On the errors-in-variables model with inequality constraints of dependent variables for geodetic transformation

Abstract

The Total least-squares (TLS) adjustment with inequality constraints has received increased attention in geodesy over the last three years. In the most recent work, inequality constraints have been presented that can restrict unknown parameters and independent variables, but no one has provided an inequality-constrained adjustment for restricting dependent variables. In this work, we review the TLS adjustment methods in terms of different model formulations and then investigate the errors-in-variables model with inequality constraints for dependent variables. Finally, we demonstrate the practicality of our approach with a planar geodetic transformation, where the uncertainty of the target observations is reduced via the inequality constraints for dependent variables.

Keywords:

• Total least-squares
• Errors-in-variables model
• Inequality constraints
• Dependent variables
• Geodetic transformation
• Uncertainty reduction

Additional information

Funding

This work was supported by National Natural Science Foundation of China [Grant Number 41404005].