Статті в журналах: "Unknown term estimation"

1

Florens, Jean-Pierre, and Senay Sokullu. "NONPARAMETRIC ESTIMATION OF SEMIPARAMETRIC TRANSFORMATION MODELS." Econometric Theory 33, no. 4 (June 6, 2016): 839–73. http://dx.doi.org/10.1017/s0266466616000190.

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In this paper we develop a nonparametric estimation technique for semiparametric transformation models of the form:H(Y) =φ(Z) +X′β+UwhereH,φare unknown functions,βis an unknown finite-dimensional parameter vector and the variables (Y,Z) are endogenous. Identification of the model and asymptotic properties of the estimator are analyzed under the mean independence assumption between the error term and the instruments. We show that the estimators are consistent, and a$\sqrt N$-convergence rate and asymptotic normality for$\hat \beta$can be attained. The simulations demonstrate that our nonparametric estimates fit the data well.

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2

Zhang, Yuanqing. "Estimation of Partially Specified Spatial Autoregressive Model." Journal of Systems Science and Information 2, no. 3 (June 25, 2014): 226–35. http://dx.doi.org/10.1515/jssi-2014-0226.

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Abstract In this paper, we study estimation of a partially specified spatial autoregressive model with heteroskedasticity error term. Under the assumption of exogenous regressors and exogenous spatial weighting matrix, we propose an instrumental variable estimation. Under some sufficient conditions, we show that the proposed estimator for the finite dimensional parameter is root-n consistent and asymptotically normally distributed and the proposed estimator for the unknown function is consistent and also asymptotically distributed though at a rate slower than root-n. Monte Carlo simulations verify our theory and the results suggest that the proposed method has some practical value.

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3

Zhang, Xiao, Feng Ding, Ling Xu, Ahmed Alsaedi, and Tasawar Hayat. "A Hierarchical Approach for Joint Parameter and State Estimation of a Bilinear System with Autoregressive Noise." Mathematics 7, no. 4 (April 17, 2019): 356. http://dx.doi.org/10.3390/math7040356.

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This paper is concerned with the joint state and parameter estimation methods for a bilinear system in the state space form, which is disturbed by additive noise. In order to overcome the difficulty that the model contains the product term of the system input and states, we make use of the hierarchical identification principle to present new methods for estimating the system parameters and states interactively. The unknown states are first estimated via a bilinear state estimator on the basis of the Kalman filtering algorithm. Then, a state estimator-based recursive generalized least squares (RGLS) algorithm is formulated according to the least squares principle. To improve the parameter estimation accuracy, we introduce the data filtering technique to derive a data filtering-based two-stage RGLS algorithm. The simulation example indicates the efficiency of the proposed algorithms.

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4

Zhou, Yanli, Shican Liu, Tianhai Tian, Qi He, and Xiangyu Ge. "Using Particle Swarm Optimization Algorithm to Calibrate the Term Structure Model." Mathematical Problems in Engineering 2021 (January 4, 2021): 1–11. http://dx.doi.org/10.1155/2021/8893940.

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One of the advantages of stochastic differential equations (SDE) is that they can follow a variety of different trends so that they can establish complex dynamic systems in the economic and financial fields. Although some estimation methods have been proposed to identify the unknown parameters in virtue of the results in the SDE model to speed up the process, these solutions only focus on using explicit approach to solve SDEs, and therefore they are not reliable to deal with data source merged being large and varied. Thus, this study makes progress in creating a new implicit way to fill in the gaps of accurately calibrating the unknown parameters in the SDE model. Essentially, the primary goal of the article is to generate rigid SDE simulation. Meanwhile, the particle swarm optimization method serves a purpose to search and simultaneously obtain the optimal estimation of the model unknown parameters in the complicated experiment of parameter space in an effective way. Finally, in an interest rate term structure model, it is verified that the method effectively deals with parameter estimation in the SDE model.

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5

Zhang, Zhengyu. "SEMIPARAMETRIC ESTIMATION OF PARTIALLY LINEAR TRANSFORMATION MODELS UNDER CONDITIONAL QUANTILE RESTRICTION." Econometric Theory 32, no. 2 (December 19, 2014): 458–97. http://dx.doi.org/10.1017/s0266466614000887.

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This article is concerned with semiparametric estimation of a partially linear transformation model under conditional quantile restriction with no parametric restriction imposed either on the link functional form or on the error term distribution. We describe for the finite-dimensional parameter a$\sqrt n$-consistent estimator which combines the features of Chen (2010)’s maximum integrated score estimator as well as Lee (2003)’s average quantile regression. We show the remaining two infinite-dimensional unknown functions in the model can be separately identified and propose estimators for these functions based on the marginal integration method. Furthermore, a simple approach is proposed to estimate the average partial quantile effect. Two important extensions, i.e., random censoring as well as estimating a transformation model with an endogenous regressor are also considered.

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6

Kou, Junke, Qinmei Huang, and Huijun Guo. "Pointwise Wavelet Estimations for a Regression Model in Local Hölder Space." Axioms 11, no. 9 (September 10, 2022): 466. http://dx.doi.org/10.3390/axioms11090466.

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This paper considers an unknown functional estimation problem in a regression model with multiplicative and additive noise. A linear wavelet estimator is first constructed by a wavelet projection operator. The convergence rate under the pointwise error of linear wavelet estimators is studied in local Hölder space. A nonlinear wavelet estimator is provided by the hard thresholding method in order to obtain an adaptive estimator. The convergence rate of the nonlinear estimator is the same as the linear estimator up to a logarithmic term. Finally, it should be pointed out that the convergence rates of two wavelet estimators are consistent with the optimal convergence rate on pointwise nonparametric estimation.

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7

Chen, Gang, Yong Zhou, TingTing Gao, and Qicai Zhou. "Unknown Disturbance Estimation for a PMSM with a Hybrid Sliding Mode Observer." Mathematical Problems in Engineering 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/316360.

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A hybrid sliding mode observer that combines high gain feedback and a high-order sliding mode term is developed to identify the time-varying disturbance for a permanent-magnet synchronous motor (PMSM). Based on the measurable current and the position, the unknown disturbance can be identified from the sliding mode term without digital filter effect. It is then used to enhance the robustness of the speed control dynamics. For ease of implementation in real applications, such as DSP and FPGA, the proposed observer is properly designed to avoid complex mathematical operators. Simulation results are given to illustrate the performance of the proposed observer.

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8

Papadopoulos, Pavlos, Andreas Tsiartas, and Shrikanth Narayanan. "Long-Term SNR Estimation of Speech Signals in Known and Unknown Channel Conditions." IEEE/ACM Transactions on Audio, Speech, and Language Processing 24, no. 12 (December 2016): 2495–506. http://dx.doi.org/10.1109/taslp.2016.2615240.

