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A leapfrog navigation system

There may be situations where positioning is required, but no service is available either due to signal blockage or cost of installing infrastructure. I suggest an architecture where the navigation system is carried along as a group of people/devices are moving. For simple 2-D positioning, a set of 4 ranging transponders are needed. Initially, 2 of these devices are placed in fixed and “known” local positions (e.g. by a doorway), while the two others can roam freely into the area of interest. Their position can be calculated with respect to the “known” initial position. At some point one or both of the mobile units are commanded to stop, and one or both of the fixed units are allowed to move. As time progresses, all units take turns acting as fixed or mobile stations, and the entire group can leapfrog their way towards a common goal. Positioning accuracies will deteriorate predictably as a function of network topology and individual ranging accuracies. Applications may range from firemen navigating through burning buildings or tunnels to groups of rovers exploring distant planets.