Hopefully helpful!
Definitely sounds like marking/dominant behavior. Does he do this on your walks as well? My other question is, do you have a training collar? (one of those w/the 'horrible looking spikes'--they don't actually hurt the dog btw

--or another version of a training collar?)
Do you notice a pattern as to when this seems to take place? Is is always when you're gone? Is it always when he enters that area of the house, after a walk, etc.? If there seems to be a 'pattern' then neurologically he's got a 'routine' that needs tweaking, and the best time to work on this behavior is going to be during that 'routine'. If it appears to be random, then it's just marking/dominance and he simply needs to learn you're the pack leader and not to do it in the house on your stuff ...
I worked as a basic trainer for about a year, and based on what's been shared, here's a few ideas:
With the training collar/leash on. Have the leash loose, but have one hand holding a few feet away from the collar. Walk him around the area (you mentioned the carport posts)... make the rounds w/him, stopping at each object that he likes to 'christen'
If you've noticed he goes in a set pattern, follow that pattern.
Stop and wait a few seconds at the object --if he lifts his leg/or begins to sniff/do any of the 'pre-behavior' excitement stuff, he gets a correction verbally and w/the collar (do them at the same time--the collar correction is a quick jerk back and release w/the leash using your wrist, it acts as a fellow pack mate would for correcting inappropriate behavior--not to patronize, but to be clear;-)Have him 'sit', 'wait,' 'down' whatever command you'd like for a few seconds before releasing him ('okay') circling around and coming back to that same object.
Go through all the 'spots' this way. You're trying to break the association of him 'hiking' his leg and it being 'okay' for him to do so w/these objects/in that space, etc.
The reverse is also true...if you don't care that he 'marks' the trees in the yard, then take him outside to these 'ok' areas, let him mark, and give praise.
But for awhile, you're going to have to be 'tough' on entering that area of the house w/him on the leash w/the corrections for him to begin to understand/make that connection.
I would also recommend, depending on how much he already gets, more exercise. This 'routine' could also be in part to him not getting enough satisfaction out of his current exercise. If every time he's out for a walk, he's having to 'mark' his territory then his mind is focused on that instead of moving on to just enjoying the walk/being active outdoors. So, even when he's home, his mind is 'stuck' on maintaining his turf instead of resting. Boosting his exercise could help lessen his 'need' to mark...especially paired w/showing him where it is appropriate for him to do so.
Someone else also recommended a 'fresh' start at potty training. This too, could be a good solution. You CAN teach an 'old' dog new tricks, but it generally takes longer, and you have to be so consistent, that the people usually bail out before the dog does!
This isn't going to 'fix' things overnight...and as someone else said, this will take consistency and patience on your part. And everyone in the family has to be in on it (they have to behave consistently w/the dog) for it to really be effective.
I would also recommend the Dog Whisperer, Cesar Millan's book, Be the Pack Leader...his website is also a treasure trove of information that may help w/this situation.
Okay, that was hard to explain in words! It's soo much easier to show people how to do all of this stuff!...maybe when I move, I'll do 'house call's for problem behaviors

Sorry so long! but hope it was helpful!