This study attempts to improve the performance of Generalized Likelihood Ratio Test-based indicators via blind filtering the of vibration signals. The key point is the optimization of the filter coefficients to maximize the indicator of interest. The filter coefficients are optimized through Rayleigh quotient iteration. The proposed method's performance and applicability are demonstrated on both simulated and real vibration signals measured on an experimental test rig. The outcome of the study shows that the Rayleigh quotient iteration is a potent tool for maximizing such complex condition monitoring indicators. Inspections over the filtered signals reveal that the optimal filters promote particular signal patterns linked to a bearing fault in vibration signals. The indicator estimated over the filtered signals is able to detect the bearing fault more robustly when compared to the raw signals.