Novel techniques for estimation and tracking of radioactive sources

Radioactive source signal measurements are Poisson distributed due to the underlying radiation process. This fact, coupled with the ubiquitous normally occurring radioactive materials (NORM), makes it challenging to localize or track a radioactive source or target accurately. This leads to the necessity to either use highly accurate sensors to minimize measurement noise or many less accurate sensors whose measurements are averaged to minimize the noise. The cost associated with highly accurate sensors places a bound on the number that can realistically be deployed. Similarly, the degree of inaccuracy in cheap sensors also places a lower bound on the number of sensors needed to achieve realistic estimates of location or trajectory of a radioactive source in order to achieve reasonable error margins.

We first consider the use of the smallest number of highly accurate sensors to localize radioactive sources. The novel ideas and algorithms we develop use no more than the minimum number of sensors required by triangulation based algorithms but avoid all the pitfalls manifest with triangulation based algorithms such as multiple local minima and slow convergence rate from algorithm reinitialization. Under the general assumption that we have a priori knowledge of the statistics of the intensity of the source, we show that if the source or target is known to be in one open half plane, then N sensors are enough to guarantee a unique solution, N being the dimension of the search space. If the assumptions are tightened such that the source or target lies in the open convex hull of the sensors, then N+1 sensors are required. Suppose we do not have knowledge of the statistics of the intensity of the source, we show that N+1 sensors is still the minimum number of sensors required to guarantee a unique solution if the source is in the open convex hull of the sensors.

Second, we present tracking of a radioactive source using cheap low sensitivity binary proximity sensors under some general assumptions. Suppose a source or target moves in a straight line, and suppose we have a priori knowledge of the radiation intensity of the source, we show that three binary sensors and their binary measurements depicting the presence or absence of a source within their nominal sensing range suffices to localize the linear trajectory. If we do not have knowledge of the intensity of the source or target, then a minimum of four sensors suffices to localize the trajectory of the source.

Finally we present some fundamental limits on the estimation accuracy of a stationary radioactive source using ideal mobile measurement sensors and provide a robust algorithm which achieves the estimation accuracy bounds asymptotically as the expected radiation count increases.