Dynamic-transmission-based recursive filtering algorithm for microseismic event detection under sensor saturations

Abstract

This paper is dedicated to dealing with the recursive filtering problem for a class of microseismic signal arrival time picking with dynamic transmission mechanism (DTM) and sensor saturation (SS). Firstly, the microseismic wave and its environmental noise are established as an exponentially decaying cyclic wave and a Markov process, respectively, and then the state space expression of the microseismic system is exhibited. Next, the phenomenon of the SS is taken into account to describe the practical microseismic system. Simultaneously, the DTM is introduced to avoid the waste of communication resources and energy, where more valuable measurements are transmitted to the remote filter. The purpose of this paper is to design a filter such that the arrival time of P wave and S wave (ATPSW) of microseismic signals is picked automatically in consideration of the SS and the DTM, and an upper bound of the filtering error covariance matrix is optimized by the designed filter gain at each time instant. Subsequently, a sufficient condition is given to ensure that the filtering error is exponential bounded in the sense of mean square. Finally, the effectiveness of the proposed algorithm is illustrated by a simulation experiment.