The recursive stochastic algorithms for estimating the parameters of linear discrete-time dynamic systems in the presence of disturbance uncertainty has been considered in the paper. Problems related to the construction of min-max optimal recursive algorithms are demonstrated. In addition, the robustness of the proposed algorithms has been addressed. Since the min-max optimal solution cannot be achieved in practice, an approximate optimal solution based on a recursive stochastic Newton-Raphson type procedure is suggested. The convergence of the proposed practically applicable robustified recursive algorithm is established theoretically using the martingale theory. Both theoretical and experimental analysis related to the practical robustness of the proposed algorithm are also included.
Pedagogical conceptualisation of content knowledge is a significant component of the present time teaching of ESP at higher institutions, because usually the lessons in general English are not sufficient for a successful accomplishment of the teaching process assignments and learning process outcomes. In the case of art music related ESP, it is necessary, at the teacher’s side, to have a certain amount of content knowledge in the field of art music in order to be able to find and prepare the appropriate lesson materials and organise the entire teaching process, so that the knowledge is conceptualised and properly used for English language teaching and learning. Such knowledge and its pedagogical conceptualisation will be the central topics of the paper, preceded by some introductory facts on art music and texts on art music, pedagogical content knowledge and the art music related ESP.
Abstract-Kalman filter is an optimal filtering solution in certain cases, however, it is more often than not, regarded as a non-robust filter. The slight mismatch in noise statistics or process model may lead to large performance deterioration and the loss of optimality. This research paper proposes an alternative method for robust adaptive filtering concerning lack of information of noise statistics. The method is based on the application of recurrent neural networks trained by a dynamic identity observer. The method is explained in details and tested in the case analysis of object tracking model. Performance evaluation is made for cases of the standard Kalman filter, a noise-adaptive Kalman filter, the adaptive filter with a recurrent neural network trained by a static identity observer, and the adaptive filter with recurrent neural network trained by a dynamic identity observer. The results for different noise statistics as well as noise statistics mismatches are compared and presented. It is shown that in cases with a lack of knowledge of the noise statistics it is beneficial to use the filtering method proposed in this research work.
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