Estimation Of Time-varying Parameters Research Articles

Two-dimensional identification of time-varying batch nonlinear processes with input dead-zone nonlinearity

ABSTRACT In the time dimension, the batch process with input dead-zone nonlinearity often has the characteristics of short operation time and time-varying process parameters. A two-dimensional recursive least squares (2D-RLS) identification method for time-varying nonlinear systems with input dead zone is proposed. By mining system dynamic information from the time direction of the same batch and different batch directions, the identification parameters are updated. The proposed two-dimensional identification strategy converts the time-varying parameter estimation problem of time dimension into the equivalent time-invariant parameter estimation problem of batch dimension. Sufficient production data in batch dimension ensure that the proposed identification algorithm can eliminate the influence of random measurement noise. The identification strategy with unequal length of batch data is also given. The convergence of the proposed algorithm is analysed. Finally, numerical simulation and experimental tests are used to verify the effectiveness and superiority of the proposed algorithm.

Time-Varying Parameters Estimation with Adaptive Neural Network EKF for Missile-Dual Control System

Time-Varying Parameters Estimation with Adaptive Neural Network EKF for Missile-Dual Control System

Fourier series-based approximation of time-varying parameters in ordinary differential equations

Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some unobservable system parameters may vary with time without known evolution models. In this work, we propose a novel approximation method inspired by the Fourier series to estimate time-varying parameters (TVPs) in deterministic dynamical systems modeled with ordinary differential equations. Using ensemble Kalman filtering in conjunction with Fourier series-based approximation models, we detail two possible implementation schemes for sequentially updating the time-varying parameter estimates given noisy observations of the system states. We demonstrate the capabilities of the proposed approach in estimating periodic parameters, both when the period is known and unknown, as well as non-periodic TVPs of different forms with several computed examples using a forced harmonic oscillator. Results emphasize the importance of the frequencies and number of approximation model terms on the time-varying parameter estimates and corresponding dynamical system predictions.

Bayesian model selection for COVID-19 pandemic state estimation using extended Kalman filters: Case study for Saudi Arabia.

Quantifying the uncertainty in data-driven mechanistic models is fundamental in public health applications. COVID-19 is a complex disease that had a significant impact on global health and economies. Several mathematical models were used to understand the complexity of the transmission dynamics under different hypotheses to support the decision-making for disease management. This paper highlights various scenarios of a 6D epidemiological model known as SEIQRD (Susceptible-Exposed-Infected-Quarantined-Recovered-Deceased) to evaluate its effectiveness in prediction and state estimation during the spread of COVID-19 pandemic. Then we investigate the suitability of the classical 4D epidemiological model known as SIRD (Susceptible-Infected-Recovered-Deceased) in the long-term behaviour in order to make a comparison between these models. The primary aim of this paper is to establish a foundational basis for the validity and epidemiological model comparisons in long-term behaviour which may help identify the degree of model complexity that is required based on two approaches viz. the Bayesian inference employing the nested sampling algorithm and recursive state estimation utilizing the Extended Kalman Filter (EKF). Our approach acknowledges the potential imperfections and uncertainties inherent in compartmental epidemiological models. By integrating our proposed methodology, these models can consistently generate predictions closely aligned with the observed data on active cases and deaths. This framework, implemented within the EKF algorithm, offers a robust tool for addressing future, unknown pandemics. Moreover, we present a systematic methodology for time-varying parameter estimation along with uncertainty quantification using Saudi Arabia COVID-19 data and obtain the credible confidence intervals of the epidemiological nonlinear dynamical system model parameters.

