Want additional verification beyond mobile? Perhaps that shopper has her phone turned off or chooses to not ride your Wi-Fi. Some stores have toyed with license plate recognition. This works in reverse. The customer is identified at the POS using a payment card. Digital analytics can match the face to the identity on the card.
When that person is tracked leaving the store, external security cameras can record her license plate number. Link established. The next time that license plate is detected by license plate-recognition cameras in the parking lot, your system knows who is coming and which entrance she is likely to use. And license plate tracking can sometimes be better than car tracking, since many consumers will retain a license plate when they buy a new car.
Does much of this raise privacy questions? Absolutely. But this is merely the automation of age-old retail tactics. Did anyone cry privacy when a veteran sales person noticed the car of a frequent shopper driving in? Or recognized her as she walked into the store? Why is that OK, but it's a sin when done via software?
Connecting the dots between offline and in-store can indeed be done without mobile. The question is: Why would you want to?
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