Ground clutter is a long standing issue in radar meteorology, considering that it can bring significant bias to the estimations of weather moments, polarimetric parameters, rainfall rate, hydrometeor identification, etc. Bayes' theorem is introduced and applied to signal processing of weather radar signals which distinguishes it from existing empirical methods to improve data quality. Five ground clutter detection algorithms are discussed, which are the Spectrum Clutter Identification (SCI), Simple Bayesian Classifier applied to the Dual-Scan discriminants (SBC-DS), test statistic obtained from the Generalized Likelihood Ratio Test (GLRT), Simple Bayesian Classifier applied to the Dual-Pol discriminants (SBC-DP), and Simple Bayesian Classifier applied to the Dual-Pol Dual-Scan discriminants (SBC-DPDS). One ground clutter filtering algorithm is developed, which is the Bi-Gaussian Model Adaptive Processing (BGMAP). The BGMAP algorithm will be applied to the clutter contaminated gates identified by ground clutter detection algorithms. The performances of the clutter detection and filtering algorithms are evaluated using the data collected by the OU-PRIME (University of Oklahoma-Polarimetric Radar for Innovation in Meteorology and Engineering) 5-cm polarimetric radar and PX-1000 3-cm polarimetric transportable radar.