CompuServe Messages

The position movement seen when standing still may be the result of either SA or of picking up a reflected signal from a particular satellite. If the Scout is in "navigation" mode, it probably "expects" you to be moving, so the jumps that you get within the normal spot accuracy of the system may serve to set it off tracking a false course. I'm not familiar with the Scout in any detail, but most Trimble receivers incorporate a Kalman filter (predictive) model into the positioning computation. You also have to bear in mind that the system has a particular quoted "accuracy". To get a "proper" fix on a static location you should really occupy it for a period of time, taking positions at frequent intervals. These positions will jump around a little. If you plot them out you'll get ( in 2 dimensions) a scatter plot which will usually have an elliptical shape, with size and orientation dependent on current satellite geometry. This set of positions will usually have a normal ( gaussian ) distribution. It is possible to compute the magnitude of the standard error at any orientation around the point from the size of the semi major and semi minor axes and their orientation. Unlike the standard error of a one dimensional set of observations, which identifies the limits within which around 68 percent of observations will fall, the SE value of a 2 dimensional data set indicates the limits within which 39 percent of observations will fall: ie, 61 percent of your fixes will fall *outside* the one standard error ellipse. ie, over 6/10s of your fixes taken will fall outside this ellipse, *but they are still perfectly valid fixes, since the observations falling in the *tails* of a gaussian distribution are just as valid as those falling towards the mean value. To get the size of ellipse within which 95 percent of your fixes will fall ( a fairly standard figure used as a confidence level in many applications), you need to scale up the axes of your original ellipse by a little under 2.5. This is a very empirical ( rather than theoretically rigorous) illustration, but basically, once you have established the size of your error ellipse, the fix can jump about within those ellipse boundaries as much as * it likes*… even from one end of the major axis to the other on subsequent fixes, and the receiver has still given you a *statistically valid* position. Even the odd *valid* fix ( about 5 percent of the total!) which falls outside the 95 percent ellipse boundaries must be allowed for. What this gives us, though, is not an *accuracy* for the fix… it is the *precision* of the fix…. ie, a measure of the spread of random errors within the observed system. This *precision* only accounts for random errors. Non-random errors such as biases in observation will not contribute. ie, we could have a very tight gaussian curve for a set of positions who's mean is nevertheless a long way from the "true" position due to an uncorrected bias ( such as observing a reflected range from one satellite). On the other hand, poor satellite geometry could give us a very low, wide gaussian curve who's mean is very close to the "true" position of a spot. Consequently, we have to add a factor called *reliability* to the factor called *precision* in order to obtain an estimate of the thing called *accuracy*. I don't plan to go into the statistics here, but reliability is basically a statistical determination of the likelyhood of being able to detect a gross (non-random) error of a certain size within a set of observed values. Many (most?) adverts and other literature actually quote the precision achievable with a particular instrument, rather than it's accuracy. In any event, precisions should always be quoted with a confidence figure attached ( ie, 95 percent, 2 sigma, 39 percent etc). Sorry about the lecture <g>. Most of the above may not be new to you, but I would say that 30 percent of my time is now spent explaining the above to people within the oil industry when they've been "sold a lemon" on positioning of a survey. You guys live or die by your own efforts, it seems, but in oil companies the advent of GPS has led to explorationists deciding that they no longer need surveyors, since they now have black boxes to replace them. I'm not complaining too much, though, since I'm now making more money rectifying geophysicist's screw-ups than I ever made in gathering and processing the initial data for them<bg>. Next installment will be on datums. Rob