To estimate the performance of an Aviation Multi-angular Polarimetric Radiometer (AMPR) precisely, its signals and noise were analyzed and the estimation processing for signal-to-noise ratios (SNRs) were investigated. The working principle of the AMPR was introduced and the formulas to calculate the detector SNRs and system SNRs were inferred. It indicates that the system SNR is proportional to intensity SNR while the requirement of detector SNR is inverse proportional to the polarimetric accuracy. However, the detector SNRs of AMPR should not be less than 245. The results make up the shortcoming from the traditional method that the precision of the polarization remote sensing instruments depends only on the detector SNRs. Finally, the system SNRs and the detector SNRs in a typical scene simulated by vector radiative transfer were estimated with the inferred formula and tested by a Spherical Integrating Source (SIS) and a polarization box in a dark laboratory. The results show that the SNRs of the AMPR detector meet the requirements of polarimetric detection.