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Distributed recursive least squares (RLS) algorithms have superior convergence properties compared to the least mean squares (LMS) counterpart. However, with a fixed forgetting factor (FF), they are not suitable for tracking time-varying (TV) parameters. This paper proposes a novel diffusion variable FF RLS (Diff-VFF-RLS) algorithm based on a local polynomial modeling (LPM) of the unknown TV system. The diffusion RLS solution is derived analytically such that the estimation deviation from the true value is investigated. Based on the analysis and the LPM of the TV system, a new optimal VFF formula that tries to minimize the estimation deviation is obtained. Simulations are conducted to verify the theoretical analysis in terms of the steady-state mean square deviation (MSD) and the VFF formula. Results also show that the convergence and tracking performance of the proposed algorithm compares favorably with conventional ones.

This paper considers the identification of nonlinear systems with color noise, and introduces a new time-varying forgetting factor based stochastic gradient (TVFF-SG) algorithm to estimate the system parameters. The basic idea of the time-varying forgetting factor is that when the algorithm starts, we give the forgetting factor a relative smaller value, which will speed up the convergence. In addition, the forgetting factor will increase slowly as time goes on so that the convergence procedure of the model will be more stable. Simulation results are presented to demonstrate the effectiveness of the proposed algorithm.

In the present paper, an adaptive parameter estimation algorithm applicable to linear systems with transfer functions of arbitrary structure is proposed. The approach can be applied to a wide class of linear processes, including non-linearly parameterized ones. The proposed method is applicable to fractional-order systems, distributed-parameter and delayed systems, and other classes of systems described by irrational transfer functions. In the first stage of the proposed procedure, values of the transfer function at specific frequencies are pinpointed by means of the Recursive Least Square algorithm with forgetting factor. In the second stage, the unknown parameters are found by numerically inverting complex non-linear relations linking them to the quantities estimated in the first stage. The inversion is performed by means of an iterative, gradient-based scheme. The method is illustrated by several detailedly explained numerical examples.

In this work, we present low-complexity variable forgetting factor (VFF) techniques for diffusion recursive least squares (DRLS) algorithms. Particularly, we propose low-complexity VFF-DRLS algorithms for distributed parameter and spectrum estimation in sensor networks. For the proposed algorithms, they can adjust the forgetting factor automatically according to the posteriori error signal. We develop detailed analyses in terms of mean and mean square performance for the proposed algorithms and derive mathematical expressions for the mean square deviation (MSD) and the excess mean square error (EMSE). The simulation results show that the proposed low-complexity VFF-DRLS algorithms achieve superior performance to the existing DRLS algorithm with fixed forgetting factor when applied to scenarios of distributed parameter and spectrum estimation. Besides, the simulation results also demonstrate a good match for our proposed analytical expressions.

An improved recursive Levenberg–Marquardt algorithm (RLM) is proposed to more efficiently train neural networks. The error criterion of the RLM algorithm was modified to reduce the impact of the forgetting factor on the convergence of the algorithm. The remedy to apply the matrix inversion lemma in the RLM algorithm was extended from one row to multiple rows to improve the success rate of the convergence; after that, the adjustment strategy was modified based on the extended remedy. Finally, the performance of this algorithm was tested on two chaotic systems. The results show improved convergence.

Since tracking modal parameters and estimating the structural current state from building seismic response measurement can provide useful information for building safety assessment, online or recur...

The maximum correntropy criterion (MCC) demonstrates the inherent robustness to outliers in adaptive filtering. By employing the MCC based cost function in projection approximation subspace tracking (PAST) algorithm, the MCC-PAST algorithm is deduced and utilized for the subspace tracking under impulsive noise environments. To handle the fast varying subspaces circumstances, the variable forgetting factor (VFF) technique is developed and incorporated into the MCC-PAST algorithm. To assess the robustness of the proposed MCC-PAST with VFF algorithm, SS processes are employed to comprehensively model different scenarios of impulsive noises. The simulation results show the proposed MCC-PAST algorithm with VFF performs better than the other two PAST algorithms developed for subspace tracking in impulsive noise environments, namely, the robust PAST algorithm and the robust Kalman filter based algorithm with variable number of measurements (KFVNM), especially when the noise is extremely impulsive or the GSNR (generalized signal to noise ratio) is relatively low. We address the problem of robust subspace tracking under impulsive noise environments.We examine the inherent robustness to outliers of correntropy.We deduce the maximum correntropy criterion (MCC) based PAST algorithm.We develop the method of the measurement of subspace variations.We develop the technique of variable forgetting factors (VFF) for the MCC-PAST.

