Current health management process for the aircraft engine is based on the scheduled inspections regardless of its actual conditions, which requires substantial cost and time while sometimes failing to prevent abrupt failures. To overcome this problem, recently a new technique, prognostics and health management (PHM) has drawn great attention that can enable maintenance only when necessary while ensuring safety. It requires the multiple engine sensor measurements with high fidelity, current health and its remaining life assessment based on the nonlinear physics models and data analysis techniques applied by advanced machine learning and statistics. The challenge in this process is that as the real engine operates over time, it keeps degradation which represents the long-term fault progression till the end of its life. The in-flight diagnostic systems, however, should detect only anomaly that is encountered by abrupt change or fault under this continued degradation. Unless this is reflected in the on-board fault detection, it may misinterpret the health state and may lead to the unintended false alarm. In order to accommodate this, the on-board diagnostics should be applied based to the degraded state which should be periodically updated from the off-board analysis over long time span. Then the diagnostics will be carried out always in the vicinity of the degraded engine. In this study, an approach is presented based on the Kalman filter for the improved diagnostics, which is composed of two regimes: First is the hybrid filter for the on-board diagnostics, in which the health parameters are fixed at constant, while the state is estimated for a short time span using the linearized system model based on the real-time sensor measurements. Then it is examined whether any state change is encountered that represents the anomaly. Second is the extended filter for the off-board health assessment, in which the health parameters and state are estimated together for a long-time span using the nonlinear system model and measurements history. With this architecture, the system updates to account for engine health degradation is achieved, i.e., the estimated health degradation is fed into the on-board system, from which the fault detection is accomplished with sufficient accuracy.