The Filtering-Based Multi-Innovation Hierarchical Fractional Least Mean Square Algorithm for Parameter Estimation of Bilinear-in-Parameter Autoregressive System

This paper considers the parameter estimation for multi-input output error autoregressive (OEAR) systems. The main contribution of this paper is to propose iterative algorithms for multi-input OEAR systems using the data filtering technique. Firstly, a least squares iterative (LSI) identification algorithm is given for multi-input OEAR systems as a comparison. Secondly, we transform an OEAR system into two identification models and present a data filtering based least squares iterative (F-LSI) identification algorithm. Finally, an illustrative simulation example is provided to test the proposed algorithms, the simulation results indicate that the F-LSI identification algorithm can produce more accurate parameter estimates than the LSI identification algorithm.

System identification provides many convenient and useful methods for engineering modelling. This study targets the parameter identification problems for multivariable equation-error autoregressive moving average systems. To reduce the influence of the coloured noises on the parameter estimation, the data filtering technique is adopted to filter the input and output data, and to transform the original system into a filtered system with white noises. Then the filtered system is decomposed into several subsystems and a filtering-based partially-coupled generalised extended stochastic gradient algorithm is developed via the coupling concept. In contrast to the multivariable generalised extended stochastic gradient algorithm, the proposed algorithm can give more accurate parameter estimates. Finally, the effectiveness of the proposed algorithm is well demonstrated by simulation examples.

This paper discusses the parameter estimation problems of nonlinear output error autoregressive systems and presents a data filtering-based multi-innovation stochastic gradient algorithm for improving the parameter estimation accuracy of the stochastic gradient algorithm by combining the multi-innovation identification theory and the data filtering technique. The proposed algorithm is effective and can generate highly accurate parameter estimates compared with the multi-innovation stochastic gradient algorithm. The simulation results confirm this conclusion.

SummaryThis paper focuses on the parameter estimation issues of multivariate equation‐error autoregressive moving average systems. By applying the gradient search and the multi‐innovation theory, we derive a multi‐innovation gradient based iterative (MI‐GI) algorithm. In order to improve the computational efficiency and the parameter estimation accuracy, a filtering and decomposition based gradient iterative (F‐D‐GI) algorithm is presented by using the data filtering technique and the decomposition technique. The key is to choose an appropriate filter to filter the input‐output data and to transform an original system into several subsystems. Compared with the MI‐GI algorithm, the F‐D‐GI algorithm can generate more accurate parameter estimates. Finally, an illustrative example is provided to indicate the effectiveness of the proposed algorithms.

This paper proposes a Kabaddi Game Optimizer (KGO), a sport-inspired metaheuristic for accurate solar photovoltaic (PV) modelling. KGO models Kabaddi strategies (Dubki and Akraman), adaptive weights and weak-player replacement to balance exploration and exploitation. Its performance is first validated on the CEC 2017 benchmark set against seven well-known optimizers, where KGO consistently attains the best average rank. KGO is then coupled with the Newton–Raphson method to estimate parameters of single, double, and triple diode PV models and a PWP-201 PV module. Using RTC France cell and module data, KGO achieves RMSE values of 7.729857E−04, 7.43146E−04, 7.3771E−04, and 2.0529E−03 for the single-, double-, and triple-diode models, and the PV module, respectively, demonstrating accurate, robust, and fast PV parameter estimation.

This study presents a comparative analysis of various optimization algorithms—Differential Evolution (DE), Particle Swarm Optimization (PSO), Arithmetic Optimization Algorithm (AOA), and Hippopotamus Optimization Algorithm (HOA)—for parameter identification in photovoltaic (PV) models. By utilizing RTC France solar cell data, we demonstrate that accurate parameter estimation is crucial for enhancing the efficiency of PV systems, ultimately supporting sustainable energy solutions. Our results indicate that DE achieves the lowest root mean square error (RMSE) of 0.0001 for the double-diode model (DDM), outperforming other methods in terms of accuracy and convergence speed. Both the HOA and PSO also show competitive RMSE values, underscoring their effectiveness in optimizing parameters for PV models. This research not only contributes to improved PV model precision but also aids in the broader effort to advance renewable energy technologies, thereby fostering a more sustainable future.

Fast and robust parameter estimation for statistical partial volume models in brain MRI.

The paper considers the problem of signal parameter estimation using a collection of distributed sensors called a sensor pack. Each sensor quantizes its data to one-bit information and sends it to a fusion processor for the estimation of the parameter. Estimation of a constant signal in additive noise is considered. Estimators are formulated based on one-bit sensor data and their mean squared error (MSE) performances are evaluated through simulation studies. It is shown that selecting certain threshold values for quantizing the sensor outputs can lower the MSE. Genetic algorithms are used to find the optimal threshold values for the sensors. Results from this study show that robust estimation of parameter is possible by using a moderately large number of one-bit quantized sensor data. This work has significance in applications that demand high reliability in sensor networks in spite of sensor failures, limited sensor dynamic range, resolution, bandwidth for data transmission or even data storage.

