Making a "homemade differencial GPS"

I've read about how DGPS systems basically work and, as far as my research has come, it seems that it is not impossible to be reproduced.

I thought about having a fixed GPS in a location I know  where it is (let's suppose I know it by clicking on the exact position it is on google maps and seeing it's coordinates). I measure my object's position with it's GPS system as well as the fixed base. Knowing where my base is, I know the error of the GPS and, as long as the base and the object are close to each other, I the error on the object must be similar.

Is it right? Is there something special I should have/know?

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