Wearable Data Assimilation to Estimate the Circadian Phase
Abstract
Abstract. The circadian clock is an internal timer that coordinates the daily rhythms of behavior and physiology, including sleep and hormone secretion. Accurately tracking the state of the circadian clock, or circadian phase, holds immense potential for precision medicine. Wearable devices present an opportunity to estimate the circadian phase in the real world, as they can noninvasively monitor various physiological outputs influenced by the circadian clock. However, accurately estimating circadian phase from wearable data remains challenging, primarily due to the lack of methods that integrate minute-by-minute wearable data with prior knowledge of the circadian phase. To address this issue, we propose a framework that integrates multitime scale physiological data and estimates the circadian phase, along with an efficient implementation algorithm based on Bayesian inference and a new state space estimation method called the level set Kalman filter. Our numerical experiments indicate that our approach outperforms previous methods for circadian phase estimation consistently. Furthermore, our method enables us to examine the contribution of noise from different sources to the estimation, which was not feasible with prior methods. We found that internal noise unrelated to external stimuli is a crucial factor in determining estimation results. Last, we developed a user-friendly computational package and applied it to real-world data to demonstrate the potential value of our approach. Our results provide a foundation for systematically understanding the real-world dynamics of the circadian clock.
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There have been major innovations in the estimation of circadian parameters in real‐world settings via application of mathematical models to wearables.
“there have been major innovations in the estimation of circadian parameters in real‐world settings via application of mathematical models to wearables [58, 59].”
From Essential Information About Chronobiology and Chronotherapy for the Optimal Care of People With Bipolar Disorders: An Expert Consensus (2026) · cites this paper as [59]
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The real-world association between digital markers of circadian disruption and mental health risks
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“Finally, there have been major innovations in the estimation of circadian parameters in real-world settings via application of mathematical models to wearables [58, 59].”
- Authors
- Kim, D. W., Lee, M. P., & Forger, D. B.
- Affiliations
- University of Michigan (US)
- Venue
- SIAM Journal on Applied Mathematics
- Published
- 2023-11-09
- Volume
- 84
- Issue
- 3
- Pages
- S452-S475
- ISSN
- 0036-1399 (ISSN-L)
- 1095-712X
- OpenAlex
- W4388534668
- Cited by
- 12
- References
- 56
- Citations by year
- 2026: 4 · 2025: 5 · 2024: 3
- FWCI
- 1.79
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- SIAM Journal on Applied Mathematics (publishedVersion)
- Funders
- Human Frontier Science Program (RGP0019/2018)
- Division of Mathematical Sciences (2052499)
- Topics
- Life Sciences › Neuroscience › Endocrine and Autonomic Systems › Circadian rhythm and melatonin
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Sleep and Work-Related Fatigue
- Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
- Keywords
- circadian clock, wearable devices, data assimilation, Bayesian inference, state-space estimation, internal noise, sleep, hormone secretion, precision medicine
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