Statistical techniques used to approximate the above equations include [[Kalman filter]]s and [[particle filter]]s (aka. [[Monte Carlo method]]s). They provide an estimation of the [[posterior probability functiondistribution]] for the pose of the robot and for the parameters of the map. Methods which conservatively approximate the above model using [[covariance intersection]] are able to avoid reliance on statistical independence assumptions to reduce algorithmic complexity for large-scale applications.<ref>{{cite conference | last1= Julier |first1=S. |last2=Uhlmann |first2=J. | title = Building a Million-Beacon Map. | conference = Proceedings of ISAM Conference on Intelligent Systems for Manufacturing | year = 2001|doi=10.1117/12.444158 }}</ref> Other approximation methods achieve improved computational efficiency by using simple bounded-region representations of uncertainty.<ref>{{cite conference | last1= Csorba |first1=M. |last2=Uhlmann |first2=J. | title = A Suboptimal Algorithm for Automatic Map Building. | conference = Proceedings of the 1997 American Control Conference | year = 1997|doi=10.1109/ACC.1997.611857 }}</ref>
[[Set estimation|Set-membership techniques]] are mainly based on [[interval propagation|interval constraint propagation]].<ref>
