Adaptive circadian argument estimator and its application to circadian argument control

Disruption of the circadian rhythm is detrimental to human well being, with consequences ranging from lower productivity, sleep disorder, to more serious health problems. Accurate estimation of circadian argument is critical to the assessment and treatment of circadian disruption. Circadian argument estimate is also essential for light-based circadian entrainment. Direct measurements of circadian rhythm markers such as dim light melatonin onset are inconvenient and acquired at best at low rate. Wearable continuous measurement such as actigraph is convenient but is masked by many other factors. In this paper, we present a new circadian rhythm estimation scheme based on a type of frequency tracker, called adaptive notch filter (ANF) which is commonly used in signal processing. ANF is designed to track the gain and phase of a single sinusoid from noisy data. We extend the classic ANF to multiple harmonics needed in circadian rhythm tracking. The local stability and high order harmonics robustness are analyzed. The highly noisy indirect measurements result in unreliable amplitude estimate, but the phase estimate is generally quite robust. We use this phase estimate combined with the light input to construct a black-box linear time varying (LPV) system description, parameterized by the phase estimate. The LPV model predicts the circadian rhythm response to light inputs and can be used for the design of light-based feedback control. The proposed modeling and control method is applied to three different models of circadian rhythm: Kronauer's human circadian model, Leloup's Drosophila circadian model and Neurospora circadian model. Simulation shows that our approach can generate reliable circadian argument estimation and effective gain-scheduled control of the circadian rhythm without any knowledge of the underlying model. The ability to generate circadian estimate, model, and control based only on input/output data opens up the tantalizing possibility of personalized circadian rhythm estimator and light therapy.