Fiabilitate şi Durabilitate (May 2013)
THE ASSESSMENT OF THE AMOUNT OF SOLID PARTICLES IN THE SEDIMENTARY TANKS AND THEIR EFFLUENT
Abstract
When a stochastic state space model of a given system is formulated and measurements from thesystem are obtained, the parameters are to be estimated. Even though different approaches to the estimationproblem are described in the literature (LJUNG, 1999), only the maximum likelihood method will be describedhere.The observations are considered as realizations of stochastic variables. The objective of the method is tomaximize the probability of the observations, i.e. when a maximum likelihood estimate of the parameters θ isfound, no other parameters will result in a higher probability of the observed data.In the following it is assumed that the system is observed at regular time intervals (i.e. with a constantsampling time). To simplify the notation the time is normalized with the sampling time, and thus the time indexbelongs to the set 0,1, 2, ... , N, where N is the number of observations. In general every observation is a vector.
