Last season's poor Scotstoun record was a major factor in Glasgow's failure to secure a PRO12 play-off squad for the first time in five seasons, and Peter says the players are well aware there must be improvements.
Speaking in the Evening Times, Peter said: "Before the season began all the players discussed what could make this season better and we generally hit upon improving our home form over last season, when to be honest, we let some of the standards we'd set in previous years slip.
"If you have ambitions of reaching the play-offs then home form counts for so much. In past seasons, that has played a big part in our success and we want to get back to making Scotstoun a place where teams turn up knowing just how tough a test they'll face. And we can hopefully put down that marker against the Ospreys."
Peter thinks the recent improvements to the Scotstoun pitch have inspired visiting teams.
"The G4 pitch is a magnificent surface to play on, and we love it - but so do some of our opponents, and teams are turning up looking to play a running game against us.
"That didn't really happen when we were at Firhill or on the old grass pitch at Scotstoun when at times, especially if it was a wet winter, that matches were just a slog on a heavy, muddy surface.
"Ospreys will be up for this trip. They've begun the season with a good win against Zebre. Dan Baker and Justin Tipuric looked really sharp in that one, and they have real pace out wide with Jeff Hassler. So this is a big game for us but one you really have to look forward to being part of."
Warriors launched their new campaign with an 18-12 away win over Connaught in monsoon conditions in Galway, which Peter says, was as tough an 80 minutes as he has ever faced.
"Remember what I said about Firhill and the old Scotstoun? Well, those under-foot conditions were ideal preparation for what we had to contend with in Galway.
"I have never played in anything like that win and rain. After five minutes, you were soaked, as if you'd been standing under a shower. There was little point in changing kit at half time - five minutes later you'd have been drenched again.
"The good thing - the only good thing actually - in terms of the weather was that it was quite mild. Had that been like that, in the dead of winter, you would seriously have run the risk of suffering hypothermia. You would have been frozen."