This paper proposes a hybrid Gaussian process (GP) approach to robust economic model predictive control under unknown future disturbances in order to reduce the conservatism of the controller. The proposed hybrid GP is a combination of two well-known methods, namely, kernel composition and nonlinear auto-regressive. A switching mechanism is employed to select one of these methods for disturbance prediction after analyzing the prediction outcomes. The hybrid GP is intended to detect not only patterns but also unexpected behaviors in the unknown disturbances by using past disturbance measurements. \textcolor{black}{A novel forgetting factor concept is also utilized in the hybrid GP, giving less weight to older measurements, in order to increase prediction accuracy based on recent disturbances values.} The detected disturbance information is used to reduce prediction uncertainty in economic model predictive controllers systematically. The simulation results show that the proposed method can improve the overall performance of an economic model predictive controller compared to other GP-based methods in cases when disturbances have discernible patterns.

Clutter suppression, especially in time-varying environments is a hindrance that must be solved for radar systems applied to unmanned vehicles. However, exponential moving average (EMA) method, a common background subtraction technique, does not handle such a situation very well because the fixed parameter constrains the updating of the estimated clutter. In this paper, we propose a novel adaptive clutter suppression algorithm to adjust the parameter of EMA method under the background of time-varying clutter. The main idea is to adopt a low-complexity time-averaged variable forgetting factor (TAVFF) mechanism. The proposed algorithm is assessed with data recording measured background clutter and a simulated moving target. The simulation results demonstrate our proposed algorithm has achieved both fast convergence and good steady-state performance.

In this paper, we have implemented Gradient Variable Forgetting Factor (GVFF) algorithm through Recursive Least Squares (RLS) method as a noise canceller for elimination of ocular artifacts from raw Electroencephalogram (EEG) signals under dynamic environment. We have recorded two reference signals such as vertical eye movements and horizontal eye movements separately. These recorded signals are processed through finite impulse response filter, whose coefficients are updated recursively using GVFF-RLS algorithm for obtaining clean EEG signals by subtraction process. Our proposed method shows least mean square error in comparison with conventional techniques.

In the omnidirectional sound source tracking using the sequential updating histogram, a forgetting factor is used to estimate DOA (Directional-Of-Arrival) by Root-MUSIC(MUltiple Signal Classification), and an updating weight is used to update a histogram made by the estimation results. However, the best value of forgetting factor and the best value of updating weight depends on a kind of speech signal. In this paper, the best value of forgetting factor and the best value of updating weight factor are verified.

This paper considers the parameter identification of dual-rate sampled Hammerstein output error moving average system. A maximum likelihood forgetting factor stochastic gradient identification algorithm is proposed for the discussed system. The effectiveness of the proposed algorithm is illustrated by a numerical simulation example.

The electromagnetic coil launcher is a special linear motor in which the position detection of the armature plays a crucial role in ensuring the reasonable triggering of each coil and analyzing the performance of the system. At present, there are inevitably some errors in common position detection methods, and the motion model of the armature has the characteristics of nonlinear and strong coupling, in this case, in order to obtain the position and speed of the armature at the same time as the error is as small as possible, an estimation algorithm based on cubature Kalman filter(CKF) and interactive multiple model(IMM) is proposed in this paper. This algorithm adopts three known motion models to replace the complex motion model of the armature, then the observation position of the armature is filtered by CKF. Finally, the IMM-CKF algorithm is verified by the actual measured data during the launch process, and compares with CKF and adaptive iterative CKF with forgetting factor. The results show that the accuracy and stability of IMM-CKF are significantly better than those of the latter two algorithms.

