The numbers in the manual are never right. They're only there as a very rough ballpark estimate. Speaking of estimates, I converted 1.75" to metric (44.5mm), doubled it and added 559mm for the bead seat diameter, and came up with a circumference of 2034mm. That's also a ballpark because most tires are not labeled accurately. If you get a number by actual roll-out with weight on the bike, and it still doesn't match up with the GPS, then there's something going on with the GPS.

How I do it: set the valve stem on the bottom of the wheel, over a chalk mark or sidewalk crack. Sit on bike and roll it forward for 3 tire revolutions of the wheel which has the sensor magnet, coming to rest with the valve stem at the bottom of the wheel. Mark the pavement and measure with a tape. If you need to convert, 1 inch = 25.4 mm. Divide by 3 to get the circumference of the tire. Using this method, you should be able to get within 0.5% accuracy.