To data-driven estimate power system sensitivity matrix considering mitigating data saturation, a series of multivariable least squares (MLS) algorithms are proposed and compared, including the ordinary MLS (OMLS), the weighted MLS (WMLS), the memory-limited OMLS (ML-ORMLS), the memory-limited WRMLS (ML-WRMLS), and the memoryfading ML-WRMLS (MF-ML-WRMLS). Considering enhancing computational efficiency and accuracy by mitigating data saturation, the last three of them are specifically derived for sensitivity matrix estimation based on time-varying online-measured data. The effectiveness of the presented algorithms is verified and compared in the Nordic 32 system for voltage sensitivity matrix estimation. The results illustrate the prime algorithm in practice.