A tree parameterization for efficiently computing maximum likelihood maps using gradient descent

In 2006, Olson et al. presented a novel approach toaddress the graph-based simultaneous localization and mappingproblem by applying stochastic gradient descent to minimizethe error introduced by constraints. Together with multi-levelrelaxation, this is one of the most robust and efficient maximumlikelihood techniques published so far. In this paper, wepresent an extension of Olson's algorithm. It applies a novelparameterization of the nodes in the graph that significantlyimproves the performance and enables us to cope with arbitrarynetwork topologies. The latter allows us to bound the complexityof the algorithm to the size of the mapped area and not tothe length of the trajectory as it is the case with both previousapproaches. We implemented our technique and compared it tomulti-level relaxation and Olson's algorithm. As we demonstratein simulated and in real world experiments, our approachconverges faster than the other approaches and yields accuratemaps of the environment.