Carbon dioxide-based occupancy estimation using stochastic differential equations

Sebastian Wolf*, Davide Calı̀, John Krogstie, Henrik Madsen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


In the existing building stock, heating, cooling and ventilation usually run on fixed schedules, in many cases, even all day. In particular, ventilation systems often run with a constant air flow rate that is adjusted based on the assumption of maximum occupancy. Hence, reducing the operation to the required extent would offer energy potential. Model-based, demand-controlled heating, ventilation and air-conditioning systems can help to achieve this. Information on the number of occupants present in a room and ventilation-related quantities, such as the room-air change rate, are important parameters to control the ventilation of a building. Hence, an automated estimation of these would help to find optimal model-based control strategies. In this work, the use of a grey-box model based on a carbon dioxide mass balance is explored to estimate room occupancy and ventilation parameters. The main contribution of this study is the employment of stochastic differential equations to describe this mass balance. In contrast to ordinary differential equations, the stochastic framework employed here is able to address measurement errors as well as errors that derive from an inevitably oversimplified description of the physical system. Due to its probabilistic nature, this approach inherently includes a method of parameter estimation using the maximum likelihood approach, which additionally provides a measure of uncertainty for every estimated parameter. The presented model was tested in one naturally ventilated and one mechanically ventilated office room. In both cases, the estimation of occupancy and of the model parameters showed promising results. This leads to the conclusion that the suggested model can be considered as a candidate to be integrated into building control systems.
Original languageEnglish
JournalApplied Energy
Pages (from-to)32-41
Publication statusPublished - 2019


  • Occupancy estimation
  • Occupant behaviour
  • Predictive control


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