Time-Varying Unknown Input Constrained UKF With Unbiased Minimum Variance Estimator for Nonlinear Dynamic Indoor Thermal Profile Estimation

Abstract

Estimating unknown inputs in indoor heating, ventilation, and air conditioning (HVac) systems, particularly under the influence of diverse environmental constraints and time-varying relative humidity, presents a significant challenge. A viable solution is to use a weighted least-squares (WLS) approach for estimating unknown inputs, which uses an unbiased minimum variance (UMV) estimator in conjunction with an unscented Kalman filter (UKF)-based nonlinear filtering technique. This allows for the simultaneous estimation of the system’s state and the unknown inputs. To accurately represent the real-life nonlinear thermal profile influenced by these uncertain inputs, it is essential to adopt an RC network-based mathematical modeling approach that captures the system’s dynamic behavior over time. The integration of the UMV-based optimal estimator with the UKF culminates in the proposed UKF with UMV for unknown inputs (UKF-UMV-UI) estimation algorithm. Extensive experimentation with the proposed UKF-UMV-UI algorithm has been conducted in a laboratory-scale realistic environment, dealing with uncertain and challenging unknown inputs. The results of the investigation indicate that the proposed method outperforms the UKF with unknown input (UKF-UI) by 41.64% and 35.85% in cumulative mean squared error (CuMSE) for two distinct measurement conditions, respectively.