An improved parameter identification and radial basis correction-differential support vector machine strategies for state-of-charge estimation of urban-transportation-electric-vehicle lithium-ion batteries

The State estimation and determination of time-varying model parameters are crucial for ensuring the safe management of lithium-ion batteries. This paper designs a limited memory recursive least square algorithm to improve the accuracy of online parameter identification. An adaptive radial basis correction-differential support vector machine model is constructed to correct the state of charge value by considering the dynamic characteristic parameters. It greatly reduces estimation error and noise, while monitoring the critical conditions for safe and reliable online battery operation. The estimation effects of the proposed model are verified under hybrid pulse power characterization and dynamic stress test working conditions. The maximum error values obtained are 0.037 % and 0.336 %, respectively, thus achieving high-precision estimation. The proposed method is adaptive to real-time battery management applications, laying a foundation for robust state estimation of lithium-ion batteries used in urban transportation electric vehicles.

Convergence analysis of a synchronous gradient estimation scheme for time-varying parameter systems

For the problem of time-varying parameter estimation and its convergence, this paper proposes an invariant matrix to represent the changing laws of time-varying parameters, which suggests a novel expression to describe the parameters by employing finite terms. A joint recursive least squares algorithm is derived by minimizing the criterion function associated with the unknown invariant matrix. For a class of time-varying systems, a joint stochastic gradient algorithm with the computational efficiency is obtained by analogy to achieve the estimation of invariant matrix and system parameters. The convergence analysis is explored to demonstrate that the time-varying parameter estimation error is bounded under the persistent excitation conditions. The simulation results also validate the effectiveness of the proposed synchronous parameter estimation approach.

International trade and economic growth in Croatia

This article argues that Croatia’s growth over the past two decades is deeply related to the dynamics of international trade. Under the premise that what is bought and sold in global markets reflects the economy’s fundamentals, we show that the rate of growth compatible with equilibrium in the balance-of-payments, i.e. the dynamic Harrod trade multiplier, is a good predictor of the country’s actual long-run growth rate. For this purpose, we apply a state–space model and the Kalman smoother to obtain time-varying parameter estimates of the exports and imports functions. We use these estimates to investigate the determinants of international non-price competitiveness. Bayesian Model Averaging (BMA) and Weighted Average Least Squares (WALS) techniques are combined to tackle model selection uncertainty. It is shown that R&D investments and human capital accumulation are the most important explanatory variables. The success of the European Union’s (EU) integration process depends on the capacity of its new members to achieve a balanced-growth path. Being the last country to join the union, the experience of this single country is particularly relevant to understand possible development alternatives for the region. We conclude by highlighting the policy relevance of our findings to the evaluation of Croatia’s catching-up performance as part of the EU.

Fast estimation of a large TVP-VAR model with score-driven volatilities

This paper proposes a fast approach to estimating a large time-varying parameter vector autoregressive (TVP-VAR) model. Based on a score-driven modeling framework, we first assume that the time-varying variances of random errors in each equation of the TVP-VAR are score-driven, and then propose filtering and smoothing procedures to estimate time-varying parameters and time-varying volatilities. We show that under the forgetting factors, the filtering estimation of time-varying parameters is equivalent to an equation-by-equation estimator, significantly reducing the dimension of state space and thus delivering fast estimation. Moreover, a fast smoothing estimation can be derived, avoiding the inverse of the super-high dimensional state equation covariance matrix. We provide dynamic model averaging (selection) and maximum likelihood estimates for forecasting and inference. Our simulation study shows that the proposed method is more accurate than the popular methods and enjoys tremendous computational gain from the equation-by-equation estimator. Finally, we conduct an empirical study on the dynamic connectedness of global stock markets, demonstrating the merits of our methods in real-time and ex-post analysis.

