On the loss of Fisher information in some multi-object tracking observation models

TL;DR

This paper explores how Fisher information behaves in multi-object tracking models, showing that it can be lost in certain observation scenarios, with concise proofs provided for these phenomena.

Contribution

It extends the concept of Fisher information to models without a reference measure and demonstrates information loss in common multi-object tracking models.

Findings

Fisher information can be lost in specific multi-object tracking models.

The paper provides concise proofs of Fisher information loss.

Extension of Fisher information concept without a reference measure.

Abstract

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.