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Identification of multi-object dynamical systems : consistency and Fisher information
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Houssineau, Jeremie, Singh, Sumeetpal S. and Jasra, Ajay (2019) Identification of multi-object dynamical systems : consistency and Fisher information. SIAM Journal on Control and Optimization, 57 (4). pp. 2603-2627. doi:10.1137/17M113873X ISSN 0363-0129.
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Official URL: https://doi.org/10.1137/17M113873X
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 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 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.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Journal or Publication Title: | SIAM Journal on Control and Optimization | ||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||
ISSN: | 0363-0129 | ||||||
Official Date: | 25 July 2019 | ||||||
Dates: |
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Volume: | 57 | ||||||
Number: | 4 | ||||||
Page Range: | pp. 2603-2627 | ||||||
DOI: | 10.1137/17M113873X | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Reuse Statement (publisher, data, author rights): | Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 3 June 2019 | ||||||
Date of first compliant Open Access: | 13 August 2019 | ||||||
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