Improved Variable Forgetting Factor Proportionate RLS Algorithm with Sparse Penalty and Fast Implementation Using DCD Iterations

The proportionate recursive least squares(PRLS)algorithm has shown faster convergence and better performance than both proportionate updating(PU)mechanism based least mean squares(LMS)algorithms and RLS algorithms with a sparse regularization term.In this paper,we propose a variable forgetting factor(VFF)PRLS algorithm with a sparse penalty,e.g.,l_(1)-norm,for sparse identification.To reduce the computation complexity of the proposed algorithm,a fast implementation method based on dichotomous coordinate descent(DCD)algorithm is also derived.Simulation results indicate superior performance of the proposed algorithm.

RLS channel estimation with adaptive forgetting factor in space-time coded MIMO-OFDM systems

Considering that channel estimation plays a crucial role in coherent detection, this paper addresses a method of Recursive-least-squares (RLS) channel estimation with adaptive forgetting factor in wireless space-time coded multiple-input and multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Because there are three different forgetting factor scenarios including adaptive, two-step and conventional ones applied to RLS channel estimation, this paper describes the principle of RLS channel estimation and analyzes the impact of different forgetting factor scenarios on the performances of RLS channel estimation. Simulation results proved that the RLS algorithm with adaptive forgetting factor (RLS-A) outperformed that with two-step forgetting factor (RLS-T) or with conventional forgetting factor (RLS-C) in both estimation accuracy and robustness over the multiple-input multiple-output (MIMO) channel, i.e., a wide-sense stationary uncorrelated scattering (WSSUS) and frequency-selective slowly fading channel. Hence, we can employ the RLS-A method by adjusting forgetting factor adaptively to track and estimate channel state parameters successfully in space-time coded MIMO-OFDM systems.

Autonomous navigation method of satellite constellation based on adaptive forgetting factors

To address the problem that model uncertainty and unknown time-varying system noise hinder the filtering accuracy of the autonomous navigation system of satellite constellation,an autonomous navigation method of satellite constellation based on the Unscented Kalman Filter with Adaptive Forgetting Factors(UKF-AFF)is proposed.The process noise covariance matrix is estimated online with the strategy that combines covariance matching and adaptive adjustment of forgetting factors.The adaptive adjustment coefficient based on squared Mahalanobis distance of state residual is employed to achieve online regulation of forgetting factors,equipping this method with more adaptability.The intersatellite direction vector obtained from photographic observations is introduced to determine the constellation satellite orbit together with the distance measurement to avoid rank deficiency issues.Considering that the number of available measurements varies online with intersatellite visibility in practical applications such as time-varying constellation configurations,the smooth covariance matrix of state correction determined by innovation and gain is adopted and constructed recursively.Stability analysis of the proposed method is also conducted.The effectiveness of the proposed method is verified by the Monte Carlo simulation and comparison experiments.The estimation accuracy of constellation position and velocity of UKF-AFF is improved by 30%and 44%respectively compared to those of the extended Kalman filter,and the method proposed is also better than other several adaptive filtering methods in the presence of significant model uncertainty.

Online Identification of Power Battery Parameters for Electric Vehicles Using a Decoupling Multiple Forgetting Factors Recursive Least Squares Method

Li-ion batteries are widely used in electric vehicles(EVs).However,the accuracy of online SOC estimation is still challenging due to the time-varying parameters in batteries.This paper proposes a decoupling multiple forgetting factors recursive least squares method(DMFFRLS)for EV battery parameter identification.The errors caused by the different parameters are separated and each parameter is tracked independently taking into account the different physical characteristics of the battery parameters.The Thevenin equivalent circuit model(ECM)is employed considering the complexity of battery management system(BMS)on the basis of comparative analysis of several common battery ECMs.In addition,decoupling multiple forgetting factors are used to update the covariance due to different degrees of error of each parameter in the identification process.Numerous experiments are employed to verify the proposed DMFFRLS method.The parameters for commonly used LiFePO4(LFP),Li(NiCoMn)O2(NCM)battery cells and battery packs are identified based on the proposed DMFFRLS method and three conventional methods.The experimental results show that the error of the DMFFRLS method is less than 15 mV,which is significantly lower than the conventional methods.The proposed DMFFRLS shows good performance for parameter identification on different kind of batteries,and provides a basis for state of charge(SOC)estimation and BMS design of EVs.

