Recursive Least Squares Identification With Variable-Direction Forgetting via Oblique Projection Decomposition

In this paper,a new recursive least squares(RLS)identification algorithm with variable-direction forgetting(VDF)is proposed for multi-output systems.The objective is to enhance parameter estimation performance under non-persistent excitation.The proposed algorithm performs oblique projection decomposition of the information matrix,such that forgetting is applied only to directions where new information is received.Theoretical proofs show that even without persistent excitation,the information matrix remains lower and upper bounded,and the estimation error variance converges to be within a finite bound.Moreover,detailed analysis is made to compare with a recently reported VDF algorithm that exploits eigenvalue decomposition(VDF-ED).It is revealed that under non-persistent excitation,part of the forgotten subspace in the VDF-ED algorithm could discount old information without receiving new data,which could produce a more ill-conditioned information matrix than our proposed algorithm.Numerical simulation results demonstrate the efficacy and advantage of our proposed algorithm over this recent VDF-ED algorithm.

Online battery model parameters identification approach based on bias-compensated forgetting factor recursive least squares

Accuracy of a lithium-ion battery model is pivotal in faithfully representing actual state of battery,thereby influencing safety of entire electric vehicles.Precise estimation of battery model parameters using key measured signals is essential.However,measured signals inevitably carry random noise due to complex real-world operating environments and sensor errors,potentially diminishing model estimation accuracy.Addressing the challenge of accuracy reduction caused by noise,this paper introduces a Bias-Compensated Forgetting Factor Recursive Least Squares(BCFFRLS)method.Initially,a variational error model is crafted to estimate the average weighted variance of random noise.Subsequently,an augmentation matrix is devised to calculate the bias term using augmented and extended parameter vectors,compensating for bias in the parameter estimates.To assess the proposed method's effectiveness in improving parameter identification accuracy,lithium-ion battery experiments were conducted in three test conditions—Urban Dynamometer Driving Schedule(UDDS),Dynamic Stress Test(DST),and Hybrid Pulse Power Characterization(HPPC).The proposed method,alongside two contrasting methods—the offline identification method and Forgetting Factor Recursive Least Squares(FFRLS)—was employed for battery model parameter identification.Comparative analysis reveals substantial improvements,with the mean absolute error reduced by 25%,28%,and 15%,and the root mean square error reduced by 25.1%,42.7%,and 15.9%in UDDS,HPPC,and DST operating conditions,respectively,when compared to the FFRLS method.

Human motion prediction using optimized sliding window polynomial fitting and recursive least squares

Human motion prediction is a critical issue in human-robot collaboration(HRC)tasks.In order to reduce the local error caused by the limitation of the capture range and sampling frequency of the depth sensor,a hybrid human motion prediction algorithm,optimized sliding window polynomial fitting and recursive least squares(OSWPF-RLS)was proposed.The OSWPF-RLS algorithm uses the human body joint data obtained under the HRC task as input,and uses recursive least squares(RLS)to predict the human movement trajectories within the time window.Then,the optimized sliding window polynomial fitting(OSWPF)is used to calculate the multi-step prediction value,and the increment of multi-step prediction value was appropriately constrained.Experimental results show that compared with the existing benchmark algorithms,the OSWPF-RLS algorithm improved the multi-step prediction accuracy of human motion and enhanced the ability to respond to different human movements.

Fast removal of ocular artifacts from electroencephalogram signals using spatial constraint independent component analysis based recursive least squares in brain-computer interface

Ocular artifacts cause the main interfering signals within electroencephalogram （EEG） signal measurements. An adaptive filter based on reference signals from an electrooculogram （EOG） can reduce ocular interference, but collecting EOG signals during a long-term EEG recording is inconvenient and uncomfortable for the subject. To remove ocular artifacts from EEG in brain-computer interfaces （BCIs）, a method named spatial constraint independent component analysis based recursive least squares （SCICA-RLS） is proposed. The method consists of two stages. In the first stage, independent component analysis （ICA） is used to decompose multiple EEG channels into an equal number of independent components （ICs）. Ocular ICs are identified by an automatic artifact detection method based on kurtosis. Then empirical mode decomposition （EMD） is employed to remove any cerebral activity from the identified ocular ICs to obtain exact altifact ICs. In the second stage, first, SCICA applies exact artifact ICs obtained in the first stage as a constraint to extract artifact ICs from the given EEG signal. These extracted ICs are called spatial constraint ICs （SC-ICs）. Then the RLS based adaptive filter uses SC-ICs as reference signals to reduce interference, which avoids the need for parallel EOG recordings. In addition, the proposed method has the ability of fast computation as it is not necessary for SCICA to identify all ICs like ICA. Based on the EEG data recorded from seven subjects, the new approach can lead to average classification accuracies of 3.3% and 12.6% higher than those of the standard ICA and raw EEG, respectively. In addition, the proposed method has 83.5% and 83.8% reduction in time-consumption compared with the standard ICA and ICA-RLS, respectively, which demonstrates a better and faster OA reduction.

