a Systematic diagram of the frequency automatic tracking system. When the frequency difference exceeds the preset frequency threshold, the synchronization determining module can provide algorithmic feedback to the frequency spillage, thus adjusting the frequency of the reading oscillator through the Joule heating effect. The whole automatic tracking process runs in a programmable control environment. b The center frequency of the synchronization range can gradually shift and ultimately completely cover the working range required. c The open-loop frequency response of the sensing resonator and reading resonator under the monitoring of the tracking system. The nonlinear frequency response of the reading resonator is shifted under Joule heating, which perfectly tracks the changes in the sensing resonator. d Demonstration experiment of the tracking system. When the frequencies of the sensing oscillator and reading oscillator are far from each other, the tracking system can sense the difference and then change the reading oscillator until the two are synchronized.