How can I prove I was not speeding?

You can't really "prove" it unless you had not just a regular GPS on your car, but one of the ones that some trucking companies and insurers use to make sure drivers are not speeding, which records your speed at all points in time; that would create strong evidence that you were not speeding, based on the read-out from the device. In the absence of that, the best you have is your testimony that you were not speeding; however, based on my experience in handling speeding tickets in NJ, I can tell you that no court is going to believe the driver, who has an obvous strong incentive to lie (or least to "remember" things favorably to him/herself) over a sworn, trained, neutral (no personal stake in the outcome) police officer, unless you one of the two following unlikely things occur:
1) The officer blurts out something on the stand or  sends some email or text which you somehow get hold of which shows either a personal bias against you or a bias against your racial or ethnic group; or 
2) Your request "discovery" (information) on the device used to track your speed (e.g. radar, laser, the officer's car's speedometer, etc.) and that information shows that the device is faulty--but note that in years of handling speeding tickets, I have never seen this occur.