FIG Peer Review Journal


A Method to Estimate a Best Fit Trajectory from Multiple Individual Trajectories (10252)

Ola Øvstedal (Norway)
Dr. Ola Øvstedal
Associate Professor
Section of Geomatics
Faculty of Science and Technology
Norwegian University of Life Sciences
Corresponding author Dr. Ola Øvstedal (email: ola.ovstedal[at], tel.: +47 67231549)

[ abstract ] [ paper ] [ handouts ]

Published on the web 2020-02-28
Received 2019-10-01 / Accepted 2020-02-03
This paper is one of selection of papers published for the FIG Working Week 2020 in Amsterdam, the Netherlands and has undergone the FIG Peer Review Process.

FIG Working Week 2020
ISBN 978-87-92853-93-6 ISSN 2307-4086


In applications like extracting hiking trials from crowd sourced data, collecting trajectories on animal movement or precise mapping av road lines, there are multiple trajectories, obtained from e.g. Global Navigation Satellite Systems (GNSS), that describe the same physical path. Due to e.g. observation techniques, occasional observational blunders and difficulty in identifying exactly the same physical path, individual trajectories will normally differ from one another. This paper proposes a method on how to estimate a best fit trajectory based on available individual trajectories. The precision of the estimated trajectory is quantified in form of standard deviations. Occasional observational blunders and failure in following the same physical path are addressed through statistical testing. A priori stochastic information regarding the individual trajectories is utilized in a weighting scheme. The proposed method is first verified using a simulated dataset. Results from processing of a relatively complex dataset stemming from individual runs with a GPS multi-sport watch, point out some advantages and drawbacks of the method. The method appears to handle well both observational blunders and changing requirements regarding following the very same physical path during data collection. Detection and subsequent deletion of erroneous observations might however introduce small jumps along the estimated trajectory. Depending on the applications, the effect of occasional small jumps can be handled by post smoothing.
Keywords: Geoinformation/GI; GNSS/GPS; Positioning; Low cost technology; trajectory clustering; volunteered geographical information; GNSS; estimation and validation