This is an old topic, but what the heck! Hopefully someone will find my answer useful
So I'm a researcher looking at just these sorts of questions. How can we quantify psychological states so we can track and measure them? My own work focuses on compassion, empathy and mindfulness, which seem very related!
I think you're right that the answer to this question is heavily dependent on how we define "inner peace". So let me float a couple of definitions by you and how we might measure them:
1) Inner peace is a lack of distress or upset. If by inner peace we mean something like "calmness", we can measure that by tracking our levels of negative emotions either individually ("anxiety", "anger", "fear", etc.) or in general ("How distressed or upset am I right now?"). This would give us a sense of just how out of control our moods are and what effect other variables in our life have on our sense of "calm". There are existing measures of mood that measure negative affect. I believe there are some single-item measures.
2) Inner peace is the extent to which we are satisfied with or accepting of our self or circumstances. Under this definition, inner peace is not as much about being calm as it is about being "okay" with ourselves and life in general (which might have the secondary effect of calmness but the two are not the same). We could measure this by asking ourselves how much we accept who we are and our current circumstances or by asking the opposite - how critical am I being of myself or the world right now (might be better to separate these questions)? Where the self and other people are concerned, we are now talking about something similar to compassion. There are existing scales of self-compassion, self-criticism, and life satisfaction. They might need to be adapted for "in the moment" measurement.
3) ??? (is there another definition I'm missing?)
The measures I'm suggesting are self-report measures and are as much about our perception as they are about what is "really happening". If anyone would like to get into specifics, let me know.