Identification of the cylindrical model of the quasi-periodic process

The dynamics of objects in many practical situations has a quasi-periodic character - the presence of noticeable periodicity with random variations of quasi-periods. For example, the noise and vibration of an aircraft engine, hydraulic unit, seasonal and daily variations in atmospheric temperature, etc. The arising tasks of monitoring (assessing the state of an object and its forecast) require the specification of a model of such a process and its identification for a specific object based on the results of its observations. In this paper, an auto-regression model is used to represent a quasi-periodic process in the form of a spiral scan of a cylindrical image. The choice of the values of a small number of parameters of this model makes it possible to describe and simulate a wide class of quasi-periodic processes. The problem of identifying a model, that is, determining the values of its parameters, for which it corresponds to a real, best observed process in a certain sense, is considered. This problem is solved using a pseudogradient adaptive procedure, the advantage of which is its operation in real time with low computational costs. In addition, this procedure makes it possible to identify the model when processing non-stationary processes, that is, to estimate the changing parameters of the model.