Exponential Forgetting Factor Research Articles

Moving-Target Circumnavigation Using Adaptive Neural Anti-Synchronization Control via Distance-Only Measurements.

In this work, we investigate the unknown moving-target circumnavigation problem in GPS-denied environments. A minimum of two tasking agents is excepted to circumnavigate the target cooperatively and symmetrically without prior knowledge of its position and velocity in order to achieve optimal sensor coverage persistently for the target. To achieve this goal, we develop a novel adaptive neural anti-synchronization (AS) controller. Based on relative distance-only measurements between the target and two tasking agents, a neural network is used to approximate the displacement of the target such that the position of the target can be estimated accurately and in real time. On this basis, a target position estimator is designed by considering whether all agents are in the same coordinate system. Furthermore, an exponential forgetting factor and a new information utilization factor are introduced to improve the accuracy of the aforementioned estimator. Rigorous convergence analysis of position estimation errors and AS error shows that the closed-loop system is globally exponentially bounded by the designed estimator and controller. Both numerical and simulation experiments are conducted to demonstrate the correctness and effectiveness of the proposed method.

Adaptive Filtering Approach With Forgetting Factor for Stochastic Signals Applied to EEG

This paper presents a new stochastic adaptive estimation-identification technique for nonstationary systems. The proposed method enhances the initial results from an on average estimation, and its identification, through a generalized adaptable function based on the Exponential Forgetting Factor (EFF), and the Sliding Mode (SM) regarding the error identification. In this form, the presented process includes the function implementation in three stages-estimation, adaptive estimation, and adaptive estimation-identification, allowing us to observe the gradual convergence to a nonstationary reference signal. Simulations first introduce convergence level checks obtained from the estimation and identification of artificial signals. After that, the algorithm is applied for real references, considering the Electroencephalogram (EEG) signals taken from a public database, finding their internal nonstationary gains, indirectly. Finally, the results include a performance comparison between the proposed strategy concerning the Recursive Least Square (RLS), the Least Mean Square (LMS), and the Kalman Filter (KF).

Adaptive Extended State Observer-Based Synergetic Control for a Long-Stroke Compliant Microstage With Stress Stiffening

In this article, the ultrahigh-precision planar motion control problem is investigated for a novel long-stroke multileaf spring based microstage, by considering the cross-axial coupling-induced varying stiffness. In particular, a discrete-time dynamical model with the stress stiffening effect is presented in a parameter varying form, where a discrete-time adaptive extended state observer (ESO) with exponential forgetting factor is developed based on Kalman-like observer method, and a synergetic control theory (SCT) approach is further proposed combining the observer structure to achieve microscale multiaxis motion control. The conditions on the convergence of the adaptive ESO and the robust stability of the closed-loop system are also derived with a theoretical analysis. Finally, the proposed control architecture is implemented (in real time) on a designed microstage, demonstrating significant performance improvement over existing results such as proportional-integral-derivative (PID) control and conventional active disturbance rejection controllers control methods.

Quality improvement and performance analysis of High Efficiency Video Coding under high quantization parameters and rain streaks

High Efficiency Video Coding standard is an advanced and widely used video coding standard in recent high-definition (HD) video application. This video codec faces many challenges during the video transmission over lower bandwidth channel. One of the main challenges is the noise removal from HD video sequences. For noise removal, this video codec has in-loop filters specifically. Although these loop filters are efficient, they are not effective in removing rain pattern from the video sequences. To overcome this problem, a denoising filter has to be added to the loop filters. For denoising, an optimized multi-delay block frequency domain (OMBFD) adaptive filter is presented in this paper. Based on the intensity of raindrop, it is identified from the successive video frames. Then, these predicted raindrops are removed using the existing loop filters. Nevertheless, still, noises present in the frame are removed using the proposed OMBFD filter. To control the process of filtering, the exponential forgetting factor which is used in the proposed denoising filter is optimized using firefly optimization algorithm. Simulation results show the proposed denoising algorithm affords promising performance improvement compared to other denoising filters.

Adaptive filtering of physiological noises in fNIRS data

The study presents a recursive least-squares estimation method with an exponential forgetting factor for noise removal in functional near-infrared spectroscopy data and extraction of hemodynamic responses (HRs) from the measured data. The HR is modeled as a linear regression form in which the expected HR, the first and second derivatives of the expected HR, a short-separation measurement data, three physiological noises, and the baseline drift are included as components in the regression vector. The proposed method is applied to left-motor-cortex experiments on the right thumb and little finger movements in five healthy male participants. The algorithm is evaluated with respect to its performance improvement in terms of contrast-to-noise ratio in comparison with Kalman filter, low-pass filtering, and independent component method. The experimental results show that the proposed model achieves reductions of 77% and 99% in terms of the number of channels exhibiting higher contrast-to-noise ratios in oxy-hemoglobin and deoxy-hemoglobin, respectively. The approach is robust in obtaining consistent HR data. The proposed method is applied for both offline and online noise removal.

