a 3D Method combining precise trigonometric levelling, reflectorless EDM, and free stationing (resection) using a Leica TPS1200 total station

$Id: method2.html,v 1.36 2008/07/03 22:10:45 james Exp $

This method combines precise trigonometric levelling (developed by Charlie Glover and popularized by Jesse Kozlowski) with reflectorless and free stationing.
The goal of this technique is to rapidly gather horizontal data that passes the 2005 ALTA positional tolerance test (relative positional accuracy or RPA) of 0.07' and 50ppm while simultaneously gathering vertical data that rivals the accuracy of a good level loop.
Most shots are taken with reflectorless.
For the few shots that have to be taken to a point on the ground, such as an initial elevation from a benchmark, a single prism pole with a pair of 8' bubbles is used in a bipod in an "unraised" position that is carefully measured. We experimented with using a non-adjustable 2m GPS pole in order to get height above thermal layers as suggested by Kozlowski, and while this works well for elevations, for our 3D purposes, it creates too much horizontal error, most likely due to the combination of the extra height and the less sensitive (40') bubble.
Because we are mixing reflectorless shots with rod shots, the height of the rod must be carefully measured. One possible technique for doing this would be to take a reflectorless shot to a point on a vertical surface, then place the rod tip on that point, held with a bipod at an angle (not plumb!), and take a shot to the prism. After averaging several shots to each point, inverse the distance between the points to get a fairly precise rod height.
In theory, a -40mm offset "true nodal" prism would place the true node of the prism directly over the plumb line of the rod regardless of prism tilt or misalignment. We have not yet tested this. In practice, a Leica -34.4mm prism works well at distances of 50ft or more, with careful aiming of the prism.
A 360 degree prism such as are frequently used with robotics does not work very well for this technique. Using ATR with the 360 prism at the shorter ranges used in this technique means that the ATR sees the EDM return signal in two prisms and will aim at the one with the stronger return, resulting in H&V error greater than that of a single circular prism. This effect seems to subside at distances of greater than 200', however, that is the outer margin of usable data for the precise trig level technique due to C&R and vertical circle accuracy of a production-grade total station.
The initial elevation is taken from a benchmark and transferred to premarks on vertical surfaces such as crows feet, tacks, bolts, or paper or vinyl adhesive targets ("sticky-backs"). Horizontal data is also collected for these points, making all such points 3D.
Because most of our shots are reflectorless to the point itself and not a rod plumbed over a point with a bubble, target centering error is eliminated for most shots. (Pointing error, circle reading error, and EDM error remain)
Because the Leica "resection" program uses not only angles but also distances, it would be more properly called a "free stationing" program.
Because we use the onboard free stationing program, every instrument setup can be a random free station, centered in the head of the instrument (HI=0.00)
By free stationing through the head of the instrument (HI=0.00) and not over a point, almost all instrument centering error (horizontal & vertical) is eliminated.
Because we avoid the target centering error of a rod bubble, the only bubble involved is the digital bubble in the instrument.
At closer ranges, 100 feet or less, using the reflectorless also eliminates prism aiming error, which is the error introduced by a prism's nodal center offset not being exactly on line.
Because we are not trying to occupy a known point, there is no centering error compared to a "point on the ground". The occupied point is in the head of the instrument, where the error is reduced to the motion of the instrument centers, quite small compared to 1.5m of plumb line over a point, and especially small compared to the error in a pocket tape measure up.
Because we thus eliminate instrument centering error, that error is not propagated forward into new control.
Because the onboard free stationing program uses least squares, we have a "most likely" position & orientation of the instrument from which to turn sets and extend our control network.
Because we use the freestationing program for every instrument setup, we have a known 3D error ellipse for the setup and residuals for the observations to the control points from which the setup position is being derived.
Because we have the coordinate quality and the observation residuals, we can decide before proceeding whether the setup is good enough from which to extend control or take sideshots.
Because we have the coordinate quality and the observation residuals, we know what size of errors we are propagating forward in our control network.
Because most of the new control is set via reflectorless shots to vertical surfaces, we eliminate target centering error as well.
Because these free stations are turned thru the head of the instrument (rather than over a point on the ground, with an imprecise pocket tape measure-up), the verticals are much more precise, and this vertical precision adds to the strength of the horizontal positioning. This is an important feature of the method. By eliminating rod bubble plumb error and target centering error, we tighten the horizontals. By eliminating instrument height (pocket tape) errors and by following precise trig level methods, we greatly reduce the vertical errors and their propagation.
Because we have eliminated instrument and target centering errors, we have eliminated the two largest error sources in a total station setup. These two errors cannot be eliminated by redundant measurements within a single setup, and with multiple setups, will only be seen as random errors. (see Ghilani & Wolf's "Adjustment Computations & Spatial Data Analysis")
Because these errors are eliminated, error propagated forward by extending the network of observations (that normally thought of as a foresight in a traverse) is greatly reduced.
Because Kozlowski suggests working in distance increments as dictated by the std. error of your instrument's vertical circle, an optimum number of horizontal and vertical combined sets can be calculated for standard procedure.
Because the centering errors of instrument and target are practically eliminated via these methods, the optimum number of sets required to achieve a given accuracy will be fewer than with traditional methods.
Initial experiments with a Leica 1203 suggest that using these methods, one can indeed move ahead extending control, 30-50m at a time, keeping an eye on residuals, and every subsequent instrument setup will have an average error ellipse (95% confidence) of 0.015' in horizontal and 0.009' in vertical.

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