A precise estimation method of probability distribution based on roughly observed data with quantized level and its application to environmental sound noise measurement

The noise fluctuation is very often measured in a quantized level form at a discrete time interval. By paying attention to this quantization procedure of the actual noise measurement, in this paper, a precise estimation method for the probability distribution form is proposed by using the roughly observed data with quantized levels. That is, we first introduce theoretically a general statistical orthonormal expression of the probability density function for the original noise level fluctuation of continuous level type before passing through the level quantization measurement mechanism. Based on this quantization mechanism and the averaging operation of statistical information, we propose a reasonable estimation method of the distribution parameters in the above statistical expression by using the statistical information on the roughly observed data. The original probability distribution form of the continuous noise level can be precisely estimated by substituting the estimated distribution parameters into the introduced probability expression of general type. On the basis of this estimation theory, a precise evaluation method for the Lx and Leq noise evaluation indices is proposed. The effectiveness of the proposed method is confirmed experimentally too by applying it to first the simulation experiment and then the actual road traffic noise data.