The stability of covariance inflation methods for SLAM

This paper analyses the consequences of using Covariance Inflation Methods for Simultaneous Localisation and Map Building (SLAM). Covariance Inflation refers to the process of adding a positive semidefinite matrix to the system covariance matrix to improve the properties of a SLAM algorithm. Because this approach can be used to decorrelate the state estimates in the covariance matrix, it has the potential to greatly reduce both computational and storage costs. However, it also raises the risk that the covariance can increase without bound. This paper analyses the properties of covariance inflation algorithms to assess their impact on performance. We prove that, to prevent the steady-state covariance from being increased, the computational and storage costs must be linear in the number of beacons. Furthermore, if the steady-state covariance is to remain finite, the inflation method cannot impose structures on the filter which are continually broken down. These results are illustrated in a simple linear example.