Positive Definiteness Analysis of the Covariance Matrix in EKF-SLAM

H. Zhang, L. Dou, H. Fang, and J. Chen (PRC)


simultaneous localization and mapping(SLAM); extended Kalman filter; robotics


This paper presented an analysis of the positive definite character of the covariance matrix in the extended Kalman filter based simultaneous localization and mapping (EKF SLAM) algorithm. It was shown that during a finite-time two-dimensional SLAM with point landmarks observed us ing a range-and-bearing sensor, the positive definiteness holds on condition that three certain Jacobian matrices keep full rank and the initial covariance matrix is positive defi nite. The popular motion and observation models were in vestigated and indicated that the conditions of Jacobians can be generally satisfied. And we argued that a posi tive definite initialization is more reasonable than a zero or completely correlative one. The positive definiteness was verified by Monte Carlo tests. Furthermore, we showed that ignoring correlations between landmarks, a popular way of reducing the computational complexity, will usually result in non-positive definite covariance matrix.

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