Method and system for tracking a mobile device

A navigation system for tracking a mobile device in a geographic area, wherein said navigation system is configured to:

• a) store or receive a topological map for said geographic area, said topological map providing a graph of topological paths through said geographic area, wherein each topological path is associated with a corresponding path direction;
• b) statistically generate, on a virtual map of said geographic area, a plurality of particles around an estimated initial position of the mobile device, a spatial dispersion of said particles representing an initial uncertainty of said estimated initial position of the mobile device;
• c) measure a series of displacements of said mobile device or receive a series of motion measurements of said mobile device and therefrom determine a measured displacement vector comprising an estimated displacement direction and an estimated displacement distance of the mobile device;
• d) displace each of said particles on the virtual map according to a randomized particle displacement vector which is derived from said measured displacement vector based on an uncertainty of the measured displacement vector and recording said particle displacement vector for each displaced particle;
• e) determine a weight of each particle based on one or more of a comparison of the respective particle displacement vector and of the path direction of an adjacent topological path and a distance of the particle to the adjacent topological path;
• f) resample the plurality of particles, wherein the system is configured to select a subset of said displaced particles based on a particle-weight dependent selection criterion, wherein said selection criterion is such that particles with lower weight are more likely to be resampled than particles with higher weight;
• and
• g) wherein the system is further configured to regenerate said selected subset of displaced particles within a particle regeneration area around a current mean location of the plurality of particles according to a probability distribution.

A non-transitory computer-readable medium storing computer readable instructions that, when executed by a processing unit cause the processing unit to implement a method with the steps of:

• a) retrieving a topological map for said geographic area, said topological map providing a graph of topological paths through said geographic area, wherein each topological path is associated with a corresponding path direction;
• b) statistically generating, on a virtual map of said geographic area, a plurality of particles around an estimated initial position of the mobile device, a spatial dispersion of said particles representing an initial uncertainty of said estimated initial position of the mobile device;
• c) determining, from said series of motion measurements, a measured displacement vector of the mobile device, the measured displacement vector representing an estimated displacement direction and an estimated displacement distance of the mobile device;
• d) displacing each of said particles on the virtual map according to a randomized particle displacement vector which is derived from said measured displacement vector based on an uncertainty of the measured displacement vector and recording said particle displacement vector for each displaced particle;
• e) determining a weight of each particle based on one or more of a comparison of the respective particle displacement vector with the path direction of an adjacent topological path and a distance of the particle to the adjacent topological path;
• f) resampling the plurality of particles, said resampling comprising selecting a subset of said displaced particles based on a particle-weight dependent selection criterion, wherein said selection criterion is such that particles with lower weight are more likely to be resampled than particles with higher weight;
• and
• g) wherein the resampling further comprises regenerating said selected subset of displaced particles within a particle regeneration area around a current mean location of the plurality of particles according to a probability distribution.