I realize that this is a point that folks who routinely adjust GPS vectors in combination with conventional observations will probably fully appreciate, but I'll post this example anyway. I positioned three control points and one boundary marker by GPS vectors on Friday. The vector lengths were short, under 3 miles, but the setting was ugly. These were all in small clearings in Live Oak and Cedar forest and hardly ideal conditions. The GPS vectors gave positions for the four points that reflected the problematic setting.
A diagram of the situation:
To give an idea of scale: 83-84 is about 70 ft. and 83-85 is about 142 ft.
The following are the positional uncertainties expressed as 95% Confidence error ellipses when the GPS vectors were run through Star*Net to compute the coordinates of the points and estimate their uncertainties.
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GPS Only
Station Coordinate Error Ellipses
(95% Confidence) US Survey Feet
Sta. Semi-Major Semi-Minor Elev.
Axis Axis
83 0.077 0.049 0.248
84 0.064 0.036 0.146
85 0.102 0.056 0.420
1222 0.090 0.041 0.270
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To verify that the GPS vectors were free of blunders and to tighten things up, I stopped back by the site today and measured angles, distances, and elevation differences between the same four points and added those conventional observations to the adjustment in combination with the GPS vectors.
A diagram showing the stations connected by additional conventional observations:
And these are what the positional uncertainties expressed as 95% Confidence error ellipses of the same points looked like when those conventional observations were included with the GPS vectors in the adjustment in Star*Net to compute the coordinates of the points and estimate their uncertainties.
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GPS + Conventional
Station Coordinate Error Ellipses
(95% Confidence) US Survey Feet
Sta. Semi-Major Semi-Minor Elev.
Axis Axis
83 0.039 0.028 0.109
84 0.045 0.024 0.109
85 0.053 0.031 0.111
1222 0.038 0.029 0.111
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Big improvement. Would recommend.
By the way, the path to the clearings where I made the ties by conventional angle and distance measurements between the four markers crossed a dry branch. This approximately 4,700-year-old point (probably an example of what is known as "Bulverde" in Texas archaeology) jumped out at me from the bed of the dry branch and, purely reflexively, I grabbed it and wrestled it into my shirt pocket.
In the first graphic the error ellipses are tilted. Why is this? Just curious.
> In the first graphic the error ellipses are tilted. Why is this?
Those error ellipses are based upon the covariances of the GPS vector solutions and so would depend upon in part upon the geometry of the satellites used in the solution. The masking effect of foliage varied somewhat from station to station.
For example, here is the vector from Pt. 10 to Pt. 85 in Star*Net covariance-weighted format:
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C 85 'SPIKE.WASHER
G0 'V797 Day228(0) 23:13 00026511.ssf
G1 10-85 -4467.373887 -109.718331 -1160.690160
G2 1.01220944258293E-005 5.44990845895729E-005 4.09846063106823E-005
G3 1.37338236131181E-005 -1.50407662522338E-005 -3.94780019011602E-005
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In the above, the quantities are:
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C 85 'DESC
G0 Vector info
G1 From-To DeltaX DeltaY DeltaZ
G2 xx yy zz
G3 xy xz yz
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All were taken directly from the Aposteriori Covariances estimated by the baseline processor.
> Those error ellipses are based upon the covariances of the GPS vector solutions...
The covariance data would affect, but not govern, the ellipse size but the direction would depend more on the delta x,y,z between redundant measurements, would it not?
Hmmmm... after review of some data, I see that the error ellipse orientation is derived from the covariance.
> Hmmmm... after review of some data, I see that the error ellipse orientation is derived from the covariance.
Yes. The covariance is what characterizes the uncertainty in the nominal vector expressed by the DeltaX, DeltaY, and DeltaZ values.
This is why one can enter OPUS-derived positions in Star*Net as vectors of nominal length of zero (DeltaX, DeltaY, and DeltaZ = 0) about the NAD83 position reported by OPUS, and with the variances and covariances (xx, yy, zz, xy, xz, and yz) extracted from the covariance matrix reported by OPUS used to form the G2 and G3 lines.
I don't pay as much attention to the error ellipses as I do the residuals. Once I'm happy with those I'll scan the ellipses for magnitude, but hardly ever for orientation. I long ago shut off the ellipse display in the plot screen.
> I don't pay as much attention to the error ellipses as I do the residuals. Once I'm happy with those I'll scan the ellipses for magnitude, but hardly ever for orientation. I long ago shut off the ellipse display in the plot screen.
I usually take a look at the error ellipse display on the screen with the ellipses drawn at sufficiently exaggerated scale to shown up clearly. I find it gives a quick qualitative overview of the survey, making it easier to diagnose weak spots.
Otherwise, the standard errors in N, E, and Up are the figures of merit I like since the object is to get them within the limits that I know from experience can be met with minimal increase in effort.
