With the one answer given so far (as at November 2nd), you commented, "The word PERSON is not in the question, THEREFORE it MUST be defined in the answer." This was because the answer given dealt a lot with the Father being a person, the Son being a person, and the Holy Spirit being a person. That is the Trinitarian stance, one definition being that three persons subsist in the one being of God [or essence, or substance].
Most people who take Trinitarians to task fail to grasp the significant difference between 'person' and 'being', so that is why I am responding to your comment. Yes, the word 'person' needs to be defined (with respect to the one God the Bible speaks of.) The apostle Peter spoke of this one God, for he never spoke of 'gods' (plural) in such contexts.
The real issue here is the problem we have using English words that have been translated, first from old Latin, which, in turn, were translated from the original koine Greek. This is where misunderstanding arises. Here is how this is explained in the source below:
"Our English word 'person' comes from Latin and it has lost something
in its translation from Greek. The original Greek word 'ousia' meant
essence or substance. The usual Latin for that is 'substantia',
meaning essence or substance.
The Greek word 'hypostasis' meant person, or a second meaning was
substance. The usual Latin is 'persona', meaning person, or a
second meaning of actor, or role.
The Greek word 'prosopon' meant face or mask, with a second meaning
of person. The usual Latin for that is 'persona', and that is where
we get our understanding of 'person' from.
But in the original Greek of the Bible New Testament, we see that
'essence' or 'substance' was the meaning, and it is that language
that the Trinity doctrine is all about. [Most English speaking
people today only think of it simply as an individual person.]
The Greeks described the Trinity as 'mia ousia en trisin
hypostasesi' = one substance (essence) in three subsistenes
[persons]." Unfortunately, that could be misunderstood as saying, "one
essence in three substances", which would be 3 gods. When the Latins
then said, 'una substantia in tribus personis' = one substance in
three persons", they could be misunderstood as saying one 'hypostasis'
(person) in three roles." [Bear in mind the link between a role and
a face-mask, as with actors.]
We are 16 centuries removed from this, when Sabellianism opposed Trinitarianism. Yet the modern-day opposition and the teaching back then remains the same as today - "Three - Father, Son and Holy Spirit - are God, yet God is not three, but One." That is why I said that English translation from Latin loses something in the translation. And Latin translation from Greek lost something as well. There's nothing like sticking to the original koine Greek that the NT was written in, but few of us are linguists, and it was never going to be easy, getting a verbal handle on the awesomeness of Deity.
Source - Heresies and Orthodoxy in the History of the Church, Harold O.J. Brown pp 63, 128-130 (Hendrickson 1998)
Finally, to answer your actual question (now that I've exposed the tangle of misunderstandings we English-speaking people get into), for as long as there is not clarity with the meaning of translated words, some will insist Peter could only mean a simple God comprised of one person (or Spirit). Whereas others will insist Peter knew the one God to be a complex being, revealed in the incarnation, and through the teaching of the Holy Spirit.
Nobody will get anywhere asking, "What did Peter believe as to who his God was?" for what Peter said will be interpreted in light of one's theology. We all like to claim it is the other way around, with us - we discover what the Bible states and our theology is based on that. All I can say is that I stoutly and passionately believed in a simple God and that Jesus was created by this God, and the Holy Spirit was just energy, power, used by God. Then in later life, the Holy Spirit revealed to me just who this Son of God really is; that the Father and the Son share the one, divine nature, with absolute unity of the Spirit in that nature. I expect you to totally disagree, but that's not a problem here, on this site, as long as nobody starts trying to argue in comments that an answer is wrong.
