The idea is to have a master clock, GPS locked with built in 433 MHz transmitter, which will send an accurate time signal to the other clocks to bring them into sync. The transmitter will be triggered randomly, at least once every 24 hours, or by a push button connected to pin 12.
I'll be re-using the code from the quick and dirty 7-segment GPS clock here, and some of the code for the transmit function from the dehumidifier project.
I've added a 4x20 LCD display, with I2C piggyback interface board, and the u-blox GPS module we've used in the GPS logger.
The GPS module will be configured by the sketch itself, to 200mS refresh rate.
There's two sketches, the GPS clock itself, and a simple test receiver sketch to check everything's working as it should.
The I2C display is a generic display, purchased from eBay, and uses the PCF8574 I2C receiver IC. I tried a couple of different libraries, but eventually settled with the library from https://bitbucket.org/fmalpartida/new-liquidcrystal/downloads which works well with my display.
Well also use the virtual wire library to handle our comms, https://www.pjrc.com/teensy/td_libs_VirtualWire.html and the most excellent TinyGPS++ http://arduiniana.org/libraries/tinygpsplus/
There's an LED connected to pin 9, which blinks on and off every time the seconds are updated.
Here's the schematic...
... and the hardware lashed up for testing.
The second arduino is acting as our test receiver. There's no RF module in there as yet.. It's coupled to the clock arduino, GND is coupled, and pin 10 on the clock is connected to pin 9 on the receiver board. It's also supplying 5V to the other board.
Here's the data being displayed. Date (in UK format DD/MM/YYYY) , UTC time, latitude, longitude, no of satellites in use, horizontal dilution of precision and the number of seconds until the next transmission.

Here's the output from our terminal window, connected to the receiver board, showing the time and date are being correctly received when A3 is pulled to ground.
You can see the antenna is simply a straight piece of wire, 173mm long (for 433 MHz modules, other frequencies will need a different length)
OK, so to the code....
This is the transmitter code:
and the test receiver code...
Now all that remains is to box it up, and create some clocks!