Simultaneous estimation of heat flux and temperature field using optimal two-stage Kalman filters

•OTSKF is introduced to solve IHTP.•A new method WOTSKF is developed to improve the inverse performances of OTSKF.•Effect of forgetting factor in WOTSKF was analyzed and optimal value was obtained.•Estimation performances of OTSKF and WOTSKF are compared under different conditions.•Proposed WOTSKF has faster tracking ability and stronger robustness than OTSKF. Inverse estimation of unknown input heat flux and temperature field plays an important role in thermal state monitoring. Optimal two-stage Kalman filter (OTSKF) is introduced into the inverse estimation of thermal state in this work. To further improve its performance, a new method weighted optimal two-stage Kalman filter (WOTSKF) algorithm is developed, in which a forgetting factor is used to modify OTSKF. The estimation performances of OTSKF and WOTSKF are compared in a two-dimensional heat transfer system. They are employed to estimate the state with heat flux of temporal, spatial, and spatiotemporal variation. Additionally, the effects of forgetting factor and measurement noises on the estimation accuracy of heat flux and temperature are investigated. Though decreasing the forgetting factor can improve the tracking ability and estimation accuracy of WOTSKF, it should not be too low due to the reason that low α causes fluctuation of estimation results. When the standard deviation of measurement noises σr increases from 0.05 to 2.00, the mean relative error of estimated heat flux ηq using OTSKF rises from 4.03% to 10.67% and it climbs from 2.76% to 7.07% using WOTSKF. That demonstrates proposed WOTSKF has stronger robustness than OTSKF.