Recently, under the presumption of a noise-free input, the augmented complex least lncosh (ACLlncosh) method was introduced for a power system frequency estimate and showed robust performance when impulsive noise polluted the output signal. However, in practical terms, noise often contaminates input signals, which drastically reduces the efficiency of the ACLlncosh method. To enhance robustness against noisy input-output while maintaining resilience to impulsive noise in the output signal, this paper proposed an online censoring-based widely linear total least lncosh (OC-WL-TLlnC) method. This method improves performance under both balanced and unbalanced settings by filtering out less valuable data via online censoring, hence reducing the computing burden. Furthermore, a variable parameter approach is incorporated to accelerate convergence and improve steady-state accuracy, thereby ensuring adaptability to dynamic power system conditions. The proposed methods significantly enhance frequency estimate performance by addressing the constraints of current techniques and offering a computationally efficient, noise-resilient solution for real-time power system monitoring.