Base Station Orientation Calibration in 3-D Indoor UWB Positioning Brandon Merkl 1 , Aly Fathy 2 , and Mohamed Mahfouz 1 1 Department of Mechanical, Aerospace, and Biomedical Engineering, 2 Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, Tennessee, 37996, USA Abstract — A method is proposed to correct three- dimensional (3D) positioning error due to base station antenna orientation that takes into account non-boresight electrical length differences due to antenna phase center errors. An automated algorithm is used to calibrate an ultra- wideband (UWB) system using only a starting estimate of the base station position and acquired positions central to the base stations. The true positions of the acquired 3D calibration points are unknown to the calibration algorithm. Upon completion of the algorithm, the base station orientation is estimated, along with estimates of electrical length offsets due to potential cable length differences. This method is designed to minimize small errors due to base station position and orientation uncertainty. The algorithm is shown to be robust given the availability of accurate 1D ranging can be provided by the system. Index Terms — Phase center error, base station orientation, 3D localization I. INTRODUCTION In designing and constructing a high accuracy (~1mm) UWB positioning system [1,2], several types of errors and biases that are safely ignored on the decimeter scale, become significant to overall system performance. One such effect is that of phase center errors originating from transmitter-receiver mal-alignment. It will be shown these errors can be successfully removed using the Time- Difference-of-Arrival (TDOA) algorithm with knowledge of the receiving antenna orientations; however, ignoring this type of error proves impossible for the TDOA algorithm to remove. Even in a trial case involving 100 base stations, phase center errors are correlated and create considerable system error. Thus, the accuracy of the TDOA algorithm is highly dependent on the accuracy of the differences in the time of arrival (TOA) of our ultra- wideband pulses. Using an iterative approach, an algorithm has been developed and tested under simulated line-of-sight (LOS) conditions where ranging error was modeled as a zero mean Gaussian random variable with a variance equal to the amount of ranging error present in our UWB system. II. PREVIOUS WORK Much prior work has been done in the field of UWB positioning. Currently, commercial UWB positioning systems of Sapphire DART (Multispectral Solutions, Inc.) and Ubisense have indoor positioning accuracy of 10 cm and 15 cm, respectively [3,4]. Interesting results presented by Zetik et al. and Meier et al. indicate that ranging has the potential to achieve mm or even sub-mm accuracy levels [5,6]. Recent work in UWB positioning algorithms has focused on increasing the accuracy of TOA measurements in Non-Line-of-Sight (NLOS) conditions [7], increasing TOA resolution [8], and increasing TOA accuracy in the presence of interference [9]. III. MATERIALS AND METHODS The purpose of the experiments described previously is to expose and eliminate the error due to antenna phase center and simultaneously positioning error due in the antenna bore sight direction uncertainty. First, a short discussion of the phase center error is included for relevance to this calibration procedure. A. Antenna Phase Center Error The single element Vivaldi antenna is used on the receiver side of our system. The design of the antenna is shown below in Fig 1. Fig. 1. Designed Vivaldi antenna, with the +z axis being the boresight direction The z-axis points in the direction of the “end fire” radiation pattern typical of antipodal antennas. This particular design of antenna is particularly sensitive to phase center variation in both the E-plane (parallel with the plane of the antenna, xz-plane in Fig. 1) and H-plane of the antenna radiation pattern as shown in Figure 2 [1]. 978-1-4244-1827-5/08/$25.00 ©2008 IEEE PROCEEDINGS OF THE 2008 IEEE INTERNATIONAL CONFERENCE ON ULTRA-WIDEBAND (ICUWB2008), VOL. 1 93