scholarly journals Nonlinear Split-Plot Design Model in Parameters Estimation using Estimated Generalized Least Square - Maximum Likelihood Estimation

2018 ◽  
Vol 9 (2) ◽  
pp. 65
Author(s):  
Ikwuoche John David ◽  
Osebekwin Ebenenzer Asiribo ◽  
Hussain Garba Dikko
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Variance Components ◽  
Likelihood Estimation ◽  
Parameters Estimation ◽  
Least Square ◽  
Design Model ◽  
Mixed Effect ◽  
Split Plot ◽  
Plot Design

This research aimed to provide a theoretical framework for intrinsically nonlinear models with two additive error terms. To achieve this, an iterative Gauss-Newton via Taylor Series expansion procedures for Estimated Generalized Least Square (EGLS) technique was adopted. This technique was applied in estimating the parameters of an intrinsically nonlinear split-plot design model where the variance components were unknown. The unknown variance components were estimated via Maximum Likelihood Estimation (MLE) method. To achieve the numerical stability in the iterative process of estimating the parameters, Householder QR decomposition was used. The results show that EGLS method presented in this research is available and applicable to estimate linear fixed, random, and mixed-effect models. However, in practical situations, the functional form of the mean in the model is often nonlinear due to the dynamics involved in the system process.

scholarly journals Calibration of MEMS Triaxial Accelerometers Based on the Maximum Likelihood Estimation Method

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yifan Sun ◽  
Xiang Xu
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Random Noise ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Least Square ◽  
Triaxial Accelerometer ◽  
Zero Bias ◽  
Estimation Function ◽  
Maximum Likelihood Estimation Method

As a widely used inertial device, a MEMS triaxial accelerometer has zero-bias error, nonorthogonal error, and scale-factor error due to technical defects. Raw readings without calibration might seriously affect the accuracy of inertial navigation system. Therefore, it is necessary to conduct calibration processing before using a MEMS triaxial accelerometer. This paper presents a MEMS triaxial accelerometer calibration method based on the maximum likelihood estimation method. The error of the MEMS triaxial accelerometer comes into question, and the optimal estimation function is established. The calibration parameters are obtained by the Newton iteration method, which is more efficient and accurate. Compared with the least square method, which estimates the parameters of the suboptimal estimation function established under the condition of assuming that the mean of the random noise is zero, the parameters calibrated by the maximum likelihood estimation method are more accurate and stable. Moreover, the proposed method has low computation, which is more functional. Simulation and experimental results using the consumer low-cost MEMS triaxial accelerometer are presented to support the abovementioned superiorities of the maximum likelihood estimation method. The proposed method has the potential to be applied to other triaxial inertial sensors.

scholarly journals On estimation in multilevel models with block circular symmetric covariance structure

2012 ◽  
Vol 16 (1) ◽  
pp. 83-96
Author(s):  
Yuli Liang ◽  
Dietrich von Rosen ◽  
Tatjana von Rosen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Parameter Space ◽  
Variance Components ◽  
Multilevel Model ◽  
Multilevel Models ◽  
Covariance Structure ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation

In this article we consider a multilevel model with block circular symmetric covariance structure. Maximum likelihood estimation of the parameters of this model is discussed. We show that explicit maximum likelihood estimators of variance components exist under certain restrictions on the parameter space.

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