Data-Driven Spectrum Allocation and Power Control for NOMA HetNets

Towards a green communication discipline, more energy-efficient wireless networks are needed. In this paper, an energy-efficient interference management technique is proposed for heterogeneous networks (HetNets) with downlink nonorthogonal multiple access (NOMA) operating in millimeter (mm) waves. The proposed technique utilizes data-driven-based power and resource blocks (RBs) allocation scheme to maximize the energy efficiency of the entire network while managing inter-user, co-tier, and cross-tier interference. The studied interference management problem is mathematically formulated as maximizing the energy efficiency of NOMA-HetNets under constraints; quality of service (QoS), successive interference cancelation condition (SIC), maximum power allocation, and the maximum capacity of each RB, which is a non-convex and combinatorial NP-hard problem that needs exhaustive search for an optimum solution. The formulated problem is relaxed into a minimization of a linear <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm problem. Then, a lowcomplex model-free data-driven based approach is proposed to find a near-optimum allocation for power and RBs based on a dynamic linearization representation of a time-varying pseudogradient parameter estimation procedure. Numerical analyses show that the proposed scheme achieves higher network energy efficiency with lower computational complexity compared to the benchmark schemes.

An analysis of stock market prices by using extended Kalman filter: The US and China cases

ABSTRACT This study decomposes the trend-cycle components of the stock market indices of the United States and China in a time series framework over the period of 1980–2021, and 1992–2021 years, respectively. Using the extended Kalman filter (EKF) method, the changing dynamics of stock market prices can be analysed more effectively since stock market prices can have a nonlinear pattern, and the EKF allows estimated system parameters to change over time under the nonlinear state-space model. As the impacts of shocks to trend and cycle on the stock market can be observed more efficiently due to flexible time-varying parameter estimation, the EKF offers more reasonable results than other decomposition tools. The empirical findings of this study prove that the EKF extracts the trend and cycle components by giving quite consistent forecasts for stock market prices in both advanced and emerging market countries.

Bayesian Predictive Distributions for Imbalance Prices With Time-Varying Factor Impacts

A dynamic Bayesian model is developed to estimate the time-varying nature of the drivers of the system imbalance prices in the British electricity market. We find that the key exogenous factors that significantly influence prices have impacts that evolve substantially over time. Thus, by modeling their evolution with time varying parameter estimation and making conditional forecasts on the latest estimates, more accurate forecasts are produced. Furthermore, using a Bayesian approach allows predictive distributions to be developed, as would be required for value-at-risk compliance purposes. These densities are also found to be more accurate at the extreme quantiles than a conventional GARCH model with static parameters. We validated the superior performance of this Bayesian time varying predictive density method with the same data as in a previously published benchmark model.

Complex modified projective synchronization of fractional-order complex-valued dynamic network with time-varying coupling and parameters estimation

The problem of Complex Modified Projective Synchronization (CMPS) for fractional-order complex-valued dynamic networks (FOCDNs) is investigated in this paper. Compared with real-valued dynamic networks, complex-valued dynamic networks have expansive application space. First, coupling weight has been generally considered as static constant in most situations, we consider time-varying coupling weight and the unknown parameters in the FOCDNs. Meanwhile, several parameter update laws are designed to estimate unknown parameters and an adaptive coupling weight is defined to adjust coupling nodes in order to solve CMPS problem of the network. Second, some effective criteria for CMPS of FOCDNs are derived by fractional calculus and Lyapunov stability theory. According to the theoretical analysis, FOCDNs with time-varying delay can achieve CMPS via adaptive controller. Finally, the effectiveness of the modified projective strategy for fractional-order complex networks is illustrated via two numerical examples in the complex-valued space.

Euler iteration augmented physics-informed neural networks for time-varying parameter estimation of the epidemic compartmental model

