Just get a Sure reciever-- about $35 US, with an antenna (mind you their antenna is pretty cheap and one of mine failed) It will give a pulse per second (PPS output) plus a usb NMEA output so you can make your RPi's time accurate to 100s of nanoseconds (Just the NMEA itself is good to tens of ms, but since we are comparing to using a recorded time that is still about 1000 to 10000 times better.)
The Sure requires 5V, delivers TTL but most serial ports will be OK with that although the RPI probably wants less than that on its GPIO pins. (stick a diode or two in series with the PPS signal should bring it low enough)
The board is about the same size as the RPi. One problem might be the power draw by the RPi if he really is running his system off a battery. It would probably double the power requirement.
But there are others-- eg
Not sure what a "blind" gps is, but they tend to be more expensive.