Estimating unknown probability density functions for random parameters of stochastic ARMAX systems

Abstract

Different from existing parameter estimation algorithms where the values of parameters are required to be estimated, this paper presents a new method to estimate the unknown probability density functions of random parameters for non-Gaussian dynamic stochastic systems. The System is represted by an ARMAX model, where the parameters and the system noise term are random processes that are characterized by their unknown probability density functions. Under the assumption that each random parameter and the noise term are independent and are identically distributed sequece, a simple mathematical relationship is established between the measured output probability density function of the system and the unknown probability density functions of the random parameters and noise term. The mement generating function in probability theory has been used to transfer the multiple convolution integration into a simple algebraic operation. An identification algorithm is then established that estimates these unknown probability density functions of the parameters and the noise term by using the measured output probability density functions and the system input.