N-Iterative Exponential Forgetting Factor for EEG Signals Parameter Estimation

Electroencephalograms (EEG) signals are of interest because of their relationship with physiological activities, allowing a description of motion, speaking, or thinking. Important research has been developed to take advantage of EEG using classification or predictor algorithms based on parameters that help to describe the signal behavior. Thus, great importance should be taken to feature extraction which is complicated for the Parameter Estimation (PE)–System Identification (SI) process. When based on an average approximation, nonstationary characteristics are presented. For PE the comparison of three forms of iterative-recursive uses of the Exponential Forgetting Factor (EFF) combined with a linear function to identify a synthetic stochastic signal is presented. The one with best results seen through the functional error is applied to approximate an EEG signal for a simple classification example, showing the effectiveness of our proposal.

Adaptive hysteresis compensation on an experimental nanopositioning platform

ABSTRACTThis paper presents a novel adaptive approach for hysteresis compensation applied to a piezoelectric actuator in one axis of an STM-like lab-made micro-/nanopositioning platform. The idea is to identify a compensating static parametric model, which imitates directly the inverse model of the nonlinearity. In this way, the approach is less complex than those based on model inversion. In addition, the identification is made online, allowing to consider a simple polynomial model, and to adapt its parameters according to the actual hysteresis curve which is faced (ascending or descending path, varying input amplitude, etc.). In order to be able to track possibly fast parameter variations, an original adaptation algorithm is proposed within the Bayesian framework, and including an exponential forgetting factor with optimal data-driven tuning. Illustrative experimental results are finally presented for tracking both triangular and sinusoidal reference signals with varying amplitude.

Adaptive observer design for discrete time LTV systems

ABSTRACTIn this paper, the discrete-time exponential forgetting factor observer is specialised for the joint estimation of state and parameters, leading to an adaptive observer in which the decay rates of the estimation errors for the two distinct objects can be quasi-separated. The effectiveness of the observer is demonstrated through numerical simulation.

Equivalent Neural Network Optimal Coefficients Using Forgetting Factor with Sliding Modes.

The Artificial Neural Network (ANN) concept is familiar in methods whose task is, for example, the identification or approximation of the outputs of complex systems difficult to model. In general, the objective is to determine online the adequate parameters to reach a better point-to-point convergence rate, so that this paper presents the parameter estimation for an equivalent ANN (EANN), obtaining a recursive identification for a stochastic system, firstly, with constant parameters and, secondly, with nonstationary output system conditions. Therefore, in the last estimation, the parameters also have stochastic properties, making the traditional approximation methods not adequate due to their losing of convergence rate. In order to give a solution to this problematic, we propose a nonconstant exponential forgetting factor (NCEFF) with sliding modes, obtaining in almost all points an exponential convergence rate decreasing. Theoretical results of both identification stages are performed using MATLAB® and compared, observing improvement when the new proposal for nonstationary output conditions is applied.

Exponential forgetting factor observer in discrete time

This paper presents the development in discrete time of a solution for the observation of deterministic linear time varying systems, whose continuous time counterpart is already available in the literature under the name of exponential forgetting factor observer. This observer has a structure similar with that of the deterministic Kalman filter and relies on the same observability property as the latter. The main difference is that convergence is achieved through a different philosophy, which provides an observer with easier tuning capabilities through a single design parameter—the so-called forgetting factor.

Regularized ${\rm RLS}$-$\lambda$ and DHOBE: An Adaptive Feedforward for a Solenoid Valve

To allow a stable and fast acting hydraulic pressure control on a continuously variable transmission (CVT) for road vehicles, an adaptive feedforward strategy is used. The Dasgupta-Huang outer bounding ellipsoid (DHOBE) and recursive least squares (RLS) with exponential forgetting factor(RLS-λ) adaptation algorithms are compared to the non-adaptive feedforward. The experiments show a clear advantage for the adaptive over the non-adaptive version by compensating for the slow drift of the valve pressure gain during the warm-up period of the transmission. Because of highly correlated input data, the adaptation algorithms offer deceiving performances with oscillating identified parameters. A regularization procedure is added to both adaptation algorithms, giving the rRLS-λ and rDHOBE. The regularized algorithms offer significantly better performances and stability than their non-regularized counterparts. Because of its implicit parametric uncertainty calculation while keeping an equivalent convergence rate, and a lower number of updates, the rDHOBE algorithm is regarded as the best solution for the application. By adapting a simple linear model, the rDHOBE adaptive feedforward succeeds in responding to an abrupt change of the external pressure setpoint with no added actuation delay while keeping the pressure error under 0.5 bar.

