http://arxiv.org/abs/1312.1349
Calibration is the process of inferring how much measured data depend on the signal one is interested in. It is essential for any quantitative signal estimation on the basis of the data. Here, we investigate the “art” of self-calibration that augments an external calibration solution using a known reference signal with an internal calibration on the unknown measurement signal itself. Contemporary self-calibration schemes try to find a self-consistent solution for signal and calibration. This can be understood in terms of maximizing their joint probability. Thus, the full uncertainty structure of this probability around its maximum is not taken into account by these schemes. Therefore better schemes — in sense of minimal square error — can be designed that also reflect the uncertainties of signal and calibration reconstructions. We argue that at least the signal uncertainty should not be neglected in typical measurement situations, since the calibration solutions suffer from a systematic bias otherwise, which consequently distorts the signal reconstruction. Furthermore, we argue that non-parametric, signal-to-noise filtered calibration should provide more accurate reconstructions than the common bin averages and provide a new, improved self-calibration scheme. We illustrate our findings with a simplistic numerical example.
Fri, 6 Dec 13
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