Adaptive Subspace Predictive Control with Time-varying Forgetting Factor

Aiming at the time-varying characteristics of industrial process, this paper introduces an adaptive subspace predictive control(ASPC) strategy with time-varying forgetting factor based on the original subspace predictive control algorithm(SPC). The new method uses model matching error to calculate the variable forgetting factor, and applies it to constructing Hankel data matrix.This makes the data represent the changes of system information better. For eliminating the steady state error, the derivation of the incremental control is made. Simulation results on a rotary kiln show that this control strategy has achieved a good control effect.

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.

Robust Parameter Identification Method of Adhesion Model for Heavy Haul Trains

A robust parameter identification method based on Kiencke model was proposed to solve the problem of the parameter identification accuracy being affected by the rail environment change and noise interference for heavy-duty trains. Firstly, a Kiencke stick-creep identification model was constructed, and the parameter identification task was transformed into a quadratic programming problem. Secondly, an iterative algorithm was constructed to solve the problem, into which a time-varying forgetting factor was added to track the change of the rail environment, and to solve the uncertainty problem of the wheel-rail environment. The Granger causality test was adopted to detect the interference, and then the weights of the current data were redistributed to solve the problem of noise interference in parameter identification. Finally, simulations were carried out and the results showed that the proposed method could track the change of the track environment in time, reduce the noise interference in the identification process, and effectively identify the adhesion performance parameters.

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.

PI-type Iterative Learning Control for Nonlinear Electro-hydraulic Servo Vibrating System

For the electro-hydraulic servo vibrating system（ESVS） with the characteristics of non-linearity and repeating motion, a novel method, PI-type iterative learning control（ILC）, is proposed on the basis of traditional PID control. By using memory ability of computer, the method keeps last time＇s tracking error of the system and then applies the error information to the next time＇s control process. At the same time, a forgetting factor and a D-type learning law of feedforward fuzzy-inferring referenced displacement error under the optimal objective are employed to enhance the systemic robustness and tracking accuracy. The results of simulation and test reveal that the algorithm has a trait of high repeating precision, and could restrain the influence of nonlinear factors like leaking, external disturbance, aerated oil, etc. Compared with traditional PID control, it could better meet the requirement of nonlinear electro -hydraulic servo vibrating system.

Kalman Filter Estimation of Lithium Battery SOC Based on Model Capacity Updating

High-precision estimation of lithium battery SOC can effectively optimize vehicle energy management,improve lithium battery safety protection,extend lithium battery cycle life,and reduce new energy vehicle costs.Based on the forgetting factor recursive least square method(FFRLS),Thevenin equivalent circuit model and Singular Value Decomposition-Unscented Kalman Filter(SVD-UKF),the SVD-UKF combined lithium battery SOC estimation algorithm with model capacity update is proposed,aiming at further improving the SOC estimation accuracy of lithium battery.The parameter identification of Thevenin model is studied by using the forgetting factor recursive least square method.To overcoming the shortcomings of Kalman filter linearization error and non-positive definite covariance matrix,the singular value decomposition unscented Kalman filter algorithm is proposed.It is worth mentioning that in order to consider the impact of battery available capacity attenuation on the estimation of lithium battery SOC,the model capacity update algorithm is used to optimize the model parameters and state joint estimation algorithm based on FFRLS&SVD-UKF.Verified by simulation and lithium battery test,the results show that the SVD-UKF algorithm based on model capacity update can accurately estimate the SOC of lithium battery in real time with the available capacity of lithium battery continuous attenuation.The purpose of improving the accuracy of SOC estimation of lithium batteries is achieved.