State of Charge (SOC) is a component of Battery Management System (BMS) which gives information on the remaining capacity of a battery. For monitoring purpose, SOC estimation is represented as ratio of the remaining capacity to the nominal capacity of a battery. In this paper, SOC estimation is carried out by using Open-Circuit-Voltage (OCV) method, i.e. converting OCV estimate to SOC estimate based on SOC-OCV relationship. For comparison purpose, Thevenin battery model and simple Battery model are considered. The OCV estimation is conducted by using Recursive-Least-Square (RLS) algorithm with forgetting factor in which the model parameters are also simultaneously estimated. To demonstrate the effectiveness of the proposed method, experiment is utilized by employing hardware devices for measuring terminal voltage and current of battery which serve as inputs to the RLS algorithm. Accordingly, a forgetting factor of 0.985 for Thevenin battery model and 0,97 for Simple Battery model is obtained to yield accurate OCV estimation with OCV estimation error of 0.014% for Thevenin battery model and Simple Battery Model 0.012%.

We propose a policy search method for synthesizing optimal feedback control laws for reference tracking directly from data. During the learning phase, the control law is optimized by using stochastic gradient descent iterations and (optionally) applied to the plant while collecting data. Differently from model-based methods, in which a full model of the open-loop plant is first identified from data, here a simple linear model is recursively identified with forgetting factor for the only reason of computing approximately the gradients required for the descent. We report examples showing that the method recovers the optimal feedback law in case the underlying plant is linear, and outperforms the best control law that is achieved by first identifying an open-loop linear model in case the underlying plant is nonlinear.

In order to establish the electro-hydraulic proportional system model of the robotic excavator quickly and accurately, an identification algorithm based on recursive least squares algorithm with forgetting factor is proposed. The basic the mathematical model of the electro-hydraulic proportional system are analyzed. Based on the theoretical models, the transfer function of the control system is obtained by recursive least square identification method. The improved recursive least squares algorithm with forgetting factor method overcomes the contradiction between the steady-state accuracy and tracking ability of the fixed forgetting factor algorithm, and makes the identification process have both higher dynamic response and higher identification accuracy. The experimental results show that the identification results are credible, which lays a foundation for system design, control characteristic analysis and intelligent control algorithm research.

The unplanned islanding appears with the variety integration of large-scale Distributed Generation ( $DG$ ) connected to grid and causes some problems and risks to human being and equipment. However, there is a great deal of interest many researchers in solving this accidental islanding problem. This paper develops a passive islanding detection method ( $IDM$ ) based on monitoring of the impedance $Z_{PCC}$ at the point of common coupling ( $PCC$ ). This passive strategy used an online grid impedance $Z_{g}$ estimation using the Forgetting Factor Recursive Least Square ( $FFRLS$ ) algorithm. Theoretical analysis and MATLAB simulation results are presented to demonstrate the effectiveness of the proposed FFRLS-Islanding approach.

Rumor is defined as an unconfirmed public opinion or gossip, which can be propagated through various channels, causing serious economic losses and disturbing the normal order of life. Therefore, studying the rumor propagation mechanism is helpful to implement effective rumor propagation control strategies. In this paper, the wise man is involved in the dynamic process of rumor propagation, and the modified rumor propagation model is established with consideration of social reinforcement and forgetting factors in heterogeneous network. The theories analysis of the model is carried out based on the mean field equation. The rumor propagation threshold is obtained, which is closely related to dual social reinforcement, wisdom conversion rate and forgetting factors. The final size of the rumor is related to positive social reinforcement and negative social reinforcement. Numerical simulations indicate that, the social positive reinforcement promotes rumor propagation and social negative reinforcement suppresses rumor propagation. And the addition of wise men reduces the number of spreaders, thus affecting the process of rumor propagation.

Nowadays, treating the data as a continuous real-time flux is an exigence explained by the need for immediate response to events in daily life. We study the data like an ongoing data stream and represent it by streaming egocentric networks (Ego-Networks) of the particular nodes under study. We use a non-standard node forgetting factor in the representation of the network data stream, as previously introduced in the related literature. This way the representation is sensible to recent events in users' networks and less sensible for the past node events. We study this method with large scale Ego-Networks taken from telecommunications social networks with power law distribution. We aim to compare and analysis some reference Ego-Networks metrics, and their variation with or without forgetting factor.

