  We present a new approach to tracking of radiation sources moving on smooth
trajectories which can be approximated with piece-wise linear joins or
piece-wise linear parabolas. We employ the use of cheap binary proximity
sensors which only indicate when a radiation source enters and leaves its
sensing range. We present two separate cases. The first is considering that the
trajectory can be approximated with piece-wise linear joins. We develop a novel
scalable approach in terms of the number of sensors required. Robustness
analysis is done with respect to uncertainties in the timing recordings by the
radiation sensors. We show that in the noise free case, a minimum of three
sensors will suffice to recover one piece of the linear join with probability
one, even in the absence of knowledge of the speed and statistics of the
radiation source. Second, we tackle a more realistic approximation of
trajectories of radiation sources -- piece-wise parabolic joins -- and show
that no more than six sensors are required in the noise free case to track one
piece of the parabola with probability one. Next we present an upper bound on
the achievable error variance in the estimation of the constant speed and the
angle of elevation of linear trajectories. Finally, a comprehensive set of
simulations are presented to illustrate the robustness of our approach in the
presence of uncertainties.
