Consistent Map-based 3D Localization on Mobile Devices

TL;DR

This paper introduces the C-SKF and sC-SKF algorithms for real-time, map-based 3D localization on mobile devices, effectively managing map uncertainty with reduced memory and processing demands, and demonstrating competitive accuracy.

Contribution

The paper presents the novel C-SKF and sC-SKF algorithms that explicitly incorporate map uncertainty using sparse Cholesky factors, improving efficiency for mobile 3D localization.

Findings

C-SKF has linear memory requirements relative to map size.

sC-SKF reduces processing complexity by dividing the map into segments.

Algorithms achieve comparable accuracy to existing methods.

Abstract

The objective of this paper is to provide consistent, real-time 3D localization capabilities to mobile devices navigating within previously mapped areas. To this end, we introduce the Cholesky-Schmidt-Kalman filter (C-SKF), which explicitly considers the uncertainty of the prior map, by employing the sparse Cholesky factor of the map's Hessian, instead of its dense covariance--as is the case for the Schmidt-Kalman filter (SKF). By doing so, the C-SKF has memory requirements typically linear in the size of the map, as opposed to quadratic for storing the map's covariance. Moreover, and in order to bound the processing needs of the C-SKF (between linear and quadratic in the size of the map), we introduce a relaxation of the C-SKF algorithm, the sC-SKF, which operates on the Cholesky factors of independent sub-maps resulting from dividing the trajectory and observations used for constructing the map into overlapping segments. Lastly, we assess the processing and memory requirements of the proposed C-SKF and sC-SKF algorithms, and compare their positioning accuracy against other approximate map-based localization approaches that employ measurement-noise-covariance inflation to compensate for the map's uncertainty.