Estimation of building occupancy levels through environmental signals deconvolution

Abstract

We address the problem of estimating the occupancy levels in rooms using the information available in standard HVAC systems. Instead of employing dedicated devices, we exploit the significant statistical correlations between the occupancy levels and the CO2 concentration, room temperature, and ventilation actuation signals in order to identify a dynamic model. The building occupancy estimation problem is formulated as a regularized deconvolution problem, where the estimated occupancy is the input that, when injected into the identified model, best explains the currently measured CO2 levels. Since occupancy levels are piecewise constant, the zero norm of occupancy is plugged into the cost function to penalize non-piecewise constant inputs. The problem then is seen as a particular case of fused-lasso estimator by relaxing the zero norm into the e1 norm. We propose both online and offline estimators; the latter is shown to perform favorably compared to other data-based building occupancy estimators. Results on a real testbed show that the MSE of the proposed scheme, trained on a one-week-long dataset, is half the MSE of equivalent Neural Network (NN) or Support Vector Machine (SVM) estimation strategies.