Optimal Trilateration Is an Eigenvalue Problem

The problem of estimating receiver or sender node positions from measured receiver-sender distances is a key issue in different applications such as microphone array calibration, radio antenna array calibration, mapping and positioning using UWB or using round-trip-time measurements between mobile phones and WiFi-units. In this paper we address the problem of optimally estimating a receiver position given a number of distance measurements to known sender positions, so called trilateration. We show that this problem can be rephrased as an eigenvalue problem. We also address different error models and the multilateration setting where an additional offset is also unknown, and show that these problems can be modeled using the same framework.