Convergence of the SMC implementation of the PHD filte
The probability hypothesis density (PHD) filter is a first moment approximation to the evolution of a dynamic point process which can be used to approximate the optimal filtering equations of the multiple-object tracking problem. We show that, under reasonable assumptions, a sequential Monte Carlo (...
| Autori principali: | , , , |
|---|---|
| Natura: | Journal article |
| Lingua: | English |
| Pubblicazione: |
2006
|
| _version_ | 1826272165366857728 |
|---|---|
| author | Johansen, A Singh, S Doucet, A Vo, B |
| author_facet | Johansen, A Singh, S Doucet, A Vo, B |
| author_sort | Johansen, A |
| collection | OXFORD |
| description | The probability hypothesis density (PHD) filter is a first moment approximation to the evolution of a dynamic point process which can be used to approximate the optimal filtering equations of the multiple-object tracking problem. We show that, under reasonable assumptions, a sequential Monte Carlo (SMC) approximation of the PHD filter converges in mean of order p ≤ 1, and hence almost surely, to the true PHD filter. We also present a central limit theorem for the SMC approximation, show that the variance is finite under similar assumptions and establish a recursion for the asymptotic variance. This provides a theoretical justification for this implementation of a tractable multiple-object filtering methodology and generalises some results from sequential Monte Carlo theory. © Springer Science + Business Media, LLC 2006. |
| first_indexed | 2024-03-06T22:08:13Z |
| format | Journal article |
| id | oxford-uuid:50e3943f-a166-4ff1-b7df-875c4efa4f4e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:08:13Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:50e3943f-a166-4ff1-b7df-875c4efa4f4e2022-03-26T16:16:14ZConvergence of the SMC implementation of the PHD filteJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:50e3943f-a166-4ff1-b7df-875c4efa4f4eEnglishSymplectic Elements at Oxford2006Johansen, ASingh, SDoucet, AVo, BThe probability hypothesis density (PHD) filter is a first moment approximation to the evolution of a dynamic point process which can be used to approximate the optimal filtering equations of the multiple-object tracking problem. We show that, under reasonable assumptions, a sequential Monte Carlo (SMC) approximation of the PHD filter converges in mean of order p ≤ 1, and hence almost surely, to the true PHD filter. We also present a central limit theorem for the SMC approximation, show that the variance is finite under similar assumptions and establish a recursion for the asymptotic variance. This provides a theoretical justification for this implementation of a tractable multiple-object filtering methodology and generalises some results from sequential Monte Carlo theory. © Springer Science + Business Media, LLC 2006. |
| spellingShingle | Johansen, A Singh, S Doucet, A Vo, B Convergence of the SMC implementation of the PHD filte |
| title | Convergence of the SMC implementation of the PHD filte |
| title_full | Convergence of the SMC implementation of the PHD filte |
| title_fullStr | Convergence of the SMC implementation of the PHD filte |
| title_full_unstemmed | Convergence of the SMC implementation of the PHD filte |
| title_short | Convergence of the SMC implementation of the PHD filte |
| title_sort | convergence of the smc implementation of the phd filte |
| work_keys_str_mv | AT johansena convergenceofthesmcimplementationofthephdfilte AT singhs convergenceofthesmcimplementationofthephdfilte AT douceta convergenceofthesmcimplementationofthephdfilte AT vob convergenceofthesmcimplementationofthephdfilte |