Mathematical Models for Tilt Measurement with a Triaxial Accelerometer

The construction of tilt parameters transducers, the types of primary sensors used, and the angles of spatial orientation that are determined are discussed. The various types of accelerometric sensors that are commonly employed in these transducers are explored. The mathematical models that are used in accelerometer-based three-axis tilt parameters transducers are obtained. These models will help us to understand the sources of instrumental errors that may affect the accuracy of the measured signals. Using these mathematical models, it is possible to implement software and algorithmic methods to correct these errors. This correction process leads to a higher level of accuracy in determining the desired spatial orientation parameters, specifically the zenith angle
$\theta$
and roll angle
$\boldsymbol{\varphi}$
, for both stationary and moving objects.