Synchronization of the vector state estimation methods with unmeasurable coordinates for intelligent water quality monitoring systems in the river

Abstract

One of the main problems of signal processing is the issue of estimation, which consists in reproducing a useful signal on the basis of another one, e.g. one burdened with unwanted interference. The use of classical filtering to eliminate disturbances carries the risk of removing an important part of the information about the useful signal. In order to avoid this phenomenon, optimal filters are used, utilizing the statistical properties of signals. Such a case of consideration concerns the issue of estimation for stochastic systems. An example is the Kalman filter in which the main aspect of research is the differential equation of the state estimate in which there is an amplification factor dependent on the covariance matrix of the estimation error. The value of this factor is determined from the non-linear Riccati differential equation, depending on the characteristics of signals affecting the object under investigation and the measurement. The paper proposes an adaptive algorithm to determine the value of the filter amplification factor which allows to avoid the inconveniences resulting from the need to estimate the characteristics of signals affecting the object under investigation. The presented approach to estimation issues does not require the need to characterize random signals due to the application of the adaptive method of state estimation. The analyzed process refers to an object described by ordinary differential equations with continuous measurements representing the state of pollution of the river using the so-called interpretation “along the characteristics”. The method used in the module of the intelligent analytical system allows for quick determination of hard-to-measure parameters of the quality of water in the river and to react to upcoming ecological threats without any delays dangerous for the system.