Position Estimation of Moving Objects: Practical Provable Approximation

Jeryes Danial, Dan Feldman, Ariel Hutterer

Research output: Contribution to journalArticlepeer-review


We consider the problem of matching a pair of point sets, each consists of k clusters, where each cluster in the first set is arbitrarily translated with additional noise, resulting in a cluster of the second point set. The goal is to compute k translations and a matching that minimizes the sum of squared distances between corresponding pairs of points. This is a fundamental problem for tracking systems (e.g., OptiTrack or Vicon) where the user registers k objects (rigid bodies) by attaching a set of markers to each object. Based on the position of these markers in real time, the system estimates the position of the moving objects by simultaneously clustering, matching, and transforming the n observed markers to the k objects. Similarly, an autonomous robot equipped with a camera may estimate its position by tracking n visual features from k recognized objects. The result can be used as a seeding clustering for existing algorithms, e.g., to compute the optimal rotation on each cluster. We suggest the first provable algorithm for solving this point matching problem. Unlike common heuristics, it yields a constant factor approximation for the global optimum in expected O(n2n) time. We validate our theoretical results with experimental results using low cost (< 30) 'toy' quadcopters that are safe and lawful for indoor navigation due to their <200 g weight. Comparisons to existing algorithms and commercial system are provided, together with open source code and a demonstration video.

Original languageEnglish
Article number8642359
Pages (from-to)1985-1992
Number of pages8
JournalIEEE Robotics and Automation Letters
Issue number2
StatePublished - Apr 2019

Bibliographical note

Funding Information:
Manuscript received September 10, 2018; accepted January 16, 2019. Date of publication February 14, 2019; date of current version February 28, 2019. This letter was recommended for publication by Associate Editor J. A. Shah and Editor T. Asfour upon evaluation of the reviewers comments. This work was supported by PHENOMICS Consortium, administered by The Israel Innovation Authority. (Corresponding author: Dan Feldman.) The authors are with the Robotics & Big Data Lab, Computer Science Department, University of Haifa, Haifa 3498838, Israel (e-mail:, dannyf.post@ gmail.com; dannyf.post@gmail.com; ahuttere@gmail.com). Digital Object Identifier 10.1109/LRA.2019.2899430

Publisher Copyright:
© 2016 IEEE.


  • Visual Tracking
  • localization
  • multi-robot systems
  • object detection
  • optimization and optimal control
  • segmentation and categorization
  • swarms

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Biomedical Engineering
  • Human-Computer Interaction
  • Mechanical Engineering
  • Computer Vision and Pattern Recognition
  • Computer Science Applications
  • Control and Optimization
  • Artificial Intelligence


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