A Comprehensive Least Squares Adjustment Tool

Ez-Adjust: A Comprehensive Least Squares Adjustment Tool

Hashimi, Sayed R


Ez-Adjust is a comprehensive least squares adjustment package for the surveying professional. The main components of the package are: adjustment of GPS and terrestrial observations, 2D horizontal control network adjustment with the option of reducing the observations to grid using a plane coordinate system such as State Plane Coordinates, level network adjustment, four-parameter coordinate transformation, and a geodetic calculator. The adjustment modules have data entry features using the keyboard. Each module contains context-sensitive on-line help, several tutorials, example data sets, and a complete printable manual in pdf format. The software is available free of charge to all academic institutions in the U.S. and can be downloaded from http: //www.srh-leastsquares.com.

Adjustment Modules

The package is divided into two main modules; EzaPro for GPS and terrestrial observations, and Eza for 2D and level network. The supporting sub-modules within EzaPro are: Data Entry, Import Base Line Files, Geoid Modeling, Geodetic Calculator, Define Instrument, and Coordinate Transformation. The sub-modules within Eza are: Data Entry for 2D and level network, and Leica Digital Level Import. Each of these sub-modules is discussed further in the following sections.


This module of Ez-Adjust performs adjustment of GPS base lines forming a control network. The adjustment project can include terrestrial observations (both horizontal and vertical angles, and distances). The input options are accomplished inside the Project Setup dialog box as shown in Figure 1.

Control files contain points whose coordinates need to be held fixed. We distinguish between geographic (latitude, longitude, and height above ellipsoid), State Plane (northing, easting and height above ellipsoid), or geocentric (X, Y and Z) coordinates. An adjustment project may contain any number of Control, GPS Base Line, and Terrestrial Observation files. Some of the other options within the Project Setup include selection of a plane coordinate system, redefining the parameters of a plane coordinate zone, and incorporating errors in centering and antenna heights (Figures 2 and 3).

Output Options

Displaying the adjusted results in a more meaningful way, such that one can see the observations with the largest residuals (as shown in Figure 4), is another important feature of Ez-Adjust. To view the results, the user only needs to click the appropriate residual column heading to initiate sorting of a given type of observation. The file name where the observation resides is shown in the last column of the Residuals displays. Double clicking the file name opens the corresponding file inside a multi-document editor.

GPS Base Line Import Files

This utility, as shown in Figure 5, is designed to facilitate the importation of processed base lines that have been generated by a GPS manufacturers’ base line processing software. The import function also provides a user-defined data format as shown in Figure 6.

Geoid Modeling

This module enables the computation of the geoidal separation using the NGS geoid 2003 model (Figure 7). The geoid modeling utility accepts input from the keyboard or from an ASCII file. Similarly, one can write the contents of each table to the printer using the Export option, or manually select parameters in the desired order and export them.

Coordinate Transformation

This function provides a four-parameter-similarity coordinate transformation. Its input options include full covariance information (Figure 8), and the input data can be adjusted using three adjustment options (Figure 9).

Instrument Definition Table

The Instrument Definition Table supports 3D adjustment by storing specifications for up to ten different instruments that can be used in the adjustment.

Data Entry

Ez-Adjust expects all input data in an ASCII file in a specific format. The file for processed base lines is created automatically using the Import Base Line Files utility (see Figure 5) discussed earlier. The Control file and the Terrestrial Observations file can be created using any text editor or the Data Entry module. An overview of the Data Entry is shown in Figure 11.

The Data Entