High Accurate Mathematical Tools to Estimate the Gravity Direction Using Two Non-Orthogonal Inclinometers

Abstract

This study provides two mathematical tools to best estimate the gravity direction when using a pair of non-orthogonal inclinometers whose measurements are affected by zero-mean Gaussian errors. These tools consist of: (1) the analytical derivation of the gravity direction expectation and its covariance matrix, and (2) a continuous description of the geoid model correction as a linear combination of a set of orthogonal surfaces. The accuracy of the statistical quantities is validated by extensive Monte Carlo tests and the application in an Extended Kalman Filter (EKF) has been included. The continuous geoid description is needed as the geoid represents the true gravity direction. These tools can be implemented in any problem requiring high-precision estimates of the local gravity direction.

A Return to the Sextant—Maritime Navigation Using Celestial Bodies and the Horizon

“…In addition, atmospheric deflection is a known function of the star elevation over the local horizon, and the local horizon can always be computed by two orthogonal inclinometers, as suggested in Ref. [ 14 ].…”

“…It is considered that the proposed techniques in this work cannot operate in those conditions. However, the suggested technique of using two inclinometers in association may help [ 14 ].…”

“…The paper might be treated as a sequel to [ 14 ], which considers the terrestrial celestial navigation problem using a pair of two orthogonal inclinometers instead of a horizon sensor. Even though the horizon is less available than the Earth’s gravity, it is not affected by the motion of the ship, which may even occur while stationary by the roll of ocean waves.…”