Robust Position Estimation using Range Measurements from Transmitters with Inaccurate Positions

The problem of position estimation using range measurements from transmitters with inaccurately known positions is considered. The true position of each transmitter is assumed to lie within a disk of a known radius, centered at the inaccurate position. A robust estimation framework is proposed, formulating a min-max optimization problem and presenting a tractable solution approach. A sensitivity map is constructed to quantify the positioning error in different regions due to inaccuracies in the transmitters’ positions. Numerical simulations are presented demonstrating the construction and application of the sensitivity map for estimating the position of a mobile receiver. It is shown that the sensitivity map yields invaluable insights to the expected positioning error in various regions within the environment. Experimental results are presented of a vehicle navigating in a real-world GPS-jammed environment using pseudorange measurements from 7 cellular transmitters whose positions are inaccurately known. The vehicle’s positioning error is justified utilizing the offline-generated sensitivity map.