Map matching trajectories

A computer implemented method (400) of locating a plurality of mobile device trajectories (301) relative to each other and a map (1, 1'), the mobile device trajectories (301) comprising a time series of position nodes (303) joined by edges (305), the method (400) comprising: obtaining an input pose graph (311) comprising a plurality of mobile device trajectories (301) and a plurality of first constraints (309) defining the position and orientation of nodes (303) and edges (305) of the trajectories relative to each other; performing a non-linear optimisation process on the input pose graph (311) based on the first constraints (309), to reduce a cost function associated with the first constraints (309), the non-linear optimisation process providing a modified pose graph (313); extracting one or more sub-graphs from the modified pose graph (313), and for each sub-graph, individually processing the sub-graph to map match the nodes (303) and edges (305) of the sub-graph to features defined in the map (1,1'); and generating second constraints (317) based on the one or more map matched sub-graphs.