Application of the Weierstrass Theorem for Sensors Signal Modelling

Abstract

Modelling of sensor signals is a key element in implementing the procedures for estimation and tracking, sensor data fusion, fault detection and diagnosis, etc. In many cases, using traditional approaches to solve this problem is impossible due to lack of prior information about the observed process or particular sensor characteristics. Starting only from the finite rate of change of the signal at the output of real sensors, the Weierstrass theorem assumes the existence of a polynomial that approximates the signal, but does not specify how to find it. The present work attempts to solve this problem by assuming that the approximating polynomial has to retain that information in the signal which would allow its Bayesian estimation. The described approach has been successfully applied to model a humidity sensor signal, but it can be used in other cases without any problem.