Error analysis of the extended Kalman filter applied to the simultaneous localization and mapping problem

Simultaneous localization and mapping (SLAM) is a process wherein a robotic system acquires a map of its environment while simultaneously localizing itself relative to this map. A common solution to the SLAM problem involves the use of the extended Kalman filter (EKF). This filter is used to calculate the posterior probability of the robot pose and map given observations and control inputs. From the EKF, one estimates the mean and error covariance of the robot pose and map features by using nonlinear motion and observation models. In this article, the conditions required for the convergence of the errors in the EKF estimates obtained by linearizing the nonlinear system equations are studied and applied to the SLAM problem. In particular, the observability condition of the system describing the typical SLAM problem is studied. Numerical studies are carried out to compare the accuracy of the EKF estimates for a representative SLAM formulation which is not observable with a SLAM formulation that satisfies the observability condition.

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