Consistency analysis of EKF-based SLAM by measurement noise and observation times

Inconsistency is a fundamental problem in simultaneous localization and mapping (SLAM). Previous works from predecessors have studied the inconsistent problem of extended Kalman filter (EKF) SLAM algorithm focusing on the linearization errors. In this paper, we studied the inconsistency issue of EKF SLAM in theory based on measurement noise and observation time. In a simplified situation, we deduced some useful theorems of estimated covariance matrix. Then, we made use of them to investigate the inconsistency issue. We showed that the measurement noise and the observation times can drive the EKF SLAM out of consistency. Moreover, we demonstrated the explicit effects of measurement noise and observation times on inconsistency of the EKF SLAM. Our simulation experiments verified the results.