Linear Quadratic Integral Control for the Active Suspension of Vehicle

The quarter model of an active suspension is established in the form of controllable autoregressive moving average （CARMA） model. An accelerometer can be mounted on the wheel hub for measuring road disturbance; this signal is used to identify the CARMA model parameters by recursive forgetting factors least square method. The linear quadratic integral （LQI） control method for the active suspension is presented. The LQI control algorithm is fit for vehicle suspension control, for the control performance index can comprise multi controlled variables. The simulation results show that the vertical acceleration and suspension travel both are decreased with the LQI control in the low frequency band, and the suspension travel is increased with the LQI control in the middle or high frequency band. The suspension travel is very small in the middle or high frequency band, the suspension bottoming stop will not happen, so the vehicle ride quality can be improved apparently by the LQI control.

Iterative identification of output error model for industrial processes with time delay subject to colored noise

To deal with colored noise and unexpected load disturbance in identification of industrial processes with time delay, a bias-eliminated iterative least-squares(ILS) identification method is proposed in this paper to estimate the output error model parameters and time delay simultaneously. An extended observation vector is constructed to establish an ILS identification algorithm. Moreover, a variable forgetting factor is introduced to enhance the convergence rate of parameter estimation. For consistent estimation, an instrumental variable method is given to deal with the colored noise. The convergence and upper bound error of parameter estimation are analyzed. Two illustrative examples are used to show the effectiveness and merits of the proposed method.

Heading rate controller for unmanned helicopters based on modified ADRC

A modified heading rate active disturbance rejection controller(ADRC)for miniature unmanned helicopters is presented to improve the transient performance and adaptability of working conditions.First,a tail-locking mathematical model is introduced,and the amplification factor is defined.Second,a standard ADRC controller is presented.Because the amplification factor plays an important role in both parts of the content and is primarily influenced by the main rotor speed,an online forgetting factor recursive least square algorithm is used to identify it,and the identification result is condensed into a function of the main rotor speed,adapting to various working conditions.This function is also included in the proposed ADRC controller to supplement the standard scheme.Finally,experiments were conducted on a small electric helicopter.A reduction of approximately 40%in the transient time(compared with an off-the-shelf PID controller)was achieved in the experiment.The comparative results show that the proposed ADRC scheme outperforms the classic PID and standard ADRC schemes in terms of transient performance and adaptability to working conditions.

A New Method for Estimating Lithium‑Ion Battery State‑of‑Energy Based on Multi‑timescale Filter

Accurate estimation of the state-of-energy(SOE)in lithium-ion batteries is critical for optimal energy management and energy optimization in electric vehicles.However,the conventional recursive least squares(RLS)algorithm struggle to track changes in battery model parameters under dynamic conditions.To address this,a multi-timescale estimator is proposed.A variable forgetting factor RLS approach is used to determine the model parameters at a macro timescale,and the H infinity filter is utilized to estimate the SOE at a micro timescale.The proposed algorithm is verified and analyzed and shown to have accurate and robust identification of battery model parameters.Finally,experiments under dynamic cycles demonstrate that the proposed algorithm has a high level of accuracy for SOE estimation.

REAL-TIME FLOOD FORECASTING METHOD WITH 1-D UNSTEADY FLOW MODEL

A real-time forecasting method coupled with the I-D unsteady flow model with the recursive least-square method was developed. The 1-D unsteady flow model was modified by using the time-variant parameter and revising it dynamically through introducing a variable weighted forgetting factor, such that the output of the model could be adjusted for the real time forecasting of floods. The application of the new real time forecasting model in the reach from Yichang to Luoshan of the Yangtze River was demonstrated. Computational result shows that the forecasting accuracy of the new model is much higher than that of the original 1-D unsteady flow model. The method developed is effective for flood forecasting, and can be used for practical operation in the flood forecasting.

