Estimation of an Uncertain Source Power from Monitors at Multiple Distant Locations

The general problem of estimating the level (or spectrum) of a steady source, using data from one or more monitor locations, is addressed. The monitors are assumed to be distant from the source such that propagation effects (ground reflections, atmospheric refraction, scattering by turbulence, etc.) are complex and imperfectly characterized, thus making it impossible to exactly infer the source level from the levels observed at the monitors. To systematically estimate the source level and its uncertainty, a model is needed for the distribution of the received signal(s). For a single transmission path, a number of suitable single-variate distributions are available. Here we propose modeling random scattered signal variations with a gamma distribution, and the uncertainty in the mean transmission loss with an inverse gamma distribution. This approach is suitable for weak or strong scattering, leads to convenient source-level estimates by the maximum-posterior likelihood method, and is amendable to sequential Bayesian updating. For multiple transmission paths (multiple monitors and/or multiple source locations), we propose extending the single-variate approach using matrix gamma distributions. Although the analysis is more complicated, this approach is shown to have the same advantages as with the single-variate case.