We consider the problem of determining the relative position of dual-microphone sub-arrays. The proposed solution is mainly developed for binaural hearing aid systems (HASs), where each hearing aid (HA) in the HAS has two microphones at a known distance from each other. However, the proposed algorithm can effortlessly be applied to acoustic sensor network applications. In contrast to most state-of-the-art calibration algorithms, which model the calibration problem as a non-linear problem resulting in high computational complexity, we model the calibration problem as a simple linear system of equations by utilizing a far-field assumption. The proposed model is based on target signals time-difference-of-arrivals (TDOAs) between the HAS microphones. Working with TDOAs avoids clock synchronization between sound sources and microphones, and target signals need not be known beforehand. To solve the calibration problem, we propose a least squares estimator which is simple and does not need any probabilistic assumptions about the observed signals.

While there is scientific consensus that global and local mean sea level (GMSL and LMSL) has risen since the late nineteenth century, the relative contribution of natural and anthropogenic forcing remains unclear. Here we provide a probabilistic upper range of long-term persistent natural GMSL/LMSL variability (P=0.99), which in turn, determines the minimum/maximum anthropogenic contribution since 1900. To account for different spectral characteristics of various contributing processes, we separate LMSL into two components: a slowly varying volumetric component and a more rapidly changing atmospheric component. We find that the persistence of slow natural volumetric changes is underestimated in records where transient atmospheric processes dominate the spectrum. This leads to a local underestimation of possible natural trends of up to B1mm per year erroneously enhancing the significance of anthropogenic footprints. The GMSL, however, remains unaffected by such biases. On the basis of a model assessment of the separate components, we conclude that it
is virtually certain (P=0.99) that at least 45% of the observed increase in GMSL is of anthropogenic origin.