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This paper presents the novel estimation algorithm that generates all signals of an object described by nonlinear ordinary differential equations based only on easy-to-implement measurements. Unmeasured signals are estimated by using an adaptive approach. For this purpose, a filtering equation with a continuously modified gain vector is used. Its value is determined by an incremental method, and the amount of correction depends on the current difference between the generated signal and its measured counterpart. In addition, the study takes into account the aging process of measurements and their random absence. The application of the proposed approach can be realized for any objects with a suitable mathematical description. A biochemically polluted river with an appropriate transformation of the notation of partial differential equations was chosen as an object. The results of numerical experiments are promising, and the process of obtaining them involves little computational necessity, so the approach is aimed at the needs of control implemented online.
Kwater et al. (Tue,) studied this question.