Microphone array position calibration by basis-point classical multidimensional scaling

Classical multidimensional scaling (MDS) is a global, noniterative technique for finding coordinates of points given their interpoint distances. We describe the algorithm and show how it yields a simple, inexpensive method for calibrating an array of microphones with a tape measure (or similar measuring device). We present an extension to the basic algorithm, called basis-point classical MDS (BCMDS), which handles the case when many of the distances are unavailable, thus yielding a technique that is practical for microphone arrays with a large number of microphones. We also show that BCMDS, when combined with a calibration target consisting of four synchronized sound sources, can be used for automatic calibration via time-delay estimation. We evaluate the accuracy of both classical MDS and BCMDS, investigating the sensitivity of the algorithms to noise and to the design parameters to yield insight as to the choice of those parameters. Our results validate the practical applicability of the algorithms, showing that errors on the order of 10-20 mm can be achieved in real scenarios.