An Effective Multiple Model Least Squares Method in Tracking of a Maneuvering Target

A polynomial model, time origin shifting model(TOSM, is used to describe the trajectory of a moving target .Based on TOSM, a recursive laeast squares(RLS) algorithm with varied forgetting factor is derived for tracking of a non-maneuvering target. In order to apply this algorithm to maneuvering targets tracking ,a tracking signal is performed on-line to determine what kind of TOSm will be in effect to track a target with different dynamics. An effective multiple model least squares filtering and forecasting method dadpted to real tracking of a maneuvering target is formulated. The algorithm is computationally more effcient than Kalman filter and the percentage improvement from simulations show both of them are considerably alike to some extent.

Identification of time-varying system and energy-based optimization of adaptive control in seismically excited structure

The combination of structural health monitoring and vibration control is of great importance to provide components of smart structures.While synthetic algorithms have been proposed,adaptive control that is compatible with changing conditions still needs to be used,and time-varying systems are required to be simultaneously estimated with the application of adaptive control.In this research,the identification of structural time-varying dynamic characteristics and optimized simple adaptive control are integrated.First,reduced variations of physical parameters are estimated online using the multiple forgetting factor recursive least squares(MFRLS)method.Then,the energy from the structural vibration is simultaneously specified to optimize the control force with the identified parameters to be operational.Optimization is also performed based on the probability density function of the energy under the seismic excitation at any time.Finally,the optimal control force is obtained by the simple adaptive control(SAC)algorithm and energy coefficient.A numerical example and benchmark structure are employed to investigate the efficiency of the proposed approach.The simulation results revealed the effectiveness of the integrated online identification and optimal adaptive control in systems.

Prediction of Time Series Empowered with a Novel SREKRLS Algorithm

For the unforced dynamical non-linear state–space 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 Mackey–Glass 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.

Online Identification of Lithium-ion Battery Model Parameters with Initial Value Uncertainty and Measurement Noise

Online parameter identification is essential for the accuracy of the battery equivalent circuit model(ECM).The traditional recursive least squares(RLS)method is easily biased with the noise disturbances from sensors,which degrades the modeling accuracy in practice.Meanwhile,the recursive total least squares(RTLS)method can deal with the noise interferences,but the parameter slowly converges to the reference with initial value uncertainty.To alleviate the above issues,this paper proposes a co-estimation framework utilizing the advantages of RLS and RTLS for a higher parameter identification performance of the battery ECM.RLS converges quickly by updating the parameters along the gradient of the cost function.RTLS is applied to attenuate the noise effect once the parameters have converged.Both simulation and experimental results prove that the proposed method has good accuracy,a fast convergence rate,and also robustness against noise corruption.

Anti-interference self-alignment algorithm by attitude optimization estimation for SINS on a rocking base

The performance of a strapdown inertial navigation system(SINS)largely depends on the accuracy and rapidness of the initial alignment.A novel anti-interference self-alignment algorithm by attitude optimization estimation for SINS on a rocking base is presented in this paper.The algorithm transforms the initial alignment into the initial attitude determination problem by using infinite vector observations to remove the angular motions,the SINS alignment is heuristically established as an optimiza-tion problem of finding the minimum eigenvector.In order to further improve the alignment precision,an adaptive recursive weighted least squares(ARWLS)curve fitting algorithm is used to fit the translational motion interference-contaminated reference vectors according to their time domain characteristics.Simulation studies and experimental results favorably demonstrate its rapidness,accuracy and robustness.

