A navigation process is to start from a known (initial) position and to ensure a continued localisation of the user during the movement. Consider a pedestrian navigation system which contains a GPS receiver and a set of inertial sensors connected with the map database. The problem to solve is to determine the users location using the map database and measurements of the inertial sensors. Indoors the position of each step is determined as a function of the previous position and inertial measurements. Thus the trajectory is defined in a local coordinate system and with an arbitrary orientation. A dedicated motion model transforms the trajectory from set of consecutive points to a polygon. Then we must associate similar details from both data sources, the modified trajectory and the link-node model. The trajectory can be considered as the history of the route and its last point as the actual position of the user. In this research we propose a solution based on statistical methods and map-matching. The determination of the absolute position is entirely represented by its probability density function (PDF) in the frame of Bayesian inference. Following this approach the posterior estimation of the users position can be calculated using prior information and actual measurements. Because of the non-linear nature of the estimation problem, non-linear filtering techniques like particle filters (sequential Monte Carlo methods) are applied
