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Consistent Estimation of Randomly Sampled Ornstein–Uhlenbeck Process Long-Run Mean for Long-Term Target State Prediction
Abstract
In this letter, we study the problem of estimating the long-run mean of the Ornstein-Uhlenbeck (OU) stochastic process and its effect on the long-term prediction of future vessel states, which is a crucial problem for Maritime Situational Awareness (MSA). We employ a sample mean estimator (SME) to estimate the key OU parameter from the observations, computing the closedform SME covariance error in both the random and constant sampling time regimes, providing a fundamental building block of the overall long-term state prediction covariance. We show also that the SME is: √n-consistent when the sampling time is random; asymptotically efficient when the sampling time is constant; and very close to the Cramer-Rao lower bound in the cases of practical interest for MSA.
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An unsupervised graph-based methodology has been developed to identify the spatiotemporal dynamics of ship routes and efficiently extract a compact representation of global maritime patterns from large volumes of historical AIS data in the form of a maritime traffic graph.
“Successful advancements on vector-based knowledge discovery [21], [22] have recently led to the development of an unsupervised graph-based methodology to identify the spatiotemporal dynamics of ship routes, and efficiently extract a compact representation of global maritime patterns from large volumes of historical AIS data, in the form of a maritime traffic graph (MTG).”
From Space-Based Global Maritime Surveillance. Part II: Artificial Intelligence and Data Fusion Techniques (2021) · cites this paper as [22]
The MTG method builds on recent advances in long-term vessel motion modeling whereby the dynamics of ships can be effectively described by a piecewise Ornstein-Uhlenbeck mean-reverting stochastic process.
“This method builds on recent advances in long-term vessel motion modeling [23], [24] whereby the dynamics of ships can be effectively described by a piecewise Ornstein-Uhlenbeck (OU) mean-reverting stochastic process.”
From Space-Based Global Maritime Surveillance. Part II: Artificial Intelligence and Data Fusion Techniques (2021) · cites this paper as [24]
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Soldi, G., Gaglione, D., Forti, N., Millefiori, L. M., Braca, P., Carniel, S., Simone, A. D., Iodice, A., Riccio, D., Daffina, F. C., et al. (2021) · IEEE Aerospace and Electronic Systems Magazine · doi:10.1109/maes.2021.3070884 · Cited by 44
“This method builds on recent advances in long-term vessel motion modeling [17], [25] whereby the dynamics of ships can be effectively described by a piecewise Ornstein–Uhlenbeck (OU) mean-reverting stochastic process.”
MethodSelf-citationd'Afflisio, E., Braca, P., Millefiori, L. M., & Willett, P. (2018) · 2018 21st International Conference on Information Fusion (FUSION) · doi:10.23919/icif.2018.8455854 · Cited by 33
Self-citationAnomaly Detection and Tracking Based on Mean–Reverting Processes with Unknown Parameters
Forti, N., Millefiori, L. M., Braca, P., & Willett, P. (2019) · ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) · doi:10.1109/icassp.2019.8683428 · Cited by 29
Self-citationHybrid Bernoulli Filtering for Detection and Tracking of Anomalous Path Deviations
Forti, N., Millefiori, L. M., & Braca, P. (2018) · 2018 21st International Conference on Information Fusion (FUSION) · doi:10.23919/icif.2018.8455567 · Cited by 14
Self-citation
Metadata
- Authors
- Millefiori, L. M., Braca, P., & Willett, P.
- Affiliations
- NATO Centre for Maritime Research and Experimentation (IT)
- Venue
- IEEE Signal Processing Letters
- Published
- 2016-11
- Volume
- 23
- Issue
- 11
- Pages
- 1562-1566
- ISSN
- 1070-9908 (ISSN-L)
- 1558-2361
- OpenAlex
- W2520171618
- Cited by
- 30
- References
- 0
- Citations by year
- 2025: 1 · 2024: 1 · 2023: 3 · 2022: 2 · 2021: 5 · 2020: 5 · 2019: 5 · 2018: 6 · 2017: 2
- FWCI
- 3.57
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Signal Processing Letters (publishedVersion)
- CINECA IRIS Institutial research information system (University of Pisa) (submittedVersion)
- Funders
- NATO
- SACT (SAC000608)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Target Tracking and Data Fusion in Sensor Networks
- Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
- Physical Sciences › Engineering › Ocean Engineering › Maritime Navigation and Safety
- Keywords
- Ornstein-Uhlenbeck process, maritime situational awareness, estimator consistency, asymptotic efficiency, Cramer-Rao lower bound
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