Approach to estimation of vehicle-road longitudinal friction coefficient

According to the road adaptive requirements for the vehicle longitudinal safety assistant system an estimation method of the road longitudinal friction coefficient is proposed.The method can simultaneously be applied to both the high and the low slip ratio conditions. Based on the simplified magic formula tire model the road longitudinal friction coefficient is preliminarily estimated by the recursive least squares method.The estimated friction coefficient and the tires model parameters are considered as extended states. The extended Kalman filter algorithm is employed to filter out the noise and adaptively adjust the tire model parameters. Then the final road longitudinal friction coefficient is accurately and robustly estimated. The Carsim simulation results show that the proposed method is better than the conventional algorithm. The road longitudinal friction coefficient can be quickly and accurately estimated under both the high and the low slip ratio conditions.The error is less than 0.1 and the response time is less than 2 s which meets the requirements of the vehicle longitudinal safety assistant system.

Bus mass estimation algorithm based on kinetic energy theorem

Bus mass is an important factor that affects fuel consumption and one of the key input parameters associated with automatic shift and hybrid electric vehicle （HEV） energy management strategy. A city bus mass estimation method based on kinetic energy theorem was proposed in this paper. The real-time data including vehicle speed and engine torque were collected by a remote data acquisition system. The samples in the process of being accelerated were selected to conduct vehicle mass estimation at the same bus stop with the same gear. The average estimation error is 2. 92% after the verification by actual data. Compared with the method based on recursive least squares, the algorithm based on kinetic energy theorem requires less sample length and the estimation error is smaller. Therefore, the method is more suitable for the bus mass estimation. The influences of gear, rolling resistance coefficient, wind resistance coefficient and road slope on mass estimation accuracy were analyzed.

Application of RLS adaptive filteringin signal de-noising

In view of the problem that noises are prone to be mixed in the signals,an adaptive signal de-noising system based on reursive least squares （RLS） algorithm is introduced.The principle of adaptive filtering and the process flow of RLS algorithm are described.Through example simulation,simulation figures of the adaptive de-noising system are obtained.By analysis and comparison,it can be proved that RLS adaptive filtering is capable of eliminating the noises and obtaining useful signals in a relatively good manner.Therefore,the validity of this method and the rationality of this system are demonstrated.

Multi-loop adaptive internal model control based on a dynamic partial least squares model

A multi-loop adaptive internal model control (IMC) strategy based on a dynamic partial least squares (PLS) frame-work is proposed to account for plant model errors caused by slow aging,drift in operational conditions,or environmental changes.Since PLS decomposition structure enables multi-loop controller design within latent spaces,a multivariable adaptive control scheme can be converted easily into several independent univariable control loops in the PLS space.In each latent subspace,once the model error exceeds a specific threshold,online adaptation rules are implemented separately to correct the plant model mismatch via a recursive least squares (RLS) algorithm.Because the IMC extracts the inverse of the minimum part of the internal model as its structure,the IMC controller is self-tuned by explicitly updating the parameters,which are parts of the internal model.Both parameter convergence and system stability are briefly analyzed,and proved to be effective.Finally,the proposed control scheme is tested and evaluated using a widely-used benchmark of a multi-input multi-output (MIMO) system with pure delay.

NonliNonlinear GPC with In-place Trained RLS-SVM Model for DOC Control in a Fed-batch Bioreactor

In this study, Saccharomyces cerevisiae (baker's yeast) was produced in a fed-batch bioreactor at the optimal dissolved oxygen concentration (DOC) and growth medium temperature. However, it is very difficult to control the DOC using conventional controllers because of the poorly understood and constantly changing dynamics of the bioprocess. A generalized predictive controller (GPC) based on a nonlinear autoregressive integrated moving average exogenous (NARIMAX) model is presented to stabilize the DOC by manipulation of air flow rate. The NARIMAX model is built by an improved recursive least-squares support vector machine, which is trained by an in-place computation scheme and avoids the computation of the inverse of a large matrix and memory reallocation. The proposed nonlinear GPC algorithm requires little preliminary knowledge of the fermentation process, and directly obtains the nonlinear model in matrix form by using iterative multiple modeling instead of linearization at each sampling period. By application of an on-line bioreactor control, experimental results demonstrate the robustness, effectiveness and advantages of the new controller.

