Identification of multiobject dynamical systems: Consistency and fisher information

Jeremie Houssineau, Sumeetpal S. Singh, Ajay Jasra

Research output: Contribution to journalArticlepeer-review

Abstract

Learning the model parameters of a multiobject 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 aim to help fill this gap and study the identifiability of the model parameters and the consistency of the corresponding maximum likelihood estimate (MLE) under assumptions on the different components of the underlying multiobject 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 multitarget 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. To the best of the authors' knowledge, these are new theoretically backed insights on the subtleties of MTT parameter learning.
Original languageEnglish (US)
Pages (from-to)2603-2627
Number of pages25
JournalSIAM Journal on Control and Optimization
Volume57
Issue number4
DOIs
StatePublished - Jul 25 2019

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