About parametric identification algorithms of discrete-continuous processes

Researches presented in the paper are devoted to parametric modelling of multidimensional processes of discrete- continuous type in the condition of priori information lack. Similar processes occur in the space industry, for example, in the manufacture of products based on electronic components. The article considers multidimensional processes with unknown mathematical description. Using parametric approach, we choose the structure of investigated process with the accuracy to within parameters, and the next step is to estimate the model parameters from the available sample of observations of the process input and output variables. The paper examines the case when due to the lack of priori knowledge about the object an error is allowed at the stage of parametric structure choosing. The relative approxima- tion error is used to estimate the model accuracy, which shows the difference between model and object outputs. A comparative analysis of several parametric models for one investigated object is carried out is. Using the method of least squares we obtain estimates of the parameters. The paper presents the results of a series of computational experiments illustrating the dependence of the modelling error on the object noise level, as well as on the sample size of observations of the input and output variables. One of the obvious parametric models advantages is the ease of its applying. However, if the dimension of the input variables vector is high, the process has a complex structure, and there is no priori information about the object structure, then it is difficult to use parametric methods. In this case, it is advisable to use nonparametric identification methods. In this paper we use a nonparametric estimation of the regression function on observations of Nadaraya-Watson as an estimate of the process output variable. However, such estimates require a large number of initial data, also they are sensitive to various kinds of defects in the initial samples of observations. Besides that, the paper compares nonpara- metric model with parametric one for the investigated process.