Relative localization and mapping combining multidimensional scaling and Levenberg-Marquardt optimization

Sensory systems for localization and mapping based on ranging allows to obtain not only the position of a mobile object but also the position of the beacons or landmarks. Using only ranging, the beacon positions are often calculated without needing to compute all the spatial relations among them. In this work, a preliminary study about the use of relative positioning algorithm to obtain a map of active landmarks or beacon is described. The used architecture is able to easily compute spatial relations with beacons without increasing the hardware architecture. The used algorithm is based on a first position approximation by multidimensional scaling techniques; then, an optimization, using Levenberg-Marquardt algorithm, is applied to the non-linear equations, which involves the observations carried out between beacons and mobile objects.