A closed form solution to the single degree of freedom simultaneous localisation and map building (SLAM) problem

Presents a closed form solution to the estimation-theoretic simultaneous localisation and map building (SLAM) problem. The solution is obtained by explicit solution of the differential Riccati equation associated with the n-landmark SLAM problem. The solution describes and explains the many experimental and theoretical results obtained so far in the study of the SLAM problem. Further, the solution, for the first time, allows a precise means of analysing the performance of different SLAM algorithms and enables the design of efficient SLAM systems.