Direction cosine matrix estimation from vector observations using a matrix kalman filter

D. Choukroun, H. Weiss, I. Y. Bar-Itzhack, Y. Oshman

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


This work presents several algorithms that use vector observations in order to estimate the direction cosine matrix (DCM) as well as three constant biases and three time-varying drifts in body-mounted gyro output errors. All the algorithms use the matrix Kalman filter (MKF) paradigm, which preserves the natural formulation of the DCM state-space model equations. Focusing on the DCM estimation problem, the assumption of white noise in the gyro and in the vector observations errors yields reduced and efficient filter covariance computations. The orthogonality constraint on the DCM is handled via the technique of pseudomeasurement, which is naturally embedded in the MKF. Two additional known "brute-force" procedures are implemented for the sake of comparison. Extensive Monte-Carlo simulations illustrate the performances of the different estimators. When estimating only the DCM, it is shown that all the proposed orthogonalization procedures accelerate the estimation convergence. Nevertheless, the pseudomeasurement technique shows a smoother and shorter transient than the brute-force procedures, which on the other hand yield more accurate steady-states. The reduced covariance computations yield a more accurate steady-state than the full covariance computations but show a slower transient. When estimating the DCM as well as the gyro biases and drifts, enforcing orthogonalization seems to penalize the DCM estimation as long as the biases are not correctly identified. For the sake of computation savings during long duration missions, a mixed estimator, switching between long periods of DCM-only estimation and short periods of DCM-biases estimation, appears to be a promising strategy.

Original languageEnglish
Article number5417148
Pages (from-to)61-79
Number of pages19
JournalIEEE Transactions on Aerospace and Electronic Systems
Issue number1
StatePublished - 1 Jan 2010

ASJC Scopus subject areas

  • Aerospace Engineering
  • Electrical and Electronic Engineering


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