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9

Yakoub , Zaineb, Omar Naifar, and Dmitriy Ivanov. "Unbiased Identification of Fractional Order System with Unknown Time-Delay Using Bias Compensation Method." Mathematics 10, no. 16 (August 22, 2022): 3028. http://dx.doi.org/10.3390/math10163028.

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In the field of engineering, time-delay is a typical occurrence. In reality, the inner dynamics of many industrial processes are impacted by delay or after-effect events. This paper discusses the identification of continuous-time fractional order system with unknown time-delay using the bias compensated least squares algorithm. The basic concept is to remove the imposed bias by including a correction term into the least squares estimations. The suggested approach makes a significant contribution by the estimation, iteratively, of fractional order system coefficients as well as the orders and the time-delay using a nonlinear optimization algorithm. The main advantage of this method is to provide a simple and powerful algorithm with good accuracy. The suggest method performances are assessed through two numerical examples.

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10

Li, Liangliang, Xianpeng Wang, Xiang Lan, Gang Xu, and Liangtian Wan. "Reweighted Off-Grid Sparse Spectrum Fitting for DOA Estimation in Sensor Array with Unknown Mutual Coupling." Sensors 23, no. 13 (July 6, 2023): 6196. http://dx.doi.org/10.3390/s23136196.

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In the environment of unknown mutual coupling, many works on direction-of-arrival (DOA) estimation with sensor array are prone to performance degradation or even failure. Moreover, there are few literatures on off-grid direction finding using regularized sparse recovery technology. Therefore, the scenario of off-grid DOA estimation in sensor array with unknown mutual coupling is investigated, and then a reweighted off-grid Sparse Spectrum Fitting (Re-OGSpSF) approach is developed in this article. Inspired by the selection matrix, an undisturbed array output is formed to remove the unknown mutual coupling effect. Subsequently, a refined off-grid SpSF (OGSpSF) recovery model is structured by integrating the off-grid error term obtained from the first-order Taylor approximation of the higher-order term into the underlying on-grid sparse representation model. After that, a novel Re-OGSpSF framework is formulated to recover the sparse vectors, where a weighted matrix is developed by the MUSIC-like spectrum function to enhance the solution’s sparsity. Ultimately, off-grid DOA estimation can be realized with the help of the recovered sparse vectors. Thanks to the off-grid representation and reweighted strategy, the proposed method can effectively and efficiently achieve high-precision continuous DOA estimation, making it favorable for real-time direction finding. The simulation results validate the superiority of the proposed method.

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11

Fraanje, Rufus, René Beltman, Fidelis Theinert, Michiel van Osch, Teade Punter, and John Bolte. "Sensor Fusion of Odometer, Compass and Beacon Distance for Mobile Robots." International Journal of Artificial Intelligence and Machine Learning 10, no. 1 (January 2020): 1–17. http://dx.doi.org/10.4018/ijaiml.2020010101.

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The estimation of the pose of a differential drive mobile robot from noisy odometer, compass, and beacon distance measurements is studied. The estimation problem, which is a state estimation problem with unknown input, is reformulated into a state estimation problem with known input and a process noise term. A heuristic sensor fusion algorithm solving this state-estimation problem is proposed and compared with the extended Kalman filter solution and the Particle Filter solution in a simulation experiment.

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12

Bouassem, Karim, Abdellatif El Assoudi, Jalal Soulami, and El Hassane El Yaagoubi. "Unknown Input Observer Design for a Class of Linear Descriptor Systems." E3S Web of Conferences 229 (2021): 01019. http://dx.doi.org/10.1051/e3sconf/202122901019.

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This paper addresses the problem of unknown inputs observer (UIO) design for a class of linear descriptor systems. The unknown inputs affect both state and output of the system. The basic idea of the proposed approach is based on the separation between dynamic and static relations in the descriptor model. Firstly, the method used to separate the differential part from the algebraic part is developed. Secondly, an observer design permitting the simultaneous estimation of the system state and the unknown inputs is proposed. The developed approach for the observer design is based on the synthesis of an augmented model which regroups the differential variables and unknown inputs. The exponential stability of the estimation error is studied using the Lyapunov theory and the stability condition is given in term of linear matrix inequality (LMI). Finally, to illustrate the efficiency of the proposed methodology, a heat exchanger pilot model is considered.

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13

Lin, Haiping, Hanlie Gu, Jinyu Ma, and Shengdong Yu. "Practical tracking control of piezoelectric actuators with time-delay estimation and nonsingular terminal sliding mode." MATEC Web of Conferences 355 (2022): 03062. http://dx.doi.org/10.1051/matecconf/202235503062.

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A novel type of nonlinear robust control strategy is proposed in view of uncertain nonlinear factors, such as hysteresis, creep, and high-frequency vibration, of piezoelectric actuators (PEAs). This strategy can be used for the precise trajectory tracking of PEAs. The Bouc–Wen dynamic model is reasonably simplified to facilitate engineering application. The hysteresis term is summarized as an unknown term to avoid its nonlinear parameter identification. The controller robustness is achieved due to the nonsingular terminal sliding mode control, and the online estimation of unknown disturbances is realized because of the delay estimation technology; thus, no prior knowledge of the unknown boundary of the system is required. The precision robust differentiator is used to estimate the speed and acceleration signals in real time on the basis of the obtained displacement signals. The closed-loop stability of the system is proved by the Lyapunov criterion. Experimental results show that the proposed control strategy performs better than the traditional time-delay estimation control in terms of control accuracy and energy conservation. Therefore, the proposed control strategy can play an important role in the micro/nanofield driven by PEAs.

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14

Wang, Xi, and Songnian Chen. "Semiparametric estimation of generalized transformation panel data models with nonstationary error." Econometrics Journal 23, no. 3 (May 11, 2020): 386–402. http://dx.doi.org/10.1093/ectj/utaa009.

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Summary Early studies of the generalized transformation panel data model resorted to the identical marginal distribution of the error term over time. This stationarity condition is restrictive for many applications, especially as the number of time periods increases. This paper considers nonstationary censored generalized transformation panel data models where the idiosyncratic error has an unknown nonseparable form and admits a flexible relationship between the observable and the unobservable. We propose an estimation method, and establish the consistency and asymptotic normality for the proposed estimator. Simulation results illustrate the good performance of our estimator in a finite sample. We apply the proposed method to bilateral trade issues of the U.S.A. and foreign countries.

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15

Stępień, Bartłomiej. "Confidence Intervals for the Long-Term Noise Indicators Using the Kernel Density Estimator." Archives of Acoustics 41, no. 3 (September 1, 2016): 517–25. http://dx.doi.org/10.1515/aoa-2016-0050.

