Assume that there are two identical remote objects and we want to estimate the distance to the closest of them and the distance between objects. For that purpose some device (like a ``radar'') is used, and the signal observed is the sum of signals reflected by each object. Moreover, the signal observed is corrupted by white Gaussian noise. Singularity (i.e. very poor performance of any estimate) in this problem will occur if objects are very close to each other. Our purpose is to demonstrate this inherited singularity and investigate the rate of convergence of the best parameter estimates.