This article focuses on the recursive filtering problem for networked time-varying systems with randomly occurring measurement outliers (ROMOs), where the so-called ROMOs denote a set of large-amplitude perturbations on measurements. A new model is presented to describe the dynamical behaviors of ROMOs by using a set of independent and identically distributed stochastic scalars. A probabilistic encoding-decoding scheme is exploited to convert the measurement signal into the digital format. For the purpose of preserving the filtering process from the performance degradation induced by measurement outliers, a novel recursive filtering algorithm is developed by using the active detection-based method where the "problematic" measurements (i.e., the measurements contaminated by outliers) are removed from the filtering process. A recursive calculation approach is proposed to derive the time-varying filter parameter via minimizing such the upper bound on the filtering error covariance. The uniform boundedness of the resultant time-varying upper bound is analyzed for the filtering error covariance by using the stochastic analysis technique. Two numerical examples are presented to verify the effectiveness and correctness of our developed filter design approach.