Bayesian algorithm to estimate position and activity of an orphan gamma source utilizing multiple detectors in a mobile gamma spectrometry system

Abstract

To avoid harm to the public and the environment, lost ionizing radiation sources must be found and brought back under the regulatory control as soon as possible. Usually, mobile gamma spectrometry systems are used in such search missions. It is possible to estimate the position and activity of point gamma sources by performing Bayesian inference on the measurement data. The aim of this study was to theoretically investigate the improvements in the Bayesian estimations of the position and activity of a point gamma source due to introduction of data from multiple detectors with angular variations of efficiency. Three detector combinations were tested—a single 123% HPGe detector, single 4l NaI (Tl) detector and a 123% HPGe with 2x4l NaI (Tl) detector combination—with and without angular efficiency variations for each combination resulting in six different variants of the Bayesian algorithm. It was found that introduction of angular efficiency variations of the detectors did improve the accuracy of activity estimation slightly, while introduction of data from additional detectors lowered the signal-to-noise ratio threshold of the system significantly, increasing the stability and accuracy of the estimated source position and activity, for a given signal-to-noise ratio.

Accuracy of a Bayesian technique to estimate position and activity of orphan gamma-ray sources by mobile gamma spectrometry: Influence of imprecisions in positioning systems and computational approximations

“…Thus, the angular variations of the counting efficiency were taken into account in the likelihood to make the calculations more accurate. As demonstrated in [ 13 ], it is possible to express the relative angle of incidence θ using the current x i , previous x i −1 measurement coordinates and the position of the source p . Thus, for an i -th measurement, a simplified final equation depicting the physical model for the likelihood yields: where x is the measurement position and p is the source position in two spatial coordinates.…”

“…Similarly, the likelihood can be expressed as a probability distribution of measurement values, Z , provided that the measurement locations, X , position, P , and activity, A , of the source are known, π ( Z | X , P , A ). The likelihood was adapted to use data from multiple detectors in the Bayesian calculations simultaneously to increase the accuracy of the results, as was displayed in a previous study [ 13 ]. The likelihood π ( Z | X , P , A ) can then be then expressed as: where m is the number of detectors and n is the number of measurements.…”

“…For a more detailed description of the Bayesian model, the reader is referred to a previous study [ 13 ].…”

“…In our previous study [ 13 ] we have performed a feasibility test of a Bayesian algorithm using simulated data from multiple detectors with individual angular variations in counting efficiency of the detectors, estimating position and activity of point gamma emitting sources, with distances to the sources spanning the range of 10-190 m and activities reaching 1215 MBq.…”

“…From the previous study [ 13 ] it was concluded that using data from multiple detectors provided more information for the algorithm and, as a result, the estimates of the position and the activity were more accurate. This study was purely theoretical, and it is thus important to investigate how well the algorithm performs using real data, which is associated with additional uncertainties (such as varying background count rates) and technical limitations (e.g.…”