On the performance of particle filters with adaptive number of particles

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dc.contributor.author Míguez Arenas, Joaquín
dc.contributor.author Elvira Arregui, Víctor
dc.contributor.author Djuric, Petar
dc.contributor.editor Springer
dc.date.accessioned 2022-03-16T15:25:46Z
dc.date.available 2022-03-16T15:25:46Z
dc.date.issued 2021-10-01
dc.identifier.bibliographicCitation Elvira, V., Miguez, J., & Djurić, P. M. (2021). On the performance of particle filters with adaptive number of particles. En Statistics and Computing, 31(6) , pp. 1-18
dc.identifier.issn 0960-3174
dc.identifier.uri http://hdl.handle.net/10016/34394
dc.description.abstract We investigate the performance of a class of particle filters (PFs) that can automatically tune their computational complexity by evaluating online certain predictive statistics which are invariant for a broad class of state-space models. To be specific, we propose a family of block-adaptive PFs based on the methodology of Elvira et al. (IEEE Trans Signal Process 65(7):1781– 1794, 2017). In this class of algorithms, the number of Monte Carlo samples (known as particles) is adjusted periodically, and we prove that the theoretical error bounds of the PF actually adapt to the updates in the number of particles. The evaluation of the predictive statistics that lies at the core of the methodology is done by generating fictitious observations, i.e., particles in the observation space. We study, both analytically and numerically, the impact of the number K of these particles on the performance of the algorithm. In particular, we prove that if the predictive statistics with K fictitious observations converged exactly, then the particle approximation of the filtering distribution would match the first K elements in a series of moments of the true filter. This result can be understood as a converse to some convergence theorems for PFs. From this analysis, we deduce an alternative predictive statistic that can be computed (for some models) without sampling any fictitious observations at all. Finally, we conduct an extensive simulation study that illustrates the theoretical results and provides further insights into the complexity, performance and behavior of the new class of algorithms.
dc.description.sponsorship This work was partially supported by Agence Nationale de la Recherche of France under PISCES Project (ANR-17-CE40-0031-01), the Office of Naval Research (Award No. N00014-19-1-2226), Agencia Estatal de Investigación of Spain (RTI2018-099655-B-I00 CLARA), and NSF through the award CCF-2021002.
dc.language.iso eng
dc.rights © The Author(s) 2021
dc.rights Atribución 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by/3.0/es/
dc.subject.other Particle filtering
dc.subject.other Sequential Monte Carlo
dc.subject.other Predictive distributions
dc.subject.other Convergence analysis
dc.subject.other Adaptive complexity
dc.title On the performance of particle filters with adaptive number of particles
dc.type article
dc.subject.eciencia Ingeniería Industrial
dc.identifier.doi https://doi.org/10.1007/s11222-021-10056-0
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. RTI2018-099655-B-I00
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 1
dc.identifier.publicationissue 6
dc.identifier.publicationlastpage 18
dc.identifier.publicationtitle STATISTICS AND COMPUTING
dc.identifier.publicationvolume 31
dc.identifier.uxxi AR/0000030338
dc.contributor.funder Agencia Estatal de Investigación (España)
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