Mirror jitters around a bias tilt angle can make noise performance degradation for a space-borne Michelson interferometer. A numerical model simulates the Hyperspectral Infrared Atmospheric Sounder (HIRAS) spectra affected by the mirror jitters. According to the simulation, mirror jitters mainly generate spectrally correlated noise, which can be estimated by subtracting the random noise component from the total noise. The random noise is estimated through a principal component analysis (PCA) technique. Applying the PCA noise estimator as a diagnostic tool to monitor the noise level in the process of bias tilt angle tuning, optimized HIRAS noise performance is achieved with the correlated noise component minimized.