Approximate sequential Bayesian filtering to estimate ²²²Rn emanation from ²²⁶Ra sources using spectral time series

A new approach to assess the emanation of inline-formula²²²Rn from inline-formula²²⁶Ra sources based on inline-formulaγ-ray spectrometric measurements is presented. While previous methods have resorted to steady-state treatment of the system, the method presented incorporates well-known radioactive decay kinetics into the inference procedure through the formulation of a theoretically motivated system model. The validity of the inline-formula²²²Rn emanation estimate is thereby extended to regimes of changing source behavior, potentially enabling the development of source surveillance systems in the future. The inference algorithms are based on approximate recursive Bayesian estimation in a switching linear dynamical system, allowing regimes of changing emanation to be identified from the spectral time series while providing reasonable filtering and smoothing performance in steady-state regimes. The derived method is applied to an empirical inline-formulaγ-ray spectrometric time series obtained over 85 d and is able to provide a time series of emanation estimates consistent with the physics of the emanation process.