity stable solution with performance similar to the classical RLS methods.

A Novel Method for Online Extraction of Small-Angle Scattering Pulse Signals from Particles Based on Variable Forgetting Factor RLS Algorithm.

The small-angle optical particle counter (OPC) can detect particles with strong light absorption. At the same time, it can ignore the properties of the detected particles and detect the particle size singly and more accurately. Reasonably improving the resolution of the low pulse signal of fine particles is key to improving the detection accuracy of the small-angle OPC. In this paper, a new adaptive filtering method for the small-angle scattering signals of particles is proposed based on the recursive least squares (RLS) algorithm. By analyzing the characteristics of the small-angle scattering signals, a variable forgetting factor (VFF) strategy is introduced to optimize the forgetting factor in the traditional RLS algorithm. It can distinguish the scattering signal from the stray light signal and dynamically adapt to the change in pulse amplitude according to different light absorptions and different particle sizes. To verify the filtering effect, small-angle scattering pulse extraction experiments were carried out in a simulated smoke box with different particle properties. The experiments show that the proposed VFF-RLS algorithm can effectively suppress system stray light and background noise. When the particle detection signal appears, the algorithm has fast convergence and tracking speed and highlights the particle pulse signal well. Compared with that of the traditional scattering pulse extraction method, the resolution of the processed scattering pulse signal of particles is greatly improved, and the extraction of weak particle scattering pulses at a small angle has a greater advantage. Finally, the effect of filter order in the algorithm on the results of extracting scattering pulses is discussed.

Random Fourier feature kernel recursive maximum mixture correntropy algorithm for online time series prediction

In the paper, a novel kernel recursive least-squares (KRLS) algorithm named random Fourier feature kernel recursive maximum mixture correntropy (RFF-RMMC) algorithm is proposed, which improves the prediction efficiency and robustness of the KRLS algorithm. Random Fourier feature (RFF) method as well as maximum mixture correntropy criterion (MMCC) are combined and applied into KRLS algorithm afterwards. Using RFF to approximate the kernel function in KRLS with a fixed cost can greatly reduce the computational complexity and simultaneously improve the prediction efficiency. In addition, the MMCC maintains the robustness like the maximum correntropy criterion (MCC). More importantly, it can enhance the accuracy of the similarity measurement between predicted and true values by more flexible parameter settings, and then make up for the loss of prediction accuracy caused by RFF to a certain extent. The performance of the RFF-RMMC algorithm for online time series prediction is verified by the simulation results based on three datasets.

A new control method for distortions compensation and power control using microgrid connecting voltage source converters

In this paper, a new control method is proposed for microgrid-connected voltage source converters (VSCs), which generally contain voltage and current control loops. The voltage of the point of common coupling (PCC) is analyzed by recursive least squares (RLS) algorithm and its fundamental positive symmetric components are extracted by the voltage control loop. Using the fundamental positive symmetric component, the required active and reactive powers are injected into the main grid via the microgrid-connected VSC without any distortions. This control loop is equipped with two PI controllers for the DC and AC voltage regulation. On the other hand, the same as the PCC voltage assessment, the local load current signal is evaluated by the RLS algorithm in the current control loop, with its harmonics and unbalanced components extracted. Eventually, the reference signal is obtained using these two control loops for generating switching pulses of the microgrid-connected VSC. Accordingly, the VSC acts as a shunt active power filter (APF), and also simultaneously injects the required active and reactive powers to the main grid. The proposed control method has high accuracy and fast dynamic response, and also its performance is independent of system parameters. The effectiveness of the proposed method has been verified by simulation and experiment.

Offline Measurement of Induction Motor Rotor Time Constant Based on Least Squares Algorithm

In order to solve the problems of disturbance and error accumulation in the traditional off-line strategy of rotor time constant, this paper optimizes the off-line measurement method of rotor time constant of induction motor. The off-line measurement method of rotor time constant based on recursive least squares (RLS) algorithm is analyzed in detail. Through the static characteristics of induction motor, the mathematical model of induction motor is simplified, and then the linear model of RLS algorithm is derived. The simulation results show that the rotor time constant measured by the least square method is more stable than that measured by the conventional method, which proves the practicability of the off-line measurement method. Finally, the error analysis of the main factors affecting the off-line measurement results of the rotor time constant based on the least square algorithm is given.

Magnetometer-Based Orbit Determination via Fast Reconstruction of Three-Dimensional Decoupled Geomagnetic Field Model

In this paper, magnetometer-based orbit determination via the fast reconstruction of a 3-D decoupled geomagnetic field (TDGF) model is examined. For the TDGF model, the three components of the geomagnetic field vector at a certain point are calculated separately with three different independent sets of Gauss coefficients rather than one identical set. The fast reconstruction algorithm is based on a recursive least-squares algorithm with a low computational burden. According to the orbit determination accuracy requirements for near-Earth satellites with communication systems that must be operational to update the TDGF model, the on-orbit model update interval can be appropriately selected so that the orbit determination accuracy can be effectively maintained. The simulation results of real flight data from magnetic survey satellites and simulated data show that the robustness of the proposed algorithm for different values of the measurement noise covariance matrices makes the algorithm more practical and that the position estimation error achieved by the proposed algorithm can meet the requirements of low- and medium-precision missions for near-Earth micro- and nanosatellites. In this way, both the autonomy and the orbit determination accuracy of satellites are considered simultaneously at the expense of some unnecessary autonomous capabilities for satellite tasks.

Optical wireless communication performance enhancement using Hamming coding and an efficient adaptive equalizer with a deep-learning-based quality assessment.

Optical wireless communication (OWC) technology is one of several alternative technologies for addressing the radio frequency limitations for applications in both indoor and outdoor architectures. Indoor optical wireless systems suffer from noise and intersymbol interference (ISI). These degradations are produced by the wireless channel multipath effect, which causes data rate limitation and hence overall system performance degradation. On the other hand, outdoor OWC suffers from several physical impairments that affect transmission quality. Channel coding can play a vital role in the performance enhancement of OWC systems to ensure that data transmission is robust against channel impairments. In this paper, an efficient framework for OWC in developing African countries is introduced. It is suitable for OWC in both indoor and outdoor environments. The outdoor scenario will be suitable to wild areas in Africa. A detailed study of the system stages is presented to guarantee the suitable modulation, coding, equalization, and quality assessment scenarios for the OWC process, especially for tasks such as image and video communication. Hamming and low-density parity check coding techniques are utilized with an asymmetrically clipped DC-offset optical orthogonal frequency-division multiplexing (ADO-OFDM) scenario. The performance versus the complexity of both utilized techniques for channel coding is studied, and both coding techniques are compared at different coding rates. Another task studied in this paper is how to perform efficient adaptive channel estimation and hence equalization on the OWC systems to combat the effect of ISI. The proposed schemes for this task are based on the adaptive recursive least-squares (RLS) and the adaptive least mean squares (LMS) algorithms with activity detection guidance and tap decoupling techniques at the receiver side. These adaptive channel estimators are compared with the adaptive estimators based on the standard LMS and RLS algorithms. Moreover, this paper presents a new scenario for quality assessment of optical communication systems based on the regular transmission of images over the system and quality evaluation of these images at the receiver based on a trained convolutional neural network. The proposed OWC framework is very useful for developing countries in Africa due to its simplicity of implementation with high performance.