This paper treats a special topic of Bayesian filteringbased modeling concerning the analysis of the estimation process. The analysis involves the graphical representation of the estimation process. New concepts like the uncertainty range and the convergence point are defined from the graphical visualization of the estimation process. The paper structure consists of the following parts: an introduction where the principles of modeling are presented, the description of the analysis, two cases studies with simulations, and conclusions.
I INTRODUCTIONModeling deals with postulating assumptions how realworld behaves. One may refine indefinitely the model but the difference between the model and the real-world phenomenon, process or dynamical system which is subject to modeling cannot be avoided [1][2][3]. Increasing the quality of the models has been one of the favorite directions during the last years. This involves the exponential growth of artificial intelligence techniques in modeling such as fuzzy logic [4,5], neural networks [6], genetic algorithms [7,8], data mining [9,10], etc., and their merge resulting in hybrid models [11][12][13][14][15].Another modeling direction concerns the measuring of the approximation capability of models. More precisely not only the behavior of the system modeled is calculated but also the degree of truth associated with the prediction ensured by the model. This approach is a merge between the traditional modeling and the Bayesian plausible reasoning rules [16] referred in [17]. If one is able to associate degree of truth (plausibility) for the results corresponding to the model, then a decision can be taken emphasizing whether the results are either suitable or they become discordant [18]. In addition, it will be possible to increase in the appropriate moment the plausibility of the model in terms of observations. Nevertheless, the possibility to choose the appropriate time of observation and the need of measuring the plausibility of the observation considered are pointed out. In the framework of this second direction a set of rules, referred to as plausible reasoning rules, has been proposed in [19]. The proof has been done on the basis of the probability theory.Models which combine the plausible reasoning with traditional modeling have been proposed in [20]. It is important to highlight the practical aspects of this approach because the authors have constructed models based on Bayesian filtering. The models are implemented in real-time systems and emphasize a plausible reasoning problem construction. The structure of such a construction is important and it consists of two levels, the problem description and the question. The first level contains also two parts, the model specification and the parameter identifications. The main drawback of this construction is its computational cost. However the structure of the problem construction is suitable for a plausible reasoning expert but it is difficult for an engineer who is usually familiar only with traditional modeling. The aim of ...
