Efficient Time-of-Arrival Self-Calibration using Source Implicitization

In this paper we revisit the Time-of-Arrival self-calibration problem. In particular we focus on imbalanced problem instances where there are significantly more sources compared to the number of receivers, which is a common configuration in real applications. Using an implicit representation, we are able to re-parameterize the sensor node self-calibration problem using only the parameters of the receiver positions. Making the source positions implicit, we show that it is possible to linearize the maximum-likelihood error around the measured distances, resulting in a Sampson-like approximation. Given four unknown receiver positions and a large number of unknown sender positions, we show that our formulation leads to algorithms for robust calibration, with significant speed-up compared to running the full optimization over all unknowns. The proposed method is tested on both synthetic and real data.