Introduction: Differential equations governed compartmental models are known for their ability to simulate epidemiological dynamics and provide highly accurate descriptive and predictive results. However, identifying the corresponding parameters of flow from one compartment to another in these models remains a challenging task. These parameters change over time due to the effect of interventions, virus variation and so on, thus time-varying compartmental models are required to reflect the dynamics of the epidemic and provide plausible results.Methods: In this paper, we propose an Euler iteration augmented physics-informed neural networks(called Euler-PINNs) to optimally integrates real-world reported data, epidemic laws and deep neural networks to capture the dynamics of COVID-19. The proposed Euler-PINNs method integrates the differential equations into deep neural networks by discretizing the compartmental model with suitable time-step and expressing the desired parameters as neural networks. We then define a robust and concise loss of the predicted data and the observed data for the epidemic in question and try to minimize it. In addition, a novel activation function based on Fourier theory is introduced for the Euler-PINNs method, which can deal with the inherently stochastic and noisy real-world data, leading to enhanced model performance.Results and Discussion: Furthermore, we verify the effectiveness of the Euler-PINNs method on 2020 COVID-19-related data in Minnesota, the United States, both qualitative and quantitative analyses of the simulation results demonstrate its accuracy and efficiency. Finally, we also perform predictions based on data from the early stages of the outbreak, and the experimental results demonstrate that the Euler-PINNs method remains robust on small dataset.

When artificial parameter evolution gets real: particle filtering for time-varying parameter estimation in deterministic dynamical systems

Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of these problems includes time-varying parameters with unknown evolution models that often cannot be directly observed. This work develops a systematic particle filtering approach that reframes the idea behind artificial parameter evolution to estimate time-varying parameters in nonstationary inverse problems arising from deterministic dynamical systems. Focusing on systems modeled by ordinary differential equations, we present two particle filter algorithms for time-varying parameter estimation: one that relies on a fixed value for the noise variance of a parameter random walk; another that employs online estimation of the parameter evolution noise variance along with the time-varying parameter of interest. Several computed examples demonstrate the capability of the proposed algorithms in estimating time-varying parameters with different underlying functional forms and different relationships with the system states (i.e. additive vs. multiplicative).

Data-Driven Hybrid Beamforming for Uplink Multi-User MIMO in Mobile Millimeter-Wave Systems

To enable user diversity while balancing tradeoffs between cost and flexibility, we exploit hybrid analog-digital beamforming for multi-user mobile systems. By combining array and spatial signal-processing techniques, highly directional beams can be formed with high beamforming gain to achieve sufficient link budget. In this way, fine selection of codewords for analog beamforming is essential to ensure the uplink rate, which may increase the latency of establishing a reliable communication link, especially for mobile millimeter-wave communication systems. In order to guarantee the reliability of communication, adaptive data-driven beam tracking is proposed to find the suitable beamformer/combiner pair to achieve the given signal-to-interference-plus-noise ratios constraint. Unlike the model-based approach, the proposed approach is dependent only on the real-time measurement data based on a dynamic linearization representation of a time-varying pseudo-gradient parameter estimation procedure. Numerical analyses show that the proposed beam tracking algorithm can achieve good tracking performance with lower training overhead compared with traditional schemes.

Adaptive Time-Varying Parameter Estimation via Weak Measurement

Extending quantum sensing to time-varying parameter estimation is a potential and challenging task in practical application. To achieve this goal, we propose an adaptive method to estimate an unknown time-varying parameter through light-intensity split detection and the insertion of reference phases in the weak measurement. Theoretical analysis and numerical simulation are applied to illustrate the feasibility and practical applications of our method. The results demonstrate that the method has adjustable sensitivity and linear dynamic range, and is robust to nonideal measurement conditions. Moreover, we analyze the precision of our method and show that its precision limit can surpass the standard quantum limit and approach the Heisenberg scaling when using a squeezed light of optimal Gaussian state.

Surpassing the Nyquist Sampling Limit via Postmodulation

Surpassing the Nyquist sampling limit to avoid aliasing distortion is an important issue for the task of time-varying parameter estimation. To achieve this goal, we propose a high-precision time-varying parameter estimation scheme based on split detection and postmodulation of light instead of postprocessing of data. Theoretical analysis demonstrates its advantage of surpassing the Nyquist sampling limit and the avoidance of anti-aliasing distortion. In order to illustrate the feasibility, a numerical simulation based on the acceptance rejection sampling method is performed showing the noise robustness of the scheme in terms of correlation coefficient, root-mean-square error, and mean absolute error. Our scheme provides a method for function estimation.

