A dynamic noise analysis and linewidth measurement technology based on $\mathbf{3}\times \mathbf{3}$ coupler Michelson interferometer with frequency trend extraction algorithm is proposed. It is robust to reconstruct the differential phase by using the fixed phase shift of interferometer. Under the condition of dynamic frequency sweeping, the original frequency trend information of laser is extracted by empirical mode decomposition method, and the frequency noise information is recovered. The power spectral density (PSD) of frequency noise is measured under both static and dynamic conditions of the laser, and the linewidth of the corresponding measurement time is calculated by using the integral algorithm, which verifies the effectiveness of the method under static conditions. And the PSD is calculated in a small time scale when sweeping the frequency, and the characteristics of noise under dynamic conditions are observed. This method has the advantages of complete noise frequency domain structure display and accurate frequency noise information extraction.