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Abstract A non-classical model of interval estimation based on the kernel density estimator is presented in this paper. This model has been compared with interval estimation algorithms of the classical (parametric) statistics assuming that the standard deviation of the population is either known or unknown. The non-classical model does not have to assume belonging of random sample to a normal distribution. A theoretical basis of the proposed model is presented as well as an example of calculation process which makes possible determining confidence intervals of the expected value of long-term noise indicators Aden and LN. The statistical analysis was carried out for 95% interval widths obtained by using each of these models. The inference of their usefulness was performed on the basis of results of non-parametric statistical tests at significance level α = 0.05. The data used to illustrate the proposed solutions and carry out the analysis were results of continuous monitoring of traffic noise recorded in 2004 in one of the main arteries of Krakow in Poland.

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16

Rhodes, Callum, Cunjia Liu, and Wen-Hua Chen. "Autonomous Source Term Estimation in Unknown Environments: From a Dual Control Concept to UAV Deployment." IEEE Robotics and Automation Letters 7, no. 2 (April 2022): 2274–81. http://dx.doi.org/10.1109/lra.2022.3143890.

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17

Pérez-Cruz, J. Humberto, E. Ruiz-Velázquez, José de Jesús Rubio, and Carlos A. de Alba-Padilla. "Robust Adaptive Neurocontrol of SISO Nonlinear Systems Preceded by Unknown Deadzone." Mathematical Problems in Engineering 2012 (2012): 1–23. http://dx.doi.org/10.1155/2012/342739.

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In this study, the problem of controlling an unknown SISO nonlinear system in Brunovsky canonical form with unknown deadzone input in such a way that the system output follows a specified bounded reference trajectory is considered. Based on universal approximation property of the neural networks, two schemes are proposed to handle this problem. The first scheme utilizes a smooth adaptive inverse of the deadzone. By means of Lyapunov analyses, the exponential convergence of the tracking error to a bounded zone is proven. The second scheme considers the deadzone as a combination of a linear term and a disturbance-like term. Thus, the estimation of the deadzone inverse is not required. By using a Lyapunov-like analyses, the asymptotic converge of the tracking error to a bounded zone is demonstrated. Since this control strategy requires the knowledge of a bound for an uncertainty/disturbance term, a procedure to find such bound is provided. In both schemes, the boundedness of all closed-loop signals is guaranteed. A numerical experiment shows that a satisfactory performance can be obtained by using any of the two proposed controllers.

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18

Hu, Yifei, and Jinbo Wu. "Online identification method for a system with unknown varying time-delay and parameter." Transactions of the Institute of Measurement and Control 43, no. 14 (June 22, 2021): 3267–71. http://dx.doi.org/10.1177/01423312211022447.

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An online identification method that can simultaneously estimate the unknown system parameter and the unknown time-delay is proposed. Firstly, with the help of Lagrange mean value theorem, the system with time-delay can be transformed into two terms that can be identified by modified least-square algorithm and one term that represents an approximate error. Then, a modified least-square algorithm is introduced to estimate all the unknown parameters in case of external disturbances. Additionally, an restrain term are added in the covariance matrix to enhance the robustness to deal with the approximate error which is related to the estimated error of system parameter and time-delay. Also, the boundedness of the estimation error is guaranteed via Lyapunov stability theory. Finally, the effectivity of the proposed method is verified by simulations results.

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19

Chang, Yoosoon. "VECTOR AUTOREGRESSIONS WITH UNKNOWN MIXTURES OF I(0), I(1), AND I(2) COMPONENTS." Econometric Theory 16, no. 6 (December 2000): 905–26. http://dx.doi.org/10.1017/s0266466600166058.

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This paper develops a new estimation method for nonstationary vector autoregressions (VAR's) with unknown mixtures of I(0), I(1), and I(2) components. The method does not require prior knowledge on the exact number and location of unit roots in the system. It is, therefore, applicable for VAR's with any mixture of I(0), I(1), and I(2) variables, which may be cointegrated in any form. The limit theory for the stationary component of our estimator is still normal, thereby preserving the usual VAR limit theory. Yet, the leading term of the nonstationary component of the estimator has mixed normal limit distribution and does not involve unit root distribution. Our method is an extension of the FM-VAR procedure by Phillips (1995, Econometrica 63, 1023–1078) and yields an estimator that is optimal in the sense of Phillips (1991, Econometrica 59, 283–306). Moreover, we show for a certain class of linear restrictions that the Wald tests based on the estimator are asymptotically distributed as a weighted sum of independent chi-square variates with weights between zero and one. For such restrictions, the limit distribution of the standard Wald test is nonstandard and nuisance parameter dependent. This has a direct application for Granger-causality testing in nonstationary VAR's.

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20

Yang, Junqi, Yantao Chen, Zheng Zheng, and Wei Qian. "Robust adaptive state estimation for uncertain nonlinear switched systems with unknown inputs." Transactions of the Institute of Measurement and Control 40, no. 4 (October 31, 2016): 1082–91. http://dx.doi.org/10.1177/0142331216673697.

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This paper discusses the issue of the continuous state estimation for a class of uncertain nonlinear switched systems under the two cases of both average dwell time and mode-dependent average dwell time. A robust and adaptive switched observer is developed such that the states of an original nonlinear switched system can be asymptotically estimated, where the Lipschitz constant of the nonlinear term may be unknown since the designed adaptation law can adaptively adjust it. Based on the feasible solution of an optimization problem with a linear matrix inequality constraint, the observer gain matrices are obtained and guarantee the existence of a robust switched observer. Meanwhile, the switching signals are designed such that the observer error dynamics is globally uniformly exponentially stable, and the sufficient conditions of the existence of a robust sliding-mode switched observer are derived. Finally, the effectiveness of the proposed approaches is illustrated by a numerical example and switched Rössler chaotic dynamics.

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21

Young, G. E., K. S. Suresh Rao, and Vijay R. Chatufale. "Block-Recursive Identification of Parameters and Delay in the Presence of Noise." Journal of Dynamic Systems, Measurement, and Control 117, no. 4 (December 1, 1995): 600–607. http://dx.doi.org/10.1115/1.2801120.

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This paper presents a method for identification of parameters and delays of a linear system in the presence of noise. The estimation procedure is based on transforming the input-output data into the discrete Fourier domain. The transformed data is then solved block recursively to obtain both the system parameters and unknown delay. For systems with no delays or known delays, the equations are linear in the parameters and the standard estimation techniques can be applied. For systems with unknown delays, the resulting equations are nonlinear in the delay term. A recursive nonlinear estimation technique similar to the least-squares in the time domain has been developed. In the presence of Gaussian white noise, simulation studies indicate that the parameters converge to their true values in the mean.

