The ageing society brings attention to daily elderly care through sensing technologies. The future smart home is expected to enable in-home daily monitoring, such as fall detection, for seniors in a non-invasive, non-cooperative, and non-contact manner. The mmWave radar is a promising candidate technology for its privacy-preserving and non-contact manner. However, existing solutions suffer from low accuracy and robustness due to environment dependent features. In this paper, we present FADE (\underline{FA}ll \underline{DE}tection), a practical fall detection radar system with enhanced accuracy and robustness in real-world scenarios. The key enabler underlying FADE is an interacting multiple model (IMM) state estimator that can extract environment-independent features for highly accurate and instantaneous fall detection. Furthermore, we proposed a robust multiple-user tracking system to deal with noises from the environment and other human bodies. We deployed our algorithm on low computing power and low power consumption system-on-chip (SoC) composed of data front end, DSP, and ARM processor, and tested its performance in real-world. The experiment shows that the accuracy of fall detection is up to 95\%.