Final answer:
To achieve a GPS position resolution of 1.00 mm, timing accuracy must be in the order of picoseconds. Accuracy means the closeness of measurements to the true value, while precision is about the closeness of repeated measurements to each other.
Step-by-step explanation:
The metric for measurement accuracy with GPS-equipped beacons when processing the initial alert is typically given in feet or meters. For instance, if you seek to achieve a position resolution of 1.00 millimeter using GPS technology, the time taken by signals to reach the GPS receiver must be measured with extreme precision. Given that light and radio waves (which GPS signals essentially are) travel at approximately 299,792,458 meters per second, a 1.00 millimeter resolution would require timing accuracy on the order of 3.33564095 picoseconds, since it would take that long for light to travel 1.00 mm.
Understanding the accuracy and precision of GPS measurements is crucial. Accuracy refers to how close GPS measurements are to the true value, while precision refers to how close repeated measurements are to each other, regardless of their accuracy. When attempting to locate a position, such as a restaurant in a city, high accuracy would mean that the GPS readings are close to the real location, while high precision would mean that repeated measurements are close to one another.