Compared with the least-mean-square algorithm, the least mean $p$ th power algorithm shows a better robustness performance against impulsive noises such as the $\alpha$ -stable noises. However, it still exhibits slow convergence rate and high kernel misadjustment. To overcome this drawback, a novel recursive logarithmic least mean $p$ th (RLLMP) algorithm is proposed for the Volterra system identification under $\alpha$ -stable noise environments. Instead of minimizing the $p$ th power, the new algorithm aims to minimize the $p$ th logarithmic cost, which makes it more robust against impulsive interferences. Furthermore, to enhance tracking performance, an improved variable forgetting factor (IVFF) algorithm (IVFF-RLLMP) is proposed, which is based on the robust estimation of outliers. Simulation results are presented to demonstrate the improved performance of the RLLMP and IVFF-RLLMP.

Precise capacity and state-of-charge (SOC) estimation is crucial to assure safe and reliable operation of lithium-ion battery. To lower the influence of cross interference between these two estimated states and possible divergence existing in two-way transmitted co-estimation framework, a novel double adaptive extended Kalman filters (AEKFs) based one-way transmitted co-estimation framework for capacity and SOC is proposed in this paper. Firstly, the model parameters of the first-order RC model and open-circuit-voltage (OCV) are online obtained by forgetting factor recursive least squares. With the first derivative of OCV versus SOC, the SOC inferred through OCV-SOC table and identified parameters are inputted into AEKF1 to online estimate capacity. Subsequently, estimated capacity is further transmitted into AEKF2 to predict SOC. By simulation driving cycles, the proposed co-estimation framework is compared with AEKF based SOC algorithm without capacity calibration, whose results indicate that the presented algorithm can lower the impact of inaccurate initial capacity value on SOC estimation to more effectively track SOC. Moreover, through robustness analysis results, it is clearly found that initial erroneous SOC values will not influence capacity estimation results due to the one-way transmitted characteristic of the proposed co-estimation framework and SOC can still be estimated accurately and robustly.

A rapid iterative learning control algorithm with variable forgetting factor is applied for a class of nonlinear system with initial error and time-delay. This algorithm eliminats the limitation that the initial state should be reset to the expected one or fixed value at the start of iteration in the learning process of conventional algorithms. The error and the differences between two adjacent error is adopted to correct the controller avoiding the unstable influence of the derivative for PD type algorithm and the available information is fully used to increase convergence rate. Furthermore variable forgetting factor introduced guaranteed a fast convergence of trajectory tracking error Then, with applying the rapid algorithm to the trajectory tracking control of manipulator, the learning speed and tracking performance are both greatly improved. Meanwhile, the control strategy is proposed for the limitation of each joint rotation. The convergence of the method is also proved theoretically. Finally, simulation results illustrates the effectiveness and the real-time ability of the proposed way.

Aiming at the characteristics of small deformation range and strong correlation of multipath errors in space, a high-precision dynamic deformation monitoring model of GPS/pseudolites integrated system is proposed by introducing time forgetting factor. The model can effectively eliminate the influence of multipath of Pseudolite on combined positioning and improve the positioning accuracy and reliability in theory. The findings of the research have led the author to the conclusion that high-precision integration of GPS/pseudolites dynamic deformation monitoring model can weaken the influence of pseudolites multipath on integrated positioning more efficiently than conventional model, which increases the positioning precision largely.

A precise estimation of the lithium-ion battery’s inner state, such as the state of health (SoH) and the state of charge (SoC) of the battery, is crucial for a reliable and effective performance of a battery management system in an electric vehicle. In this paper, an improved real-time model-based battery parameters estimation method using the recursive least-square algorithm with forgetting factor (RLS-FF) is proposed. Compared to the traditional methods, the proposed model yields the capability to accurately estimate the battery SoC and SoH by including the real-time variation of open circuit voltage and internal resistance of a battery, respectively. Moreover, a forgetting factor is used to capture the online parameter variations by reducing the impact of the older data to keep the model simple and suitable for EV applications. To verify the validity of the proposed model, an experimental test is carried out on a 2012 Nissan Leaf 31.1 Ah Manganese-oxide Li-ion battery cell.

