In the process of measurement while drilling, the dynamic measurement signal of the drilling tool is often submerged in a complex noise environment. This noise is primarily caused by the strong vibrations of the bottom drilling tool, which result from the drill bit cutting through rock layers and the collisions between the drill string and the borehole wall. Such interference severely affects the attitude measurement of the drilling tool, leading to ineffective guidance and control. In order to solve this problem, this paper uses the dynamic characteristics generated by the tri-stable nonlinear system, that is, the random resonance effect, to extract the frequency of the dynamic measurement signal of the steering drilling tool. Firstly, a random resonance frequency identification method based on the scale transformation tri-stable system is proposed to solve the application limitation of the dynamic measurement signal of the drilling tool. Then, the influence of the characteristic parameters of the potential function on the resonance output of the system is studied, and the corresponding adjustment scheme of the characteristic parameters of the potential function is designed to realize the frequency extraction of the dynamic measurement signal of the drilling tool under any noise intensity. The experimental results of simulation and real drilling data show that the SNR threshold of the signal extracted by the proposed method is as low as -19.5 dB, and the stability is better than that of bis-table systems, which proves the effectiveness and stability of the proposed method.