Optimization-based Attitude Determination in Geodetic Applications

Alexander Pesterev,Ivan Matrosov,Yury Morozov

doi:10.1515/comp-2020-0146

Alexander Pesterev, Ivan Matrosov + Show 1 more

Open Access

https://doi.org/10.1515/comp-2020-0146

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Abstract

AbstractA new approach to determining the attitude of a rigid body is suggested, which does not rely on the use of magnetometers. In the framework of this approach, the problem of determining the attitude reduces to solving a minimization problem for a function of three variables (angles characterizing the initial attitude of the body). The proposed method can be employed in precise geodetic measurements carried out with the use of a geodetic pole with a satellite antenna and an IMU installed on its top when, for some reasons, the surveyor cannot position the pole vertically (e.g., near walls or buildings). The use of the traditional approach, which relies on a compass and accelerometers, in this case does not ensure the desired accuracy of the attitude determination due to magnetic disturbances (both external ones and those induced by the receiver) affecting badly compass readings. The discussion is illustrated by results of field experiments.

Highlights

In the framework of this approach, the problem of determining the attitude reduces to solving a minimization problem for a function of three variables
The proposed method can be employed in precise geodetic measurements carried out with the use of a geodetic pole with a satellite antenna and an inertial measurement units (IMUs) installed on its top when, for some reasons, the surveyor cannot position the pole vertically
We address the problem of estimating the attitude, or orientation, of a rigid body subjected to rotational motion

Summary

Introduction

The attitude of a rigid body (device) is determined traditionally with the help of inertial measurement units (IMUs), which include gyros, accelerometers, and magnetometers (e-compass). We suggest a new approach to determining the attitude of a moving body with a fixed point that does not use accelerometers and magnetometers. When the pole is inclined, the position of the antenna can be recalculated into that of the bottom end with the help of the attitude matrix, which is usually determined by the inclinometer and compass measurements. It makes use of the accelerometer measurements to determine the initial pitch and roll angles, whereas the initial heading angle is found by solving an optimization problem of reduced size

Problem Statement

Description of the Proposed Approach

Numerical Example

A Modified Version of the Method Employing Accelerometer Measurements

Conclusions