Tsallis Entropy Based q -Gaussian Density Model and Its Application in Measurement Accuracy Improvement

Abstract

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 q-Gaussian 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.