Cleaning Camera Filters have to be done very carefully since mistakes can damage coatings of your filters. Most of filters like Hoya HMC filters have Multi-Layer to give you best quality filters. You will find its pretty hard to clean them.
Due to their high precision, filters should always be handled with care and kept clean whenever possible. Filters should be cleaned gently with just a lens tissue or soft cotton cloth. Never use any chemicals, such as lens cleaning fluid, on your filters, as these can damage the coatings. If any stubborn stains occur, these can usually be washed off with some clean water and a soft cotton cloth.
I have Hoya 58mm S-HMC PRO 1 UV filter and also a Hoya 58mm HMC Circular Polarized Filter using with my Canon Powershot SX10 IS camera. So I know how hard it is clean these Multi-Layer filters.