Modeling and state of charge estimation of lithium-ion battery

Modeling and state of charge （SOC） estimation of lithium-ion （Li-ion） battery are the key techniques of battery pack management system （BMS） and critical to its reliability and safety operation. An auto-regressive with exogenous input （ARX） model is derived from RC equivalent circuit model （ECM） due to the discrete-time characteristics of BMS. For the time-varying environmental factors and the actual battery operating conditions, a variable forgetting factor recursive least square （VFFRLS） algorithm is adopted as an adaptive parameter identifica- tion method. Based on the designed model, an SOC estimator using cubature Kalman filter （CKF） algorithm is then employed to improve estimation performance and guarantee numerical stability in the computational procedure. In the battery tests, experimental results show that CKF SOC estimator has a more accuracy estimation than extended Kalman filter （EKF） algorithm, which is widely used for Li-ion battery SOC estimation, and the maximum estimation error is about 2.3%.

A New FIR Filter for State Estimation and Its Application

This paper proposes a new FIR （finite impulse response） filter under a least squares criterion using a forgetting factor. The proposed FIR filter does not require information of the noise covariances as well as the initial state, and has some inherent properties such as time-invariance, unbiasedness and deadbeat. The proposed FIR filter is represented in a batch form and then a recursive form as an alternative form. Prom discussions about the choice of a forgetting factor and a window length, it is shown that they can be considered as useful parameters to make the estimation performance of the proposed FIR filter as good as possible. It is shown that the proposed FIR filter can outperform the existing FIR filter with incorrect noise covariances via computer simulations. Finally, as a useful application, an image sequence stabilization problem is considered. Through this application, the FIR filtering based approach is shown to be superior to the Kalman filtering based approach.

Parameter estimation and reliable fault detection of electric motors

Accurate model identification and fault detection are necessary for reliable motor control. Motor-characterizing parameters experience substantial changes due to aging, motor operating conditions, and faults. Consequently, motor parameters must be estimated accurately and reliably during operation. Based on enhanced model structures of electric motors that accommodate both normal and faulty modes, this paper introduces bias-corrected least-squares （LS） estimation algorithms that incorporate functions for correcting estimation bias, forgetting factors for capturing sudden faults, and recursive structures for efficient real-time implementation. Permanent magnet motors are used as a benchmark type for concrete algorithm development and evaluation. Algorithms are presented, their properties are established, and their accuracy and robustness are evaluated by simulation case studies under both normal operations and inter-turn winding faults. Implementation issues from different motor control schemes are also discussed.

An efficient equivariant adaptive separation via independence algorithm for acoustical source separation and identification

To balance the convergence rate and steadystate error of blind source separation(BSS) algorithms, an efficient equivariant adaptive separation via independence(Efficient EASI) algorithm is proposed based on separating indicator, which was derived from the convergence condition of EASI, and can be used to evaluate the separation degree of separated signals. Furthermore, a nonlinear monotone increasing function between suitable step sizes and separating indicator is constructed to adaptively adjust step sizes, and forgetting factor is employed to weaken effects of data at the initial stage. Numerical case studies and experimental studies on a test bed with shell structures are provided to validate the efficiency improvement of the proposed method. This study can benefit for vibration & acoustic monitoring and control, and machinery condition monitoring and fault diagnosis.

Design, Implementation and Control of an Amphibious Spherical Robot

We proposed and implemented a leg-vector water-jet actuated spherical robot and an underwater adaptive motion control system so that the proposed robot could perform exploration tasks in complex environments.Our aim was to improve the kinematic performance of spherical robots.We developed mechanical and dynamic models so that we could analyze the motions of the robot on land and in water.The robot was equipped with an Inertial Measurement Unit(IMU)that provided inclination and motion information.We designed three types of walking gait for the robot,with different stabilities and speeds.Furthermore,we proposed an online adjustment mechanism to adjust the gaits so that the robot could climb up slopes in a stable manner.As the system function changed continuously as the robot moved underwater,we implemented an online motion recognition system with a forgetting factor least squares algorithm.We proposed a generalized prediction control algorithm to achieve robust underwater motion control.To ensure real-time performance and reduce power consumption,the robot motion control system was implemented on a Zynq-7000 System-on-Chip(SoC).Our experimental results show that the robot’s motion remains stable at different speeds in a variety of amphibious environments,which meets the requirements for applications in a range of terrains.