A robust parameter estimation of FHSS signals using time–frequency analysis in a non-cooperative environment

Obtaining initial parameter estimates for chaotic dynamical systems using linear associative memories

SummaryThis study investigates the parameter identification issues of bilinear‐in‐parameter systems through fractional adaptive algorithms. An auxiliary model based modified fractional least mean square algorithm is proposed for accelerating the parameter estimation accuracy based on the auxiliary model identification idea and the introduced convergence index, a normalized modified hierarchical fractional least mean square algorithm is presented for improving the computational efficiency based on the hierarchical identification principle. The proposed normalized fractional adaptive strategies are effective and could provide more accurate parameter estimates comparing with conventional counterparts for bilinear‐in‐parameter identification model based on the mean square error metrics and the average predicted output error. The effectiveness and accuracy of the proposed algorithms are further verified and validated through numerical simulations for different noise variances, fractional orders and gain parameters.

This research explores the application of metaheuristic algorithms to refine parameter estimation in dynamic systems, with a focus on the inverted pendulum model. Three optimization techniques, Particle Swarm Optimization (PSO), Continuous Genetic Algorithm (CGA), and Salp Swarm Algorithm (SSA), are introduced to solve this problem. Through a thorough statistical evaluation, the optimal performance of each technique within the dynamic methodology is determined. Furthermore, the efficacy of these algorithms is demonstrated through experimental validation on a real prototype, providing practical insights into their performance. The outcomes of this study contribute to the advancement of control strategies by integrating precisely estimated physical parameters into various control algorithms, including PID controllers, fuzzy logic controllers, and model predictive controllers. Each algorithm ran 1000 times, and the SSA algorithm achieved the best performance, with the most accurate parameter estimation with a minimum error of 0.01501 N m and a mean solution error of 0.01506 N m. This precision was further underscored by its lowest standard deviation in RMSE (1.443 99 × 10−6 N m), indicating remarkable consistency across evaluations. The 95% confidence interval for error corroborated the algorithm’s reliability in deriving optimal solutions.

Forecasting blood glucose (BG) levels with routinely collected data is useful for glycemic management. BG dynamics are nonlinear, complex, and nonstationary, which can be represented by nonlinear models. However, the sparsity of routinely collected data creates parameter identifiability issues when high-fidelity complex models are used, thereby resulting in inaccurate forecasts. One can use models with reduced physiological fidelity for robust and accurate parameter estimation and forecasting with sparse data. For this purpose, we approximate the nonlinear dynamics of BG regulation by a linear stochastic differential equation: we develop a linear stochastic model, which can be specialized to different settings: type 2 diabetes mellitus (T2DM) and intensive care unit (ICU), with different choices of appropriate model functions. The model includes deterministic terms quantifying glucose removal from the bloodstream through the glycemic regulation system and representing the effect of nutrition and externally delivered insulin. The stochastic term encapsulates the BG oscillations. The model output is in the form of an expected value accompanied by a band around this value. The model parameters are estimated patient-specifically, leading to personalized models. The forecasts consist of values for BG mean and variation, quantifying possible high and low BG levels. Such predictions have potential use for glycemic management as part of control systems. We present experimental results on parameter estimation and forecasting in T2DM and ICU settings. We compare the model's predictive capability with two different nonlinear models built for T2DM and ICU contexts to have a sense of the level of prediction achieved by this model.

The least mean square (LMS) adaptive algorithm developed by Widrow and Hoff in 1960's has been used widely to solve optimization problems arising in signal processing and control. The LMS adaptive scheme optimizes the fitness function through gradient descent approach and iteratively updates the weight vector using current value of gradient at each iteration. The LMS strategy is famous because of its simplicity and robust performance under different signal conditions but suffers from slow convergence rate. Recently, the parameter identification problem of control autoregressive autoregressive (C-ARAR) like systems has gained esteem research attention and many methods based on stochastic gradient as well as least squares approaches have been proposed for its identification. In this study, a variant of LMS with faster convergence is proposed for system identification of C-ARAR model. The design scheme i.e., momentum LMS (MomLMS), effectively exploits the gradient information by using the proportion of previous gradients for current estimate of the weight vector. The MomLMS method is faster in convergence and less prone to trap in local minimums. The accuracy and convergence of the proposed method is verified through effective identification of C-ARAR system. The adaptive variables obtained through proposed MomLMS algorithm are compared from actual parameters of the C-ARAR system as well as with the results of standard LMS to prove its correctness. The accurate estimation of C-ARAR parameters for different noise levels establishes the robustness of the adaptive strategy. The performance comparison through statistical analysis based on adequate independent runs validates the reliability and effectiveness of the MomLMS method for C-ARAR system identification.

In a general Adaptive Robust Control (ARC) framework, the emphasis is always on the guaranteed transient performance and accurate trajectory tracking in the presence of uncertain nonlinearity and parametric uncertainties. However, when secondary purposes such as system health monitoring and prognosis are of equal importance, intelligent integration of output tracking performance oriented direct adaptive robust control (DARC) and the recently proposed accurate parameter estimation-based indirect adaptive robust control (IARC) is required. In this paper, we will consider such a seamless integration for a hydraulic robotic arm. The newly developed IARC design is first applied to the trajectory tracking for the robotic arm but with an improved estimation model, in which accurate parameter estimates are obtained through a parameter estimation algorithm that is based on physical dynamics rather than the tracking error dynamics. An integrated direct/indirect adaptive robust controller (DIARC) is then presented that preserves the excellent transient tracking performance of the direct ARC designs as well as the better parameter estimation process of the IARC design. The proposed Integrated Direct/Indirect Adaptive Robust Controller (DIARC) achieves the controller-identifier separation, thus enabling certain modularity in the controller design.