You need four things:
- A GPS receiver
- A GSM modem
- An Arduino
- A Battery
Using off the shelf products you would probably end up with something about the size of a cigarette packet at best - probably bigger.
To make it small enough to be unobtrusive would take a lot of work. You would need to design your own circuitry combining everything that is contained in the three circuits above into the smallest design you can, and since most existing solutions use pre-built modules (cans) that are relatively large you would first have to discover how they work and replicate them as one single tiny module.
And then there is the battery. GPS receivers are very sensitive devices. They have quite powerful preamplifiers to detect the incredibly faint signals of the satellites. Consequently they use quite a bit of power. Similarly GSM modems are quite power hungry, especially when they are far from a cell tower.
Put those together and you have quite large power requirements - so the battery will consequently be relatively large. Many times the size of the circuit you designed above.
So if you're trying to make something that James Bond might stick on the back of someone's jumper without them noticing you're very much out of luck I'm afraid.
That is why most tracking of people is done using a larger device that most people have sat in their pocket already: a mobile phone. You can already get software for most phones that will allow you to track your children.