We've got a 15' x 4' pool too, but I grew up with an inground pool. We can keep our water clear in this one, but it takes quite a bit of work.
The two major causes of cloudy water are filters that aren't working correctly and chemicals. The chemicals breakup all the organic matter (from skincells, dirt, sunscreen, etc.) and the filter pulls it out of the water and keeps it out of circulation.
One of the things we've found is that the filter that came with our pool is WAY to small for it. (It's actually the same size as for the 10' x 2' pool we had last year.) We have to take the filter out practically daily to wash it off with the hose...you can get it nearly white again...and that helps. The manufacturer reccomends changing it completely once a week, but blasting it with the hose extends their life a bit. We're going to put off ordering a bigger filter though, since it's already August, until next year...or until they go on End of Summer Sale.
Chemical-wise I would highly reccomend either buying a "drops" type of test (as opposed to the sticks), or taking a h2o sample into your local pool/hottub store. The "stick" tests actually become HIGHLY inaccurate if they become even the least bit damp... like from a single drop of water running off your fingers into the tube...and they generally only test for 3 or 4 chemical/ph levels, as opposed to the 6 or 7 that the "drops" test.
Good Luck!
(And just keep repeating the mantra "So less expensive then 25k for an inground pool....so less expensive then 25k for an inground pool.)
~Z.