Recursive least squares (RLS) is widely used in signal processing, identification, and control, but is plagued by the inability to adjust quickly to changes in the unknown parameters. RLS with standard forgetting factor overcomes this problem but causes divergence due to the lack of persistency. Variable and directional forgetting factors have been proposed for overcoming this deficiency. The present paper proposes a targeted forgetting factor that looks directly at recent data in order to determine which directions possess new information. Targeted forgetting applies a forgetting factor directly to these directions, thereby providing a simple and effective technique for avoiding covariance divergence. Numerical examples compare targeted forgetting to standard and directional forgetting.

The existing personalized recommendation method based on time is merely a time stamp in the traditional personalized recommendation algorithm. This paper proposes an improved personalized recommendation method based on preference-aware and time factor. The forgetting curve is used to track the changed of user’s interests with time, and then a model of personalized recommendation based on dynamic time is built. Finally, the time forgetting factor is introduced in the collaborative filtering to improve the prediction effect of the interest-aware algorithm. The experimental results show that the proposed personalized recommendation method can get more accurate recommendation performance. It also can reduce the computing time and space complexity, and improve the quality of the recommendation of personalized recommendation algorithm.

As the number of cyber-attacks increases, there has been increasing emphasis on developing complementary methods of detection to the existing signature-based approaches. This work builds upon a previously discovered persistent structure within the Los Alamos National Laboratory network data sources, to develop a regression based streaming anomaly detection mechanism that can adapt to the network behaviour over time. The methodology has also been applied to a new data set of the same network to assess the extent of its pertinence in time.

Econometricians have been intensively developing tools to forecast both in economic and financial data. Despite that forecasting foreign exchange rate pairs are still problematic. In addition, predictors included in equation are not informative enough in predicting forex pairs. To remedy this obstacle, we apply Vector Autoregression (VAR) using the method socalled “Dynamic Model Averaging” to obtain estimates of the parameters. Up to 25 forex pairs are used in the DMA estimation procedures. We forecast EUR-GBP, EUR-JPY, EUR-USD, AUD-CAD, AUD-CHF and AUD-JPY with the number of horizons from $h=1$ to $h=14$ or one-day-ahead through fourteen-day-ahead prediction. We develop two model specifications in this study. The findings are: first, the Large-VAR with time-varying parameters performs well in predicting EUR-USD and AUD-JPY. Secondly, the rest of forex pairs are not well predicted using the proposed algorithm. Finally, relatively speaking, large size VARs is better in forecasting all selected forex pairs due to the more flexibility of time-varying coefficients and optimal forgetting factor. In addition, the forex market is efficient enough that using only the advanced time-series models such as Large time-varying VARs cannot confirm the profit from trading.

The paper presents a feature extraction method for signal classification tasks. The proposed method is based on linear adaptive Schur-like parametrization. The parametrization performance depends on a forgetting factor. The impact of forgetting factor, used in the adaptive procedure, on the quality of recognition was tested on well-known benchmark data.

An algorithm for damage detection in a multi-story building modeled by a wave equation with Kelvin damping is presented. Damage detection is achieved by relating stiffness loss with reduction in the shear wave velocity of the seismic induced motion propagation through the structure. In order to estimate wave velocity and damping parameters, an identification system based on the least squares method with forgetting factor is used. In addition, a parameterization is presented based on linear integral filters, which eliminates constant disturbances, attenuate measurement noise and depend only on acceleration signals. Once parameters information is available, a detection threshold is designed that compares them with reference values. The experimental results validate the feasibility of the proposed method.

Reliable parameters information is of great importance for on-board energy management and optimal power control. In this paper, we applies the online strategy of multi-forgetting factor recursive least square algorithm to identify parameters of first-order dynamic model through cyclic operating current. The output voltage of the identified model shows a good agreement with the experimental results, and the results of comparison with curve fitting method highlight the proposed method has great accuracy and convergence.

A reduced complexity inverse square-root recursive least squares algorithm based on widely-linear mechanism is introduced by adaptive forgetting-factor algorithm. The proposed reduced complexity widely-linear approaches based on inverse square-root recursive least squares algorithm is presented for a relation between widely-linear and reduced complexity scheme. By means of mean square deviation approach, an optimal forgetting-factor scheme is proposed in terms of optimal gain sequence. Adaptive forgetting-factor inverse square-root recursive least squares algorithm is used with regard to an optimal forgetting-factor algorithm. Results of simulation depict that the performance of proposed algorithm is shown similar to widely-linear scheme comparison with the existing algorithm.