I've just spent a week beating on this problem so I can refrain from sending SMS home alarms to my wife when she's at work.
Pinging won't work because the iPhone won't respond to ICMP when asleep. Reading the ARP cache won't work because a sleeping iPhone will come and go (check it every 30 seconds for a few minutes).
The only way I have found to 'reliably' determine when my two iPhones are on my local (home) network is to use the PCAP dotnet library to look for any packets originating from either of the phones' MAC addresses. For example, if you run Wireshark with the capture filter
ether src <iphone-mac-address>
you will see a surprising amount of network discovery/announcement traffic from the phone. It still has quiescent states, but so far the longest interval I have seen between captured packets is around 10 minutes. You would have to wait until you have not heard from the phone for some interval (I use 15 minutes) before declaring it not-home.
With this technique you will find a phone quickly when it rejoins the home network, assuming your phone is configured for DHCP. I also use port mirroring on my main Ethernet switch to include traffic from my wireless access points.
I don't have a Raspberry Pi solution for this, because my linux expertise is very limited, but someone else may be able to help you along those lines. I have a Windows Service using the PCAP library and so far it works reliably, with the limitation of waiting 15 minutes before deciding an iPhone has left the network.
* update 2-3-2018 *
I have this detection algorithm down to about 5 minutes, using a combination of ping/arp messages directed to each phone, about once per minute. Seems to work great.
sudo hcitool name xx:xx:xx:xx:xx:xx
). If I get a valid response, the phone is in BT range. – Greegree