摘要
The central limit theorem guarantees the distribution of the measurand is Gaussian when the number of repeated measurement is infinity, but in many practical cases, the number of measurement times is limited to a given number. To overcome this contradiction, this paper firstly carries out the maximum likelihood estimation for parameter q in qGaussian density model developed under the maximum Tsallis entropy principle. Then the q-Gaussian probability density function is used in the particle filter to estimate and measure the nonlinear system. The estimated parameter q is related to the ratio between the measurement variance and the given variance, which indicates that the measurement accuracy cannot be improved if we only increase the repeated measurement times. Via using the proposed q-Gaussian density model,the measurement error(the average mean square error)of the estimation results can be reduced to a considerable level where the number of repeated measurement is limited. The experimental example is given to verify the proposed model and the measurement results prove the correctness and effectiveness of it.
The central limit theorem guarantees the distribution of the measurand is Gaussian when the number of repeated measurement is infinity, but in many practical cases, the number of measurement times is limited to a given number. To overcome this contradiction, this paper firstly carries out the maximum likelihood estimation for parameter q in qGaussian density model developed under the maximum Tsallis entropy principle. Then the q-Gaussian probability density function is used in the particle filter to estimate and measure the nonlinear system. The estimated parameter q is related to the ratio between the measurement variance and the given variance, which indicates that the measurement accuracy cannot be improved if we only increase the repeated measurement times. Via using the proposed q-Gaussian density model,the measurement error(the average mean square error)of the estimation results can be reduced to a considerable level where the number of repeated measurement is limited. The experimental example is given to verify the proposed model and the measurement results prove the correctness and effectiveness of it.
基金
supported by the National Natural Science Foundation of China under Grant No.60871056 and No.61371049
the specialized Research Fund for the Doctoral Program of High Education of China under Grant No.20120185110013
the Fundamental Research Funds for the Central Universities under Grant No.267ZYGX2015KYQD021
Sichuan Province Applied Basis Research Project under Grant No.2013JY0058
the Key Lab Fund Project of Key Laboratory of Fluid and Power Machinery of Ministry of Education under Grant No.SZJJ2012-042