A Kalman filter-based algorithm for IMU-camera calibration: Observability analysis and performance evaluation

Faraz M. Mirzaei, Stergios I. Roumeliotis

Research output: Contribution to journalArticlepeer-review

372 Scopus citations


Vision-aided inertial navigation systems (V-INSs) canprovide precise state estimates for the 3-D motion of a vehicle when no external references (e.g., GPS) are available. This is achieved bycombining inertial measurements from an inertial measurement unit (IMU) with visual observations from a camera under the assumption that the rigid transformation between the two sensors is known. Errors in the IMU-camera extrinsic calibration process cause biases that reduce the estimation accuracy and can even lead to divergence of any estimator processing the measurements from both sensors. In this paper, we present an extended Kalman filter for precisely determining the unknown transformation between a camera and an IMU. Contrary to previous approaches, we explicitly account for the time correlation of the IMU measurements and provide a figure of merit (covariance) for the estimated transformation. The proposed method does not require any special hardware (such as spin table or 3-D laser scanner) except a calibration target. Furthermore, we employ the observability rank criterion based on Lie derivatives and prove that the nonlinear system describing the IMU-camera calibration process is observable. Simulation and experimental results are presented that validate the proposed method and quantify its accuracy.

Original languageEnglish (US)
Pages (from-to)1143-1156
Number of pages14
JournalIEEE Transactions on Robotics
Issue number5
StatePublished - 2008

Bibliographical note

Funding Information:
Manuscript received September 24, 2007; revised March 30, 2008. First published October 3, 2008; current version published October 31, 2008. This paper was recommended for publication by Associate Editor P. Rives and Editor F. Park upon evaluation of the reviewers’ comments. This work was supported in part by the University of Minnesota (DTC) and in part by the National Science Foundation under Grant EIA-0324864, Grant IIS-0643680, and Grant IIS-0811946. A preliminary version of this paper was presented at the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems [1].


  • Extended Kalman filter
  • Inertial measurement unit (IMU)-camera calibration
  • Lie derivatives
  • Observability of nonlinear systems
  • Vision-aided inertial navigation


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