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Re: [RC] GPS accuracy - Truman Prevatt

The once per second readout is a system constraint as define by the NMEA spec. Also refer to the spec Bob Morris posted - the integration times used in most receivers for carrier tracking L1 and L2 is on the order of one second. Hence any reading taken more often than once a second would be correlated. The maximum independent information rate is once per second.

One of the reason's these units measure short is this fact. There is also an issue with going too slow. The velocity is calculated from the doppler shift on the carrier ( the measured frequency of moving toward a transmitter is higher and moving away from the transmitter lower than the transmitted frequency). The point fix is not sufficient for velocity estimation. The doppler shift gives us range rate and range rate and locations can be used to estimate the velocity. The issue come from there is a mathematical lower bound to the doppler frequency error (Cramer Rao Bound) http://en.wikipedia.org/wiki/Cram%C3%A9r-Rao_inequality. This defines the best that can be done. This gives a lower bound on velocity. You get too slow your the percentage accuracy of the velocity measurement goes to hell in a handbasket.

I just found my old GPS spec. The lower bound for velocity standard deviation is .001 Hz which is about .67 mph. This is the mathematical best that can be done. I suspect it is at least double. In reality the error will be higher and by the time DOP is thrown into the equation. For a fighter aircraft at Mach II it doesn't matter much. However, this translates to about 11 to 22% (one sigma) at 6 mph or 5.5 to 11% at 12 mph. For the speeds we are talking about - I expect Dr. Q's bladder is probably more accurate.

Truman

Sisu West Ranch wrote:
While every increase in electronic technology will improve the accuracy of GPS position measurements part of the problem with using a GPS for an odometer is inherent in how it computes the distance.

I just looked up Magellan's top of the line WAAS enabled specifications. It takes a reading every second. Lets assume the following conditions for grins and giggles:

1. Each position it calculates is right on the money. (we do know that there is random error, but they may average out.)
2. The distance is calculated by assuming that you go on a straight line between each measurement.
3. The horse is moving at 16 K per hour (10 mph). In one second it will move at 4.4 meters (~ 4.8 yards). Exactly 0.5 seconds after the fix it makes an abrupt right angle turn and continues without slowing down.


Using elementary geometry, we have described a right triangle with legs 2.2 m long and a hypotenuse of 3.11 m long. That means that during the time of this turn 1.3 m have disappeared. Or looking at things another way, the measured distance is only ~71% of the actual distance traveled.

How can this error be reduced? The slower you go, the less error you will get. Simple geometry. The fewer turns, the less error you will get.


--

“Since when have we Americans been expected to bow submissively to authority and speak with awe and reverence to those who represent us?” Justice William O. Douglas


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Replies
[RC] GPS accuracy, Sisu West Ranch