Chaotic Behaviour in Geodetic Sensors and Fractal Characteristics of Sensor Noise

Abstract

Fractal geometry and chaos theory have captured the attention and interest of researchers in various fields of science and engineering. The main reason is that fractals and chaos offer scientists a rich environment for exploring and modelling the complexity of nature. In geodesy, initial research in this field has treated problems in earth surface representation and fractal potential theory. The main purpose of this paper is to show some possible applications to dynamic systems used in geodesy. First, basic concepts of fractals and chaos are briefly introduced. Then, computer simulations for a single axis gyroscopic system are performed, which show chaotic system behaviour in certain regions. Third, the short-term sensor noise of a ring-laser gyro strapdown INS is investigated using generalized Brownian motion. This investigation strongly indicates that such INS sensor errors consist of periodic components caused by dithering and fractional differential noise. A possible explanation for the presence of such noise concludes the paper.