QA- Using Least-Squares Adjustment

What is a Least-Squares Adjustment

 When you have multiple (redundant) measurements to compute an unknown value, a least-squares adjustment might be appropriate to get the best estimate of the unknown value (using all these measurements).

 For example, when you measure a few time a linear distance, a simple average will provide you the best estimate for this distance. It turns out that this simple average is a least-squares.

 In GNSS, when you establish a network of points, you may observe a multiple of vectors connecting all these points, which makes the calculation of the best position for each of these point a complicated task.

 The least-square adjustment is the solution to this problem.

What is Redundancy in a Network of Vectors?

Least-Squares Adjustment Parameters

Basic parameters of the network adjustment are set under Tools > Options... > Network tab.

 You can adjust your network through a Fixed Stations mode or a Weighted Stations mode. To switch between modes, look in the type of adjustment dropdown list;

 You can set a confidence level of the error ellipses;

 Select the representation mode (3D or 1D+2D);

 You can toggle summary sections to customize the adjustment summary;

 Finally, you have control on the display of error ellipses in the Plan View (site ellipses or vector ellipses).

Site Positions before Adjustment

Before the adjustment, you have access to a list of all your positions in Analysis > Survey Sites > Post-Processed Coordinates.

Here is a simple rule to follow when in doubt: the network should be adjusted if the number of new point (unknown point) is less than the number of baselines (excluding vectors between known points), that means a ratio < 1.

Type of Adjustment

 

Fixed Station mode

Coordinates of reference site (site with known coordinates) are held fixed in the adjustment. The software assumes the coordinates are errorless. If they are not accurate, final positions will be biased (as well as their statistics). You can use as many fixed station as you want.

 

Note: The following modes are recommended for advanced users only.

 

Fixed Station with Auxiliary Parameters mode

Coordinates of reference sites are held fixed in the adjustment (a minimum of 3 references is required to use this mode). The software assumes the coordinates are errorless. Three rotations and one scale value are estimated along with station coordinates (this information is useful when the reference network is not well aligned WGS84).

 

Weighted Station mode

Coordinates of reference sites are not held fixed in the adjustment. A level of uncertainty is attached to each reference sites to reflect their non-perfect accuracy. This is done through sigmas (standard deviations) that can be entered in the Site Editor (Edit Sigmas).

Note that the solution type and standard deviations are not displayed if the site is connected to more than one baseline.

Site Positions after Adjustment

After the adjustment, you have access to a list of all your positions in Analysis > Survey Sites > Post-Processed Coordinates. The site standard deviations are now displayed.

How to Adjust your network

Once all your baselines are processed, go to Tools > Process Manual > Adjust Network to adjust your network according to the reference sites used and the selected adjustment parameters. Least squares results can be seen under Analysis > Network Adjustment which gives you access to the Network Adjustment Summary and the Network Adjustment Residuals.

Article: 000030

Related Products: EZSurv

Last Update: 2017-03-30 20:05:44

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