Bayesian In-Situ Calibration of Multiport Antennas for DoA Estimation: Theory and Measurements

The DoA of radio waves is used for many applications, e.g. the localization of autonomous robots and smart vehicles. Estimating the DoA is possible with a multiport antenna, e.g. an antenna array or a multi-mode antenna (MMA). In practice, DoA estimation performance decisively depends on accurate knowledge of the antenna response, which makes antenna calibration vital. As the antenna surroundings influence its response, it is necessary to measure the entire device with installed antenna to obtain the installed antenna response. Antenna calibration is often done in a dedicated measurement chamber, which can be inconvenient and costly, especially for larger devices. Thus, auto- and in-situ calibration methods aim at making antenna calibration in a measurement chamber redundant. However, existing auto- and in-situ calibration methods are restricted to certain antenna types and certain calibrations. In this paper, we propose a Bayesian in-situ calibration algorithm based on a maximum a posteriori (MAP) estimator, which is suitable for arbitrary multiport antennas. The algorithm uses received signals from a transmitter, noisy external DoA observations, takes multipath propagation into account and does not require synchronization. Furthermore, we take an estimation theoretic perspective and provide an in-depth theoretical discussion of in-situ antenna calibration in unknown propagation conditions based on Bayesian information and the Bayesian Cramér-Rao bound (BCRB). Extensive simulations show that the proposed algorithm operates close to the BCRB and the achieved DoA estimation performance asymptotically approaches the case of a perfectly known antenna response. Finally, we provide an experimental validation, where we calibrate the antenna on a robotic rover and evaluate the DoA estimation performance using measurement data. With the proposed in-situ antenna calibration algorithm, DoA estimation performance is considerably improved compared to using an antenna response obtained by simulation or in a measurement chamber.