  The concept of Fisher information can be useful even in cases where the
probability distributions of interest are not absolutely continuous with
respect to the natural reference measure on the underlying space. Practical
examples where this extension is useful are provided in the context of
multi-object tracking statistical models. Upon defining the Fisher information
without introducing a reference measure, we provide remarkably concise proofs
of the loss of Fisher information in some widely used multi-object tracking
observation models.