An Adaptive Identification and Control SchemeUsing Radial Basis Function Networks

In this paper, adaptive identification and control of nonlinear dynamical systems are investigated using radial basis function networks (RBF). Firstly, a novel approach to train the RBF is introduced, which employs an adaptive fuzzy generalized learning vector quantization (AFGLVQ) technique and recursive least squares algorithm with variable forgetting factor (VRLS). The AFGLVQ adjusts the centers of the RBF while the VRLS updates the connection weights of the network. The identification algorithm has the properties of rapid convergence and persistent adaptability that make it suitable for real-time control. Secondly, on the basis of the one-step ahead RBF predictor, the control law is optimized iteratively through a numerical stable Davidon's least squares-based (SDLS) minimization approach. Four nonlinear examples are simulated to demonstrate the effectiveness of the identification and control algorithms.

A RESEARCH OF UWB RAKE RECEIVER BASED ON NOVEL RLS ADAPTIVE ALGORITHM

A modified RAKE receiver based on novel Recursive Least Squares （RLS） adaptive algorithm is proposed. The receiver uses L-fingered correlators, which are composed of RLS adaptive filters, to enhance the performance of multipath receiving. It can also track the amplitude of the received signal to form a real-time amplitude estimation which is correlated with the power of excess delay bin. The simulation results based on the IEEE UltraWide Band （UWB） channel models （CMI to CM4） show that the novel RLS algorithm can alter the attenuation estimation with the finger＇s power delay profile, and RAKE receiver with few fingers can be employed to get high performance.

RLS and LMS blind adaptive multi-user detection method and comparison in acoustic communication

RLS and LMS blind adaptive multi-user detection algorithm and multi-user detector was proposed to solve the problem of multi-user signal detection problem encountered in underwater acoustic communication networks.In simulation analysis,RLS and the LMS blind adaptive multi-user detector were designed and tested for synchronous and asynchronous multi-user communication process.The results of SIR comparison and MMSE comparison show that,both of the two methods can realize blind adaptive detection when any user change in multi-user communication,during this process,the training communication sequences are not needed.The RLS algorithm has about 5 dB higher in SIR compared with LMS algorithm,and the convergence velocity of RLS algorithm is also higher than LMS algorithm when the communication users change.RLS algorithm has better ability in multi-user detection than that of LMS algorithm,and it has great attraction and guiding significance for solving the problem of multiple access interference(MAI) in multi-user communication.

Research of internet worm warning system based on system identification

The frequent explosion of Internet worms has been one of the most serious problems in cyberspace security. In this paper, by analyzing the worm＇s propagation model, we propose a new worm warning system based on the method of system identification, and use recursive least squares algorithm to estimate the worm＇s infection rate. The simulation result shows the method we adopted is an efficient way to conduct Internet worm warning.

Application of Fast and Robust Equalization in Communication Technology

In this paper, the authors explore the potential of several popular equalization techniques while overcoming their disadvantages. First, extensive literature survey on equalization is conducted. The focus is on popular linear equalization algorithms such as the conventional least mean square (LMS ) algorithm, the recursive least squares ( RLS ) algorithm, the filtered X LMS algorithm and their development. To overcome the slow convergence problem while keeping the simplicity of the LMS based algorithms, an H 2 optimal initialization is proposed.

Updating Methods for Real Time Flood Forecasting： A Comparison through Senegal River Basin Upstream Bakel

Heavy floods occur frequently in the Senegal River Basin, causing catastrophic flooding downstream the river rating station of Bakel. Anticipating the occurrence of such phenomena is the only way to reduce the resulting damages. Flood forecasting is a necessity. Flood forecasting plays also an important role in the implementation of flood management scenarios and in the protection of hydro electric structures. Many methods are applied. The most complete are based on the conservation laws of physics governing the free surface flow. These methods need a complete description of the geometry of the river and their implementation requires also huge investments. In practice the river basin can be considered as a system of inputs-outputs related by a transfer function. In this paper the authors first used a multiple linear regression model with constant parameters estimated by the ordinary least square method to simulate the propagation of the floods in the upstream part of the Senegal river basin. The authors then apply statistical and graphical criteria of goodness-of-fit to test the suitability of this model. Three procedures of parameters updating have then been added to this linear model： the Kalman filter method, the recursive least square method, and the stochastic gradient method The criteria of goodness-of-fit used above have shown that the stochastic gradient method, although more rudimentary, represents better the flood propagation in the head basin of the Senegal river upstream Bakel. This result is particularly interesting because data influenced by Manantali Dam are used.