  The crucial limitation of improving the sensitivity of the detection of weak
magnetic fields is the unavoidable measurement noise. In this paper, we propose
a scheme to achieve precise sensing robust against additional noise by
employing a dual-frequency bias field modulation within a cavity magnon system.
We find that the anti-rotating wave term can amplify the signal of the detected
magnetic field, but this amplification effect must coexist with the rotating
wave term. In particular, by the bias field modulation, we find the robustness
against cavity field thermal noise is substantially enhanced, quantum noise and
cavity field thermal noise is greatly reduced, and the external magnetic field
signal is amplified, thereby improving the weak magnetic field sensing system's
sensitivity. Compared with the previous scheme, our scheme requires neither an
ultra- or deep-strong coupling mechanism nor the suppression of the additional
noise by increasing the electromagnetic cooperativity. Our scheme could provide
a valuable candidate for weak magnetic field sensing.