Intelligent Scanning Detection System of Muscle Exercise Fatigue Based on Surface Electromyography.

In order to use the surface EMG signal to automatically detect the muscle fatigue state, a research method of the muscle exercise fatigue intelligent scanning detection system based on surface EMG was proposed, and the sEMG signal features of 10 subjects before and after fatigue were extracted. A time-varying parameter autoregressive model is established. By introducing the Legendre basis function, the parameter identification of the linear nonstationary process is transformed into the parameter identification of the linear time-invariant system. Combined with the correlation index, the optimal Legendre base function dimension of the time-varying system parameter estimation can be obtained, then the best model fitting effect can be obtained, and the time-invariant parameters are solved by the least square method. Using the rate of change of the first time-varying parameter (ARC1) of the autoregressive model before and after fatigue as an index to detect muscle fatigue sensitivity, a two-tailed t test was used to compare the mean power frequency (MPF) and the median frequency (MF) with the rate of change. The results showed that the change rates of ARC1, MPF, and MF before and after fatigue were34.33% ± 2.5%, 68% + 2.03%, and 22.80% + 2.19%, which were 41% and 25%, respectively. The rate of change of ACR1 was significantly higher than that of MPF and MF (P < 0.05). When detecting muscle fatigue by sEMG signal, it has the advantages of short time and high sensitivity. It can be used for online real-time analysis of muscle fatigue, providing a potential analysis tool for limb muscle strain, rehabilitation, and ergonomics assessment.

Bayesian data assimilation for estimating instantaneous reproduction numbers during epidemics: Applications to COVID-19.

Estimating the changes of epidemiological parameters, such as instantaneous reproduction number, Rt, is important for understanding the transmission dynamics of infectious diseases. Current estimates of time-varying epidemiological parameters often face problems such as lagging observations, averaging inference, and improper quantification of uncertainties. To address these problems, we propose a Bayesian data assimilation framework for time-varying parameter estimation. Specifically, this framework is applied to estimate the instantaneous reproduction number Rt during emerging epidemics, resulting in the state-of-the-art 'DARt' system. With DARt, time misalignment caused by lagging observations is tackled by incorporating observation delays into the joint inference of infections and Rt; the drawback of averaging is overcome by instantaneously updating upon new observations and developing a model selection mechanism that captures abrupt changes; the uncertainty is quantified and reduced by employing Bayesian smoothing. We validate the performance of DARt and demonstrate its power in describing the transmission dynamics of COVID-19. The proposed approach provides a promising solution for making accurate and timely estimation for transmission dynamics based on reported data.

Design and analysis of two-phase studies with multivariate longitudinal data.

Two-phase studies are crucial when outcome and covariate data are available in a first-phase sample (e.g., a cohort study), but costs associated with retrospective ascertainment of a novel exposure limit the size of the second-phase sample, in whom the exposure is collected. For longitudinal outcomes, one class of two-phase studies stratifies subjects based on an outcome vector summary (e.g., an average or a slope over time) and oversamples subjects in the extreme value strata while undersampling subjects in the medium-value stratum. Based on the choice of the summary, two-phase studies for longitudinal data can increase efficiency of time-varying and/or time-fixed exposure parameter estimates. In this manuscript, we extend efficient, two-phase study designs to multivariate longitudinal continuous outcomes, and we detail two analysis approaches. The first approach is a multiple imputation analysis that combines complete data from subjects selected for phase two with the incomplete data from those not selected. The second approach is a conditional maximum likelihood analysis that is intended for applications where only data from subjects selected for phase two are available. Importantly, we show that both approaches can be applied to secondary analyses of previously conducted two-phase studies. We examine finite sample operating characteristics of the two approaches and use the Lung Health Study (Connett etal. (1993), Controlled Clinical Trials, 14, 3S-19S) to examine genetic associations with lung function decline overtime.