Traffic state estimators (TSEs) based on the cell transmission model (CTM) are vulnerable to biased initial estimates of traffic flow parameters, in particular the critical density. For example, an overestimated (underestimated) initial estimate of critical density can cause a delayed (premature) switching of a TSE from free-flow working mode to congestion working mode, hence distorting estimates of traffic states. Only augmenting the traffic flow parameters into the state vector cannot resolve the issue of biased initial estimate of the critical density, because the critical density is unobservable under free-flow mode. To overcome this issue, this paper proposes an innovative supervisory observer to inform the TSE of correct instants for mode switching. In particular, the proposed supervisory observer requires no a priori knowledge of any traffic flow parameter. The idea is to make decisions for mode switching through capturing anomalies in the residuals of the extended Kalman filter (EKF) of the TSE. This paper also proposes, for the first time in relevant literature, to augment capacity drop proportion into state vector so that its value can be calibrated online. Simulation experiments show that the proposed method can correctly capture mode switching times and generate satisfactory estimates of traffic states and track time-varying traffic flow parameters.