A closed form for false location injection under time difference of arrival

We consider a sensor network, which in the presence of a rogue sensor, is tasked with estimating emitter location under the time difference of arrival (TDOA) method. The rogue seeks to maximally degrade estimation accuracy by injecting a single false report of sensor position. Our closed form solution gives a set of false positions that minimize the network's Fisher Information Matrix (FIM). We find that the rogue sensor should report a false position along the vector pointing from the emitter to its valid paired sensor. Further, a method for finding the false location that not only minimizes the FIM but is also robust to the location network's ability to detect and reject erroneous TDOA measurements is developed.