Re: GPS speed accuracy
Probably more information than is needed (Wikipedia):
GPS includes a (currently disabled) feature called Selective Availability (SA) that can introduce intentional, slowly changing random errors of up to a hundred meters (328 ft) into the publicly available navigation signals to confound, for example, the guidance of long range missiles to precise targets. When enabled, the accuracy is still available in the signal, but in an encrypted form that is only available to the United States military, its allies and a few others, mostly government users. Even those who have managed to acquire military GPS receivers would still need to obtain the daily key, whose dissemination is tightly controlled.
Prior to being turned off, SA typically added signal errors of up to about 10 meters (32 ft) horizontally and 30 meters (98 ft) vertically. The inaccuracy of the civilian signal was deliberately encoded so as not to change very quickly. For instance, the entire eastern U.S. area might read 30 m off, but 30 m off everywhere and in the same direction. To improve the usefulness of GPS for civilian navigation, Differential GPS was used by many civilian GPS receivers to greatly improve accuracy.
During the 1990-91 Gulf War, the shortage of military GPS units and the ready availability of civilian ones caused many troops to buy their own civilian GPS units: their wide use among personnel resulted in a decision to disable Selective Availability. This was ironic, as SA had been introduced specifically for these situations, allowing friendly troops to use the signal for accurate navigation, while at the same time denying it to the enemy?but the assumption underlying this policy was that all U.S. troops and enemy troops would have military-specification GPS receivers and that civilian receivers would not exist in war zones. But since many American soldiers were using civilian devices, SA was also denying the same accuracy to thousands of friendly troops; turning it off (by removing the added-in error) presented a clear benefit to friendly troops.
In the 1990s, the FAA started pressuring the military to turn off SA permanently. This would save the FAA millions of dollars every year in maintenance of their own radio navigation systems. The amount of error added was "set to zero"[42] at midnight on May 1, 2000 following an announcement by U.S. President Bill Clinton, allowing users access to the error-free L1 signal. Per the directive, the induced error of SA was changed to add no error to the public signals (C/A code). Clinton's executive order required SA to be set to zero by 2006; it happened in 2000 once the US military developed a new system that provides the ability to deny GPS (and other navigation services) to hostile forces in a specific area of crisis without affecting the rest of the world or its own military systems.[42]
Selective Availability is still a system capability of GPS, and error could, in theory, be reintroduced at any time. In practice, in view of the hazards and costs this would induce for US and foreign shipping, it is unlikely to be reintroduced, and various government agencies, including the FAA,[43] have stated that it is not intended to be reintroduced.
One interesting side effect of the Selective Availability hardware is the capability to correct the frequency of the GPS cesium and rubidium atomic clocks to an accuracy of approximately 2 ? 10-13 (one in five trillion). This represented a significant improvement over the raw accuracy of the clocks.[citation needed]
On 19 September 2007, the United States Department of Defense announced that future GPS III satellites will not be capable of implementing SA,[44] eventually making the policy permanent.[45]
I haven't seen a speed accuracy spec on a gps, either. Yes, position accuracy, but not speed. Your calculations assumed you traveled a mile with GPS, but in fact it is only how far you have traveled within the update cycle. In many cases, that is one second. So, with GPS, the faster you go, the longer distance you travel in that time interval, the gps becomes more speed accurate. If you just sit stationary the gps will tend to wander around by so many feet. So at very slow speeds, such as 0-2mph the accuracy will be much less, than at 60mph. 
