GEOG 862
GPS and GNSS for Geospatial Professionals

The One-percent Rule of Thumb

 illustration of thumbs up
Source: Big Thumbs Up by 
Charles LeBlanc is licensed under 
CC BY-SA 2.0

Here is convenient approximation. The maximum resolution available in a pseudorange is about 1 percent of the chipping rate of the code used, whether it is the P(Y) code or the C/A code. In practice, positions derived from these codes are rather less reliable than described by this approximation; nevertheless, it offers a basis to evaluate pseudoranging in general and compare the potentials of P(Y) code and C/A code pseudoranging in particular. A P(Y) code chip occurs every 0.0978 of a microsecond. In other words, there is a P(Y) code chip about every tenth of a microsecond. That’s one code chip every 100 nanoseconds. Therefore, a P(Y) code based measurement can have a maximum precision of about 1 percent of 100 nanoseconds, or 1 nanosecond. What is the length of 1 nanosecond? Well, multiplied by the speed of light, it's approximately 30 centimeters, or about a foot. So, just about the very best you can do with a P(Y) pseudorange is a foot or so. Because its chipping rate is 10 times slower, the C/A code based pseudorange is 10 times less precise. Therefore, one percent of the length of a C/A code chip is 10 times 30 centimeter, or 3 meters. Using the rule of thumb, the maximum resolution of a C/A code pseudorange is nearly 10 feet. Actually, this is a bit optimistic. The actual positional accuracy of a single C/A code receiver was about ±100 m with selective availability, SA, turned on. It was ±30 m with SA turned off in May of 2000 and is a bit better today.

You might ask, at this point, if the pseudorange isn't the full answer, then how do we get the extraordinary accuracies that we depend upon GPS to produce? Here's a convenient approximation rule of thumb, the 1% rule of thumb, to help answer that question.

Generally speaking, if you're trying to use a signal to do positioning or to measure a distance, you can resolve that signal to 1% of its wave length or 1% of its chipping length; that is the best you can do when everything is in your favor. You may remember that if we talk about the P-Code, that would mean a maximum precision would be about 1% of 1/10th of a microsecond, that is a nanosecond. One nanosecond multiplied times the speed of light, as I've mentioned, is about 30 centimeters and approaching a foot. This is also in direct correlation with that 96-feet, a chip length that we saw with the P-Code. 1% of that is approximately a foot.

The C/A Code is 10 times less precise, remember it's 10 times slower. Instead of 30 centimeters, the maximum resolution of the C/A code is about three meters. Again, this is in direct correlation with that chipping length of 960 feet. 1% of 960 feet is 9.6 feet, approximately. Those are the best answers that we can get with a pseudorange. But, of course, we would like to do much better than that.