Identification of multi-object dynamical systems: consistency and Fisher information

TL;DR

This paper investigates the theoretical aspects of learning parameters in multi-object dynamical systems, focusing on identifiability, consistency of maximum likelihood estimation, and the impact of observation noise on Fisher information.

Contribution

It provides the first theoretical analysis of parameter identifiability and MLE consistency in multi-object systems, including effects of noise and data association issues.

Findings

Identifiability and consistency of MLE are established under certain assumptions.

Observation noise and data association issues reduce Fisher information.

Quantitative analysis of how detection failures affect parameter learning.

Abstract

Learning the model parameters of a multi-object dynamical system from partial and perturbed observations is a challenging task. Despite recent numerical advancements in learning these parameters, theoretical guarantees are extremely scarce. In this article, we study the identifiability of these parameters and the consistency of the corresponding maximum likelihood estimate (MLE) under assumptions on the different components of the underlying multi-object system. In order to understand the impact of the various sources of observation noise on the ability to learn the model parameters, we study the asymptotic variance of the MLE through the associated Fisher information matrix. For example, we show that specific aspects of the multi-target tracking (MTT) problem such as detection failures and unknown data association lead to a loss of information which is quantified in special cases of interest.