In vibration-based condition monitoring, the damaged signal components are often masked by extraneous com- ponents and need to be extracted or enhanced to perform detection, identification, and trending. This can be performed using optimal filters. In this work, the optimal filtering problem is presented using different opti- misation formulations, objective functions, and optimisation algorithms. The performance of the methods for fault detection, and trending are compared under time-varying speed conditions. The work demonstrates that the objective function, optimisation formulation and optimisation algorithm can have a significant impact on the performance of the methods and should be carefully selected for vibration-based condition monitoring ap- plications under time-varying speed conditions.