A new estimate of a heater/air conditioner duty cycle based on the maximum likelihood theory

The objective is to derive a duty cycle of a heater/air conditioner unit that correctly accounts for the effects of the driving process noise. The unit is modeled by using a stochastic hybrid state model driven by a white Gaussian process. Using the Kolmogorov backward equation, first passage theory, and the theory of maximum likelihood-estimation, a duty cycle is derived that shows the effects of the noise term that models the random influences introduced by the environment/customer. The derived duty cycle accounts explicitly for the statistics of the driving process. The proposed method leads to a more accurate estimate of the duty cycle. Existing duty cycles are derived as a special case of this approach