Consistency analysis of EKF-SLAM for a basic scenario

The consistency of the extended Kalman filter-based simultaneous localization and mapping (EKF-SLAM) is addressed in this article. It is theoretically proven that, for a basic scenario that the mobile robot is stationary and keeps observing a stationary landmark, the estimates of the position and its uncertainty of the robot remain the same as the initial values on condition that the initial covariance matrix of the robot pose is diagonal. The estimate of heading uncertainty will become inconsistent as the number of observation increases. The distributions of the lower bounds of robot heading and landmark position are obtained by Monte Carlo simulations. Simulation results show that both of two distributions follow a normal distribution, hence the EKF-SLAM algorithm provides unbiased estimates of the SLAM state vector in the sense of probability.