Pulse estimation in nonlinear detectors with nonstationary noise

We present an algorithm for the least-squares measure of pulse size in the presence of non-stationary system noise through the signal event, which is optimal in both the linear and nonlinear regime. In the case of a linear detector with stationary noise, the algorithm reduces to the Wiener filter. This algorithm is of particular interest with recent advances in the performance of transition edge superconductor (TES) detectors. While these devices can perform near the theoretical limits, their resolution is often limited by the high heat capacities required for linearity at the highest energies. With a robust algorithm for saturated pulse analysis, we can provide significant improvements in resolution while maintaining response over the full energy range. We show the ultimate resolution achievable with TES detectors.