| There are times and places where conventional navigation systems, such as the Global Positioning System (GPS), are unavailable due to anything from temporary signal occultations to lack of navigation system infrastructure altogether. The goal of the Leapfrog Navigation System (LNS) is to provide localized positioning services for such cases.; The concept behind leapfrog navigation is to advance a group of navigation units teamwise into an area of interest. In a practical 2-D case, leapfrogging assumes known initial positions of at least two currently stationary navigation units. Two or more mobile units can then start to advance into the area of interest. The positions of the mobiles are constantly being calculated based on cross-range distance measurements to the stationary units, as well as cross-ranges among the mobiles themselves. At some point the mobile units stop, and the stationary units are released to move. This second team of units (now mobile) can then overtake the first team (now stationary) and travel even further towards the common goal of the group. Since there always is one stationary team, the position of any unit can be referenced back to the initial positions. Thus, LNS provides absolute positioning.; I developed navigation algorithms needed to solve leapfrog positions based on cross-range measurements. I used statistical tools to predict how position errors would grow as a function of navigation unit geometry, cross-range measurement accuracy and previous position errors. Using this knowledge I predicted that a 4-unit Leapfrog Navigation System using 100 m baselines and 200 m leap distances could travel almost 15 km before accumulating absolute position errors of 10 m (1σ).; Finally, I built a prototype leapfrog navigation system using 4 GPS transceiver ranging units. I placed the 4 units in the vertices a 10m x 10m square, and leapfrogged the group 20 meters forwards, and then back again (40 m total travel). Average horizontal RMS position errors never exceeded 16 cm during these field tests. |
