TOA Sensor Network Calibration for Receiver and Transmitter Spaces with Difference in Dimension

Abstract:
We study and solve the previously unstudied problem of finding both sender and receiver positions from time of arrival (TOA) measurements when there is a difference in dimensionality between the affine subspaces spanned by receivers and senders. Anchor-free TOA network calibration has uses both in sound, radio and radio strength applications. Using linear techniques and requiring only a minimal number of receivers and senders, an algorithm is constructed for general dimension p for the lower dimensional subspace. Degenerate cases are determined and partially characterized as when receivers or senders inhabits a lower dimensional affine subspace than was given as input. The algorithm is further extended to the overdetermined case in a straightforward manner. Simulated experiments show good accuracy for the minimal solver and good performance under noisy measurements. An indoor environment experiment using microphones and speakers gives a RMSE of 2.35cm on receiver and sender positions compared to computer vision reconstruction.