About the problem formulation

[zzt007]

Hi, thanks for your great job!
There is a problem bother me a lot , which about the paper's problem formulation.

N_0 means the total count of tracked objects in the sequence, and the T_h means the observation horizon.
However, during the sequence length, the N_0 may change, and here is appears to be a fixed value?
In other words, the lifetime of the tracked object may be less than the sequence length.
So I don't know how to due with these 'variables' in my model.
Looking forward to your early reply!