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22

Al-Shuka, Hayder. "FAT-based adaptive backstepping control of an electromechanical system with an unknown input coefficient." FME Transactions 49, no. 1 (2021): 113–20. http://dx.doi.org/10.5937/fme2101113a.

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This paper is focused on orthogonal function approximation technique FAT-based adaptive backstepping control of a geared DC motor coupled with a rotational mechanical component. It is assumed that all parameters of the actuator are unknown including the torque-current constant (i.e., unknown input coefficient) and hence a control system with three motor control modes is proposed: 1) motor torque control mode, 2) motor current control mode, and 3) motor voltage control mode. The proposed control algorithm is a powerful tool to control a dynamic system with an unknown input coefficient. Each uncertain parameter/term is represented by a linear combination of weighting and orthogonal basis function vectors. Chebyshev polynomial is used as a strong approximator for estimation of uncertainty. The designed control law includes three terms: a feedforward term, a feedback term and a robust term for compensation of modeling error. Lyapunov stability is used to prove the validity of the proposed controller and to derive the update laws for the weighting vectors of orthogonal Chebyshev approximators. A case study of a geared DC motor in connection with a rotating output load is simulated to prove the effectiveness of the proposed controller structure.

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23

AL-Samarraie, Shibly Ahmed, and Mustafa H. Mishary. "High Order Sliding Mode Observer-Based Output Feedback Controller Design For Electro-Hydraulic System." Al-Khwarizmi Engineering Journal 12, no. 4 (December 18, 2017): 1–11. http://dx.doi.org/10.22153/kej.2016.06.002.

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A perturbed linear system with property of strong observability ensures that there is a sliding mode observer to estimate the unknown form inputs together with states estimation. In the case of the electro-hydraulic system with piston position measured output, the above property is not met. In this paper, the output and its derivatives estimation were used to build a dynamic structure that satisfy the condition of strongly observable. A high order sliding mode observer (HOSMO) was used to estimate both the resulting unknown perturbation term and the output derivatives. Thereafter with one signal from the whole system (piton position), the piston position make tracking to desire one with a simple linear output feedback controller after canceling the perturbation term. The numerical simulation results showed excellent performance of the proposed output feedback controller in forcing the piston position to follow the desired reference position. Moreover, the control effort spent was minimal.

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24

Barge-Gil, Andrés, and Alfredo Garcia-Hiernaux. "Staking in Sports Betting Under Unknown Probabilities: Practical Guide for Profitable Bettors." Journal of Sports Economics 21, no. 6 (May 1, 2020): 593–609. http://dx.doi.org/10.1177/1527002520921227.

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Kelly staking has been proven to maximize long-term bankroll growth of bettors with positive expected yield (profitable bettors). However, it demands for an estimation of the true probabilities for each event. Thus, many sport tipsters opt for simpler flat ( unit-loss) or unit-win staking plans. We analyze under which assumptions these strategies correspond to the Kelly method and propose a different staking plan, unit-impact, under the hypothesis that it fits better with Kelly’s. We test our predictions using data of professional tipsters from the betting database pyckio.com. Results show empirical support for our hypothesis.

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25

Wang, Cheng, Kaicheng Li, and Shuai Su. "Hierarchical Newton Iterative Parameter Estimation of a Class of Input Nonlinear Systems Based on the Key Term Separation Principle." Complexity 2018 (October 24, 2018): 1–11. http://dx.doi.org/10.1155/2018/7234147.

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This paper investigates the identification problem for a class of input nonlinear systems whose disturbance is in the form of the moving average model. In order to improve the computation complexity, the key term separation principle is introduced to avoid the redundant parameter estimation. Based on the decomposition technique, a hierarchical Newton iterative identification method combining the key term separation principle is proposed for enhancing the estimation accuracy and handling the computational load with the presence of the high dimensional matrices. In the identification procedure, the unknown internal items or vectors are replaced with their iterative estimates. The effectiveness of the proposed identification methods is shown via a numerical simulation example.

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26

Adonijah Maxwell, Awoingo, and Isaac Didi Essi. "Econometric Estimation of Production Function with Applications." Academic Journal of Applied Mathematical Sciences, no. 56 (June 15, 2019): 57–61. http://dx.doi.org/10.32861/ajams.56.57.61.

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This study focuses on Monte Carlo Methods in parameter estimation of production function. The ordinary least square (OLS) method is used to estimate the unknown parameters. The Monte Carlo simulation methods are used for the data generating process. The Cobb-Douglas production model with multiplicative error term is fitted to the data generated. From tables 1.1 to 1.3, the mean square error (MSE) of 1 are 0.007678, 0.001972 and 0.001253 respectively for sample sizes 20, 40 and 80. Our finding showed that the mean square error (MSE) value varies with the sum of the powers of the input variables.

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27

Kuang, Nenghui, Chunli Li, and Huantian Xie. "Sequential Maximum Likelihood Estimation for the Parameter of the Linear Drift Term of the Rayleigh Diffusion Process." International Journal of Nonlinear Sciences and Numerical Simulation 16, no. 1 (February 1, 2015): 35–41. http://dx.doi.org/10.1515/ijnsns-2013-0101.

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AbstractIn this paper, we investigate the properties of a sequential maximum likelihood estimator of the unknown linear drift parameter for the Rayleigh diffusion process. The estimator is shown to be closed, unbiased, normally distributed and strongly consistent. Finally a simulation study is presented to illustrate the efficiency of the estimator.

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28

Kaba, Aziz, and Emre Kiyak. "Artificial bee colony–based Kalman filter hybridization for three–dimensional position estimation of a quadrotor." Aircraft Engineering and Aerospace Technology 92, no. 10 (August 24, 2020): 1523–32. http://dx.doi.org/10.1108/aeat-01-2020-0015.

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Purpose The purpose of this paper is to introduce an artificial bee colony-based Kalman filter algorithm along with an extended objective function to ensure the optimality of the estimator of the quadrotor in the presence of unknown measurement noise statistics. Design/methodology/approach Six degree-of-freedom mathematical model of the quadrotor is derived. Position controller for the quadrotor is designed. Kalman filter-based estimation algorithm is implemented in the sensor feedback loop. Artificial bee colony-based hybrid algorithm is used as an optimization method to handle the unknown noise statistics. Existing objective function is extended with a penalty term. Mathematical proof of the extended objective function is derived. Results of the proposed algorithm is compared with de facto genetic algorithm-based Kalman filter. Findings Artificial bee colony algorithm-based Kalman filter and extended objective function duo are able to optimize the measurement noise covariance matrix with an absolute error as low as 0.001 [m2]. Proposed method and function is capable of reducing the noise from 2 to 0.09 [m] for x-axis, 3.4 to 0.14 [m] for y-axis and 3.7 to 0.2 [m] for z-axis, respectively. Originality/value The motivation behind this paper is to bring a novel optimization-based solution for the estimation problem of the quadrotor when the measurement noise statistics are unknown along with an extended objective function to prevent the infeasible solutions with mathematical convergence analysis.