Adaptive observer for discrete time state affine systems

In this paper, the discrete-time exponential forgetting factor observer for state affine systems is specialized for the joint estimation of state and parameters, leading to an adaptive observer in which the decay rates of the estimation errors for the two distinct objects to be estimated can be disjoined. Experimental results for the adaptive observation of rotor time constant and stator resistance of an induction motor are presented as example of application.

Variable Regularized Square Root Recursive Least Square Method

In this paper, we develop the variable regularized square root recursive least square method which is in order to track time-varying parameters extended by an exponential forgetting factor (EF-VR-SRRLS). The proposed approach is arisen from the exact recursification of the original batch mode method solving the restricted quadratic problem. The meanings of the restricted conditions lie in the removal of ambiguity of the cost function and thus to ensure the regularity of the direction matrix. In the examined approach, the regularization terms are the matrix weighting the difference between the next parameter estimate and the initial parameter estimate and the time-varying matrix weighting the distance of the parameter estimate from its currently available estimate. Because the incorporation of the Potter's square root technique requires the actualization of direction matrix using the data dyads only, an effective form of implementation based on the updating quantity of the rank one was performed. The performance of the suggested algorithm combining variable regularization and the square root filtering technique is verified via simulation studies.

Adaptive Estimation of OEMA Model via Variable Regularized Recursive Least Squares Method

In this paper, we present a recursive least squares method with variable regularization which is in order to track time varying parameters extended by an exponential forgetting factor (EF-VR-RLS). Regularization of a direction matrix is achieved by adding restricting conditions into the cost function. By definition of the standard recursive least-squares method (RLS) implies that the method removes the ambiguity of the cost function using a constant regularization. The RLS method is therefore an exact formulation of multi-criteria problem. In this case regularization element is the initial value of the direction matrix, which penalizes Euclidean distance between the estimated parameters and their initial values. At the proposed approach the cost function is extended by the penalization of weighted difference between the investigated vector of parameters and its currently available estimate. By introducing the element of variable regularization is possible to better effect the rate of convergence and the actual position of equilibrium than by employing of the standard RLS method. Main emphasis is placed on the efficiency of numerical solution method, in order to implement into the microcontroller.

Statistical properties of support vector machines with forgetting factor

Introducing a forgetting factor allows a support vector machine to solve time-varying problems adaptively. However, the exponential forgetting factor proposed in an earlier work does not ensure convergence of average generalization error even for a simple linearly separable problem. To guarantee convergence, we propose a factorial forgetting factor which decays factorially over time. We approximately derive the average generalization error of the factorial forgetting factor as well as that of the exponential forgetting factor using a simple one-dimensional problem, and confirm our theory by computer simulations. Finally, we show that our theory can be extended to arbitrary types of forgetting factors for simple linearly separable cases.

Neural Network Control of Resistive Wall Modes in Tokamaks

A neural network (NN) implementation of an adaptive optimal stochastic output feedback control is developed to stabilize the resistive wall mode (RWM), a critically important instability in fusion machines like tokamaks. The design of an adaptive optimal stochastic output feedback control was discussed and reported earlier by Sun, Sen, and Longman. The system dynamics is experimentally determined via the extended least square method with an exponential forgetting factor and covariance resetting. The optimal output feedback controller is redesigned periodically online based on the system identification. The output measurements and past control inputs are used to construct new control inputs. These are achieved by an architecture of NNs consisting of a pool of sequentially linked Hopfield networks and implemented in hardware with digital NN processors made by the Accurate Automation Corporation. The simulations have shown that the NN adaptive output controller can stabilize the time-dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of the inverse of the nonlinear growth rate, which is the time scale of the development of the possibly dangerous levels of fluctuations. This stabilization is similar to that of the simulation with a C++ implementation. It is expected that significant gains can be achieved for the systems of a higher order, which are to be found in future fusion devices.

