Cramer-Rao bounds for circadian rhythm parameter estimation

Zarowski and Kropyvnytskyy [1] have reported a new algorithm called the modified iterative cosinor algorithm (MICA) for estimation of circadian rhythms in brain-injured human patients. Circadian rhythm parameter estimation is the problem of estimating the parameters of a sinusoid in noise and interference. The data from which the parameter estimates are derived are various physiological data sets such as body core temperature, heart rate, blood pressure, etc. The noise is assumed to be white Gaussian noise, while the interference (trend) components are the harmonics and subharmonics of the patients fundamental rhythm. In [1] it was mentioned that we have Cramer-Rao bounds on the variance of parameter estimates, but space did not permit their presentation at the time. In this paper we therefore present the bounds mentioned in [1].