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29

Ye, Jing Jie, Yu Wan Cen, Xiao Hua Ye, Pei Min Xu, and Zi Wei Pan. "An Observer and Observer Based Modeling Lateral Dynamics For Moving Steel Strip." Advanced Materials Research 422 (December 2011): 286–95. http://dx.doi.org/10.4028/www.scientific.net/amr.422.286.

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The steel strip processing systems rely on accurate lateral positioning to achieve high processing speeds and improved product quality. In real steel strip process systems are not just nonlinear and time-varying but also highly uncertain. This research focuses on the disturbance estimation approach to modeling unknown dynamics of physical plant. The Euler’s beam theory with boundary condition is considered to derive the equation of the moving steel strip. To consider unknown dynamics in the real steel strip, a nonlinear state space equation is employed to describe unknown dynamics of the moving steel strip. The nonlinear part of this system is proposed as an unknown disturbance input to this system. The neural-based observer (NNO) is designed to estimate nonlinear unknown dynamics. The online weight-updating mechanism is a modified version of the backpropagation algorithm with a simple structure together with an error-modification term added to guarantee the robustness of the observer. The measure of sensor and estimation of observer pair of input and output is used to train the weight of NN. The simulation and measure result shown that the NNO can track the un-modeling dynamic of nonlinear systems.

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30

Di Ronco, Andrea, Francesca Giacobbo, and Antonio Cammi. "A Kalman Filter-Based Approach for Online Source-Term Estimation in Accidental Radioactive Dispersion Events." Sustainability 12, no. 23 (November 30, 2020): 10003. http://dx.doi.org/10.3390/su122310003.

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In the present work, a online data assimilation approach, based on the Kalman filter algorithm, is proposed for the source term reconstruction in accidental events with dispersion of radioactive agents in air. For this purpose a Gaussian plume model of dispersion in air is embedded in the Kalman filter algorithm to estimate unknown scenario parameters, such as the coordinates and the intensity of the source, on the basis of measurements collected by a mobile sensor. The approach was tested against pseudo-experimental data produced with both the Gaussian plume model and the Lagrangian puff model SCIPUFF. The results show the good capabilities of the proposed approach in retrieving the values of the unknown parameters when (i) one or more release parameters are poorly known and (ii) a sufficient number of experimental measurements describing the evolution of the dispersion process can be collected in a short time by means of mobile sensors. Thanks to its flexibility and computational efficiency, and due to the exploitation of the Kalman filter potentialities through the use of a simplified model of dispersion in air, the proposed approach can constitute a useful tool for the management of emergency scenarios.

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31

Gerstoft, Peter, Christoph Mecklenbrauker, Santosh Nannuru, and Geert Leus. "DOA Estimation in Heteroscedastic Noise with sparse Bayesian Learning." Applied Computational Electromagnetics Society 35, no. 11 (February 5, 2021): 1439–40. http://dx.doi.org/10.47037/2020.aces.j.351188.

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We consider direction of arrival (DOA) estimation from long-term observations in a noisy environment. In such an environment the noise source might evolve, causing the stationary models to fail. Therefore a heteroscedastic Gaussian noise model is introduced where the variance can vary across observations and sensors. The source amplitudes are assumed independent zero-mean complex Gaussian distributed with unknown variances (i.e., source powers), leading to stochastic maximum likelihood (ML) DOA estimation. The DOAs are estimated from multi-snapshot array data using sparse Bayesian learning (SBL) where the noise is estimated across both sensors and snapshots.

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32

Li, Qi, and Jeffrey M. Wooldridge. "SEMIPARAMETRIC ESTIMATION OF PARTIALLY LINEAR MODELS FOR DEPENDENT DATA WITH GENERATED REGRESSORS." Econometric Theory 18, no. 3 (May 15, 2002): 625–45. http://dx.doi.org/10.1017/s0266466602183034.

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In this paper we consider the problem of estimating a semiparametric partially linear model for dependent data with generated regressors. This type of model comes naturally from various econometric models such as a semiparametric rational expectation model when the surprise term enters the model nonparametrically, or a semiparametric type-3 Tobit model when the error distributions are of unknown forms, or a semiparametric error correction model. Using the nonparametric kernel method and under primitive conditions, we show that the [square root]n-consistent estimation results of the finite-dimensional parameter in a partially linear model can be generalized to the case of generated regressors with weakly dependent data. The regularity conditions we use are quite weak, and they are similar to those used in Robinson (1988, Econometrica 56, 931–954) for independent and observed data.

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33

Krief, Jerome M. "AN INTEGRATED KERNEL-WEIGHTED SMOOTHED MAXIMUM SCORE ESTIMATOR FOR THE PARTIALLY LINEAR BINARY RESPONSE MODEL." Econometric Theory 30, no. 3 (November 29, 2013): 647–75. http://dx.doi.org/10.1017/s0266466613000431.

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This paper considers a binary response model with a partially linear latent equation, where ϕ is an unknown function and β is a finite-dimensional parameter of interest. Using the principle of smoothed maximum score estimation (Horowitz, 1992; Econometrica 60(3), 505–531), a consistent and asymptotically normal (C.A.N.)estimator for β is proposed under the restriction that the median of the error conditional on the covariates is equal to 0. Furthermore, the rate of convergence in probability is close to the parametric rate, if certain functions admit enough derivatives. This method neither restricts the form of heteroskedasticity in the error term nor suffers from the curse of dimensionality whenever ϕ is multivariate. Some Monte Carlo experiments suggest that this estimator performs well compared with conventional estimators.

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34

Rojanasirivanit, Suttavee, Poramet Pathumsoot, and Areeya Chantasri. "Estimating unknown qubit phase under telegraph noises using recurrent neural network." Journal of Physics: Conference Series 2431, no. 1 (January 1, 2023): 012103. http://dx.doi.org/10.1088/1742-6596/2431/1/012103.

