scholarly journals A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 541 ◽  
Author(s):  
Patricia Román-Román ◽  
Juan José Serrano-Pérez ◽  
Francisco Torres-Ruiz
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Inflection Point ◽  
Random Noise ◽  
Likelihood Estimation ◽  
Gompertz Model ◽  
Type Pattern ◽  
Polynomial Term ◽  
Mean Function ◽  
Selection Of

The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is introduced whose mean function is a curve of this type, concretely a transformation of the well-known Gompertz model after introducing in its expression a polynomial term. The maximum likelihood estimation of the parameters of the model is studied, and various criteria are provided for the selection of the degree of the polynomial when real situations are addressed. Finally, some simulated examples are presented.

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.

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