SU-GG-T-15: Variation Estimation of Parotids - Towards More Accurate Image Guided Adaptive Radiation Therapy of H&n Cancers

Purpose: Patient anatomical variation identification and treatmentdose estimation are the main feedbacks in image guided adaptive radiation therapy (IGART) process. The identification/estimation can be updated during the treatment course with using online treatment observations obtained from onboard CBCTimaging. In this study, we modeled the geometric variation of parotids using a nonstationary stochastic process and utilized the time‐varying least‐square method to estimate the characteristics of the variation. Method and Materials: An estimation process with the time‐varying least‐square method was used to predict nonstationary stochastic organ variation and applied to evaluate the variation of parotids for 30 h&n cancer patients. The variations observed during the previous treatment days were wascompared to predict those of the remaining treatment. The recursive least‐square polynomial regression with exponential forgetting factor was employed to predict the mean and deviation of parotid positions. The order of polynomial and the forgetting factor were optimized based on the total estimation errors. Results: The optimized order of polynomial was zero and the optimized forgetting factor was 0.74 for the mean position estimation. The corresponding averaged total error of all patients was 1.27mm. The optimized factor for the deviation estimation was 0.94 and the corresponding averaged error was 1.27mm. The estimation errors were approximately isotropic. The predicted results were not sensitive to the patient pool. Conclusion: The developed procedure has been successfully applied to the prediction of the parotid variation. The predicted mean position was closer to the true mean position than the initial position by a factor of 2. Since the estimation process does not utilize any special futures of parotids it can be applied to other organs. Conflict of Interest: Supported by Elekta Oncology System, Inc

State and parameter estimation via discrete-time exponential forgetting factor observer

The paper presents the discrete-time counterpart of the continuous-time exponential forgetting factor observer. We obtain a Kalman-like observer to the extent that it relies on the uniform complete observability property specific to LTV systems and can be used to handle the estimation of state-affine systems. However, it does not require the complete uniform controllability property like the Kalman observer does. Like any other state observer it can be used for parameter estimation if the eventual unknown parameters are turned into state variables. This use of the observer is illustrated through an example of state and parameter estimation in the case of an AC machine.

Implementation of the Least-Squares Lattice with Order and Forgetting Factor Estimation for FPGA

A high performance RLS lattice filter with the estimation of an unknown order and forgetting factor of identified system was developed and implemented as a PCORE coprocessor for Xilinx EDK. The coprocessor implemented in FPGA hardware can fully exploit parallelisms in the algorithm and remove load from a microprocessor. The EDK integration allows effective programming and debugging of hardware accelerated DSP applications. The RLS lattice core extended by the order and forgetting factor estimation was implemented using the logarithmic numbers system (LNS) arithmetic. An optimal mapping of the RLS lattice onto the LNS arithmetic units found by the cyclic scheduling was used. The schedule allows us to run four independent filters in parallel on one arithmetic macro set. The coprocessor containing the RLS lattice core is highly configurable. It allows to exploit the modular structure of the RLS lattice filter and construct the pipelined serial connection of filters for even higher performance. It also allows to run independent parallel filters on the same input with different forgetting factors in order to estimate which order and exponential forgetting factor better describe the observed data. The FPGA coprocessor implementation presented in the paper is able to evaluate the RLS lattice filter of order 504 at 12 kHz input data sampling rate. For the filter of order up to 20, the probability of order and forgetting factor hypotheses can be continually estimated. It has been demonstrated that the implemented coprocessor accelerates the Microblaze solution up to 20 times. It has also been shown that the coprocessor performs up to 2.5 times faster than highly optimized solution using 50 MIPS SHARC DSP processor, while the Microblaze is capable of performing another tasks concurrently.

가상현실을 위한 다중 접촉 실시간 햅틱 랜더링

This paper presents a real-time haptic rendering method for multi-contact interaction with virtual environments. Haptic systems often employ physics-based deformation models such as finite-element models and mass-spring models which demand heavy computational overhead. The haptic system can be designed to have two sampling times, T and JT, for the haptic loop and the graphic loop, respectively. A multi-rate output-estimation with an exponential forgetting factor is proposed to implement real-time haptic rendering for the haptic systems with two sampling rates. The computational burden of the output-estimation increases rapidly as the number of contact points increases. To reduce the computation of the estimation, the multi-rate output-estimation with reduced parameters is developed in this paper. Performance of the new output-estimation with reduced parameters is compared with the original output-estimation with full parameters and an exponential forgetting factor. Estimated outputs are computed from the estimated input-output model at a high rate, and trace the analytical outputs computed from the deformation model. The performance is demonstrated by simulation with a linear tensor-mass model.