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Abstract We consider a system of qubits affected by an environmental random-telegraph process (RTP) noise and investigate the recently proposed idea of using a spectator qubit (SQ) as a noise probe to remove noise effects from a data qubit (DQ). By measuring the SQ at various times with particular measurement bases, their measurement readouts can be used to extract the information of the noise effects. In this work, we propose the use of recurrent neural network (RNN), with the Long short-term memory (LSTM) layers, to process the SQ’s readouts and train the model to estimate the errors occurred in the DQ. We present numerical results of the DQ’s and SQ’s phases and show that the LSTM can estimate the unknown DQ’s phase with the estimation accuracy depending on the SQ’s noise sensitivity.

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35

Bouassem, Karim, El Mahfoud El Bouatmani, Abdellatif El Assoudi, and El Hassane El Yaagoubi. "State and Unknown Input Simultaneous Estimation for a Class of Discrete-Time Linear Implicit Models : A Heat Exchanger Pilot Process Application." E3S Web of Conferences 297 (2021): 01011. http://dx.doi.org/10.1051/e3sconf/202129701011.

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In this paper, the design problem of simultaneous estimation of unmeasurable states and unknown inputs (UIs) is investigated for a class of discrete-time linear implicit models (DLIMs). The UIs affect both state and output of the system. The approach is based on the separation between dynamic and static relations in the considered DLDM. First, the method permitting to separate dynamic equations from static equations is exposed. Next, an augmented explicit model which contains the dynamic equations and the UIs is constructed. Then an unknown inputs observer (UIO) design in explicit structure is developed. The exponential convergence of the state estimation error is studied by using the Lyapunov theory and the stability condition is given in term of linear matrix inequality (LMI). Finally, an illustrative application of a heat exchanger pilot process is given to show the good performances of the proposed method.

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36

Villaverde, Alejandro F., Nikolaos Tsiantis, and Julio R. Banga. "Full observability and estimation of unknown inputs, states and parameters of nonlinear biological models." Journal of The Royal Society Interface 16, no. 156 (July 2019): 20190043. http://dx.doi.org/10.1098/rsif.2019.0043.

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In this paper, we address the system identification problem in the context of biological modelling. We present and demonstrate a methodology for (i) assessing the possibility of inferring the unknown quantities in a dynamic model and (ii) effectively estimating them from output data. We introduce the term Full Input-State-Parameter Observability (FISPO) analysis to refer to the simultaneous assessment of state, input and parameter observability (note that parameter observability is also known as identifiability). This type of analysis has often remained elusive in the presence of unmeasured inputs. The method proposed in this paper can be applied to a general class of nonlinear ordinary differential equations models. We apply this approach to three models from the recent literature. First, we determine whether it is theoretically possible to infer the states, parameters and inputs, taking only the model equations into account. When this analysis detects deficiencies, we reformulate the model to make it fully observable. Then we move to numerical scenarios and apply an optimization-based technique to estimate the states, parameters and inputs. The results demonstrate the feasibility of an integrated strategy for (i) analysing the theoretical possibility of determining the states, parameters and inputs to a system and (ii) solving the practical problem of actually estimating their values.

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37

Safaei, Ali, and Muhammad Nasiruddin Mahyuddin. "Distributed adaptive model-free cooperative control for a network of generic unknown nonlinear systems." International Journal of Advanced Robotic Systems 15, no. 5 (September 1, 2018): 172988141880148. http://dx.doi.org/10.1177/1729881418801481.

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In this article, a distributed model-free consensus control is proposed for a network of nonlinear agents with unknown nonlinear dynamics, unknown process disturbances, and white noise measurement disturbances. Here, the purpose of the control protocol is to first synchronize the states of all follower agents in the network to a leader and then track a reference trajectory in the state space. The leader has at least one information connection with one of the follower agents in the network. The design procedure includes adaptive laws for estimating the unknown linear and nonlinear terms of each agent’s dynamics. The salient feature of the proposed control scheme is that each agent’s estimation is a model-free adaptive law, that is, the need for regressor or linear-in-parameter basis is alleviated. In addition, without requiring direct connection to the leader, the leader’s control input can still be reconstructed by virtue of a robust observer which can be defined in a distributed manner in the network. The entire design procedure is analyzed successfully for the stability using Lyapunov stability theorem. In addition, it is shown that the proposed distributed controller includes an optimal term. Besides, a modified Kalman filter is added to eliminate the measurement noise. Finally, the simulation results on three networks of unknown nonlinear systems are presented. Moreover, a comparative study is presented to evaluate the proposed algorithm against a model-based cooperative control algorithm.

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38

Zang, Qing-Pei, and Li-Xin Zhang. "A general lower bound of parameter estimation for reflected Ornstein–Uhlenbeck processes." Journal of Applied Probability 53, no. 1 (March 2016): 22–32. http://dx.doi.org/10.1017/jpr.2015.5.

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AbstractA reflected Ornstein–Uhlenbeck process is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. It is an extended model of the traditional Ornstein–Uhlenbeck process being extensively used in finance as a one-factor short-term interest rate model. Under some mild conditions, this paper is devoted to the study of the analogue of the Cramer–Rao lower bound of a general class of parameter estimation of the unknown parameter in reflected Ornstein–Uhlenbeck processes.

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39

Yu, Ming, Haotian Lu, Hai Wang, Chenyu Xiao, Dun Lan, and Junjie Chen. "Computational Intelligence-Based Prognosis for Hybrid Mechatronic System Using Improved Wiener Process." Actuators 10, no. 9 (August 30, 2021): 213. http://dx.doi.org/10.3390/act10090213.

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In this article, a fast krill herd algorithm is developed for prognosis of hybrid mechatronic system using the improved Wiener degradation process. First, the diagnostic hybrid bond graph is used to model the hybrid mechatronic system and derive global analytical redundancy relations. Based on the global analytical redundancy relations, the fault signature matrix and mode change signature matrix for fault and mode change isolation can be obtained. Second, in order to determine the true faults from the suspected fault candidates after fault isolation, a fault estimation method based on adaptive square root cubature Kalman filter is proposed when the noise distributions are unknown. Then, the improved Wiener process incorporating nonlinear term is developed to build the degradation model of incipient fault based on the fault estimation results. For prognosis, the fast krill herd algorithm is proposed to estimate unknown degradation model coefficients. After that, the probability density function of remaining useful life is derived using the identified degradation model. Finally, the proposed methods are validated by simulations.

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40

Wartenberg, Constanze, and Per Wiborg. "Precision of Exocentric Distance Judgments in Desktop and Cube Presentation." Presence: Teleoperators and Virtual Environments 12, no. 2 (April 2003): 196–206. http://dx.doi.org/10.1162/105474603321640941.

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Accuracy of space perception and distance estimation in virtual environments is an important precondition for the reliable use of virtual techniques in the design of products, workplaces, architecture, and production systems. The present study compares the accuracy of exocentric 1 distance estimations that a static perceiver achieves with two virtual presentation techniques: a desktop and an immersive cube presentation. Estimation accuracy in a physical mock-up is used as a point of reference. Subjects estimated exocentric distances in detailed models of a workplace previously unknown to them. All distances to be judged were located in the subjects' personal space (less than 1.5 m from the subject). Major differences between the two virtual presentation modes are that stereo information is available in the cube but not in desktop environment, and that, in the cube, changes in perspective are achieved by actually moving inside the cube instead of using a mouse. Furthermore, the cube provides a wider absolute field of view than the desktop environment. The experiment showed advantages of the cube over desktop presentation when estimating exocentric distances in “personal space” from a static position. The magnitude of distance estimation errors was significantly higher in the desktop than in the cube environment. However, estimation errors tended to be overestimations in the cube presentation, whereas over- and underestimation occurred with equal frequency in the desktop environment. In the discussion it is argued that the higher estimation accuracy in the cube environment may mainly be due to the availability of stereoscopic depth cues. According to Cutting (1997), these cues are especially relevant for spatial perception in “personal space.” 1 The term exocentric distance is used for distances between two points external to the perceiver indicating (for example) interobject distances or distances colinear with the side length of an object. These distances are to be distinguished from egocentric distances, those distances between the perceiver and one point in the environment (Waller, 1999).

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41

Merhi Bleik, Josephine. "Fully Bayesian Estimation of Simultaneous Regression Quantiles under Asymmetric Laplace Distribution Specification." Journal of Probability and Statistics 2019 (June 2, 2019): 1–12. http://dx.doi.org/10.1155/2019/8610723.

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In this paper, we are interested in estimating several quantiles simultaneously in a regression context via the Bayesian approach. Assuming that the error term has an asymmetric Laplace distribution and using the relation between two distinct quantiles of this distribution, we propose a simple fully Bayesian method that satisfies the noncrossing property of quantiles. For implementation, we use Metropolis-Hastings within Gibbs algorithm to sample unknown parameters from their full conditional distribution. The performance and the competitiveness of the underlying method with other alternatives are shown in simulated examples.

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42

Cho, Hong-Yeon, Gi-Seop Lee, and Uk-Jae Lee. "Long-gap Filling Method for the Coastal Monitoring Data." Journal of Korean Society of Coastal and Ocean Engineers 33, no. 6 (December 31, 2021): 333–44. http://dx.doi.org/10.9765/kscoe.2021.33.6.333.

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Technique for the long-gap filling that occur frequently in ocean monitoring data is developed. The method estimates the unknown values of the long-gap by the summation of the estimated trend and selected residual components of the given missing intervals. The method was used to impute the data of the long-term missing interval of about 1 month, such as temperature and water temperature of the Ulleungdo ocean buoy data. The imputed data showed differences depending on the monitoring parameters, but it was found that the variation pattern was appropriately reproduced. Although this method causes bias and variance errors due to trend and residual components estimation, it was found that the bias error of statistical measure estimation due to long-term missing is greatly reduced. The mean, and the 90% confidence intervals of the gap-filling model’s RMS errors are 0.93 and 0.35~1.95, respectively.

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43

Tong, Qiang, Hui Xie, Kang Song, and Dong Zou. "A Control-Oriented Engine Torque Online Estimation Approach for Gasoline Engines Based on In-Cycle Crankshaft Speed Dynamics." Energies 12, no. 24 (December 9, 2019): 4683. http://dx.doi.org/10.3390/en12244683.

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Engine brake torque is a key feedback variable for the optimal torque split control of an engine–motor hybrid powertrain system. Due to the limitations in available sensors, however, engine torque is difficult to measure directly. For torque estimation, the unknown external load torque and the overlap of the expansion stroke between cylinders introduce a great disturbance to engine speed dynamics. This makes the conventional cycle average engine speed-based estimation approach unusable. In this article, an in-cycle crankshaft speed-based indicated torque estimation approach is proposed for a four-cylinder engine. First, a unique crankshaft angle window is selected for load torque estimation without the influence of combustion torque. Then, an in-cycle angle-domain crankshaft speed dynamic model is developed for engine indicated torque estimation. To account for the effects of model inaccuracy and unknown external disturbances, a “total disturbance” term is introduced. The total disturbance is then estimated by an adaptive observer using the engine’s historical operating data. Finally, a real-time correction method for the friction torque is proposed in the fuel cut-off scenario. Combining the aforementioned torque estimators, the brake torque can be obtained. The proposed algorithm is implemented in an in-house developed multi-core engine control unit (ECU). Experimental validation results on an engine test bench show that the algorithm’s execution time is about 3.2 ms, and the estimation error of the brake torque is within 5%. Therefore, the proposed method is a promising way to accurately estimate engine torque in real-time.

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44

Im, Sung Jin, Jong Seok Oh, and Gi-Woo Kim. "Simultaneous Estimation of Unknown Road Roughness Input and Tire Normal Forces Based on a Long Short-Term Memory Model." IEEE Access 10 (2022): 16655–69. http://dx.doi.org/10.1109/access.2022.3149527.

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45

Biondini, Riccardo, Yan-Xia Lin, and Sifa Mvoi. "A practical procedure for estimation of linear models via asymptotic quasi-likelihood." Journal of Applied Mathematics and Decision Sciences 3, no. 1 (January 1, 1999): 21–39. http://dx.doi.org/10.1155/s1173912699000024.

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This paper is concerned with the application of an asymptotic quasi-likelihood practical procedure to estimate the unknown parameters in linear stochastic models of the form yt=ft(θ)+Mt(θ)(t=1,2,..,T) , where ft is a linear predictable process of θ and Mt is an error term such that E(Mt|Ft−1)=0 and E(Mt2|Ft−1)<∞ and F is a σ-field generated from{ys}s≤t . For this model, to estimate the parameter θ∈Θ, the ordinary least squares method is usually inappropriate (if there is only one observable path of {yt} and if E(Mt2|Ft−1) is not a constant) and the maximum likelihood method either does not exist or is mathematically intractable. If the finite dimensional distribution of Mt is unknown, to obtain a good estimate of θ an appropriate predictable process gt should be determined. In this paper, criteria for determining gt are introduced which, if satisfied, provide more accurate estimates of the parameters via the asymptotic quasi-likelihood method.

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46

Tichý, Ondřej, Lukáš Ulrych, Václav Šmídl, Nikolaos Evangeliou, and Andreas Stohl. "On the tuning of atmospheric inverse methods: comparisons with the European Tracer Experiment (ETEX) and Chernobyl datasets using the atmospheric transport model FLEXPART." Geoscientific Model Development 13, no. 12 (December 1, 2020): 5917–34. http://dx.doi.org/10.5194/gmd-13-5917-2020.

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Abstract. Estimation of the temporal profile of an atmospheric release, also called the source term, is an important problem in environmental sciences. The problem can be formalized as a linear inverse problem wherein the unknown source term is optimized to minimize the difference between the measurements and the corresponding model predictions. The problem is typically ill-posed due to low sensor coverage of a release and due to uncertainties, e.g., in measurements or atmospheric transport modeling; hence, all state-of-the-art methods are based on some form of regularization of the problem using additional information. We consider two kinds of additional information: the prior source term, also known as the first guess, and regularization parameters for the shape of the source term. While the first guess is based on information independent of the measurements, such as the physics of the potential release or previous estimations, the regularization parameters are often selected by the designers of the optimization procedure. In this paper, we provide a sensitivity study of two inverse methodologies on the choice of the prior source term and regularization parameters of the methods. The sensitivity is studied in two cases: data from the European Tracer Experiment (ETEX) using FLEXPART v8.1 and the caesium-134 and caesium-137 dataset from the Chernobyl accident using FLEXPART v10.3.

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47

Hung, Yu-Heng, and Ping-Chun Hsieh. "Reward-Biased Maximum Likelihood Estimation for Neural Contextual Bandits: A Distributional Learning Perspective." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 7 (June 26, 2023): 7944–52. http://dx.doi.org/10.1609/aaai.v37i7.25961.

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Reward-biased maximum likelihood estimation (RBMLE) is a classic principle in the adaptive control literature for tackling explore-exploit trade-offs. This paper studies the neural contextual bandit problem from a distributional perspective and proposes NeuralRBMLE, which leverages the likelihood of surrogate parametric distributions to learn the unknown reward distributions and thereafter adapts the RBMLE principle to achieve efficient exploration by properly adding a reward-bias term. NeuralRBMLE leverages the representation power of neural networks and directly encodes exploratory behavior in the parameter space, without constructing confidence intervals of the estimated rewards. We propose two variants of NeuralRBMLE algorithms: The first variant directly obtains the RBMLE estimator by gradient ascent, and the second variant simplifies RBMLE to a simple index policy through an approximation. We show that both algorithms achieve order-optimality. Through extensive experiments, we demonstrate that the NeuralRBMLE algorithms achieve comparable or better empirical regrets than the state-of-the-art methods on real-world datasets with non-linear reward functions.

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48

Kim, Yoon-Tae, and Hyun-Suk Park. "An Edgeworth Expansion for the Ratio of Two Functionals of Gaussian Fields and Optimal Berry–Esseen Bounds." Mathematics 9, no. 18 (September 10, 2021): 2223. http://dx.doi.org/10.3390/math9182223.

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This paper is concerned with the rate of convergence of the distribution of the sequence {Fn/Gn}, where Fn and Gn are each functionals of infinite-dimensional Gaussian fields. This form very frequently appears in the estimation problem of parameters occurring in Stochastic Differential Equations (SDEs) and Stochastic Partial Differential Equations (SPDEs). We develop a new technique to compute the exact rate of convergence on the Kolmogorov distance for the normal approximation of Fn/Gn. As a tool for our work, an Edgeworth expansion for the distribution of Fn/Gn, with an explicitly expressed remainder, will be developed, and this remainder term will be controlled to obtain an optimal bound. As an application, we provide an optimal Berry–Esseen bound of the Maximum Likelihood Estimator (MLE) of an unknown parameter appearing in SDEs and SPDEs.

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49

Tichý, Ondřej, Václav Šmídl, Radek Hofman, and Andreas Stohl. "LS-APC v1.0: a tuning-free method for the linear inverse problem and its application to source-term determination." Geoscientific Model Development 9, no. 11 (November 25, 2016): 4297–311. http://dx.doi.org/10.5194/gmd-9-4297-2016.

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Abstract. Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. It is typically formalized as an inverse problem using a linear model that can explain observable quantities (e.g., concentrations or deposition values) as a product of the source-receptor sensitivity (SRS) matrix obtained from an atmospheric transport model multiplied by the unknown source-term vector. Since this problem is typically ill-posed, current state-of-the-art methods are based on regularization of the problem and solution of a formulated optimization problem. This procedure depends on manual settings of uncertainties that are often very poorly quantified, effectively making them tuning parameters. We formulate a probabilistic model, that has the same maximum likelihood solution as the conventional method using pre-specified uncertainties. Replacement of the maximum likelihood solution by full Bayesian estimation also allows estimation of all tuning parameters from the measurements. The estimation procedure is based on the variational Bayes approximation which is evaluated by an iterative algorithm. The resulting method is thus very similar to the conventional approach, but with the possibility to also estimate all tuning parameters from the observations. The proposed algorithm is tested and compared with the standard methods on data from the European Tracer Experiment (ETEX) where advantages of the new method are demonstrated. A MATLAB implementation of the proposed algorithm is available for download.

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50

Chen, Jie-Wen, and Yan Wang. "Parameter-estimation Biases for Eccentric Supermassive Binary Black Holes in Pulsar Timing Arrays: Biases Caused by Ignored Pulsar Terms." Astrophysical Journal 929, no. 2 (April 1, 2022): 168. http://dx.doi.org/10.3847/1538-4357/ac5bd4.

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Abstract The continuous nanohertz gravitational waves (GWs) from individual supermassive binary black holes (SMBBHs) can be encoded in the timing residuals of pulsar timing arrays (PTAs). For each pulsar, the residuals actually contain an Earth term and a pulsar term, but usually only the Earth term is considered as a signal and the pulsar term is dropped. This leads to parameter-estimation biases (PEBs) for the SMBBHs, and currently there are no convenient evaluations of the PEBs. In this article, we formulate the PEBs for a SMBBH with an eccentric orbit. In our analyses, the unknown phases of pulsar terms are treated as random variables obeying the uniform distribution U[0, 2π), due to the fact that pulsar distances are generally poorly measured. Our analytical results are in accordance with the numerical work by Zhu et al. at 1.5σ level, which implies that our formulae are effective in estimating magnitudes of the PEBs. Additionally, we find that the biases Δφ E and Δe/e for two parameters—that is, Earth-term phase φ E and orbital eccentricity e—monotonically decrease as e increases, which partly confirms a hypothesis in our previous work. Furthermore, we also calculate the PEBs caused by the recently observed common-spectrum process (CSP). We find that if the strain amplitude of the continuous GW is significantly stronger (three times larger, in our cases) than the stochastic GW background, then the PEBs from pulsar terms are larger than those from the CSP. Our formulae of the PEBs can be conveniently applied in the future PTA data analyses.

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