Improving absolute gravity estimates by the $L_p$-norm approximation of the ballistic trajectory

TL;DR

This paper demonstrates that using IRLS for $L_p$-norm approximation of ballistic trajectories in absolute gravimeters improves the precision of gravity estimates, especially under noisy conditions, with minimal bias.

Contribution

It introduces an IRLS-based method for $L_p$-norm approximation that enhances gravity measurement accuracy over traditional least-squares methods.

Findings

IRLS achieves sufficient accuracy with two iterations.

$L_p$-approximation with $3<p<4$ improves precision under certain noise distributions.

Real data confirms simulation results under high noise conditions.

Abstract

Iteratively Re-weighted Least Squares (IRLS) were used to simulate the $L_p$-norm approximation of the ballistic trajectory in absolute gravimeters. Two iterations of the IRLS delivered sufficient accuracy of the approximation without a significant bias. The simulations were performed on different samplings and perturbations of the trajectory. For the platykurtic distributions of the perturbations, the $L_p$-approximation with $3<p<4$ was found to yield several times more precise gravity estimates compared to the standard least-squares. The simulation results were confirmed by processing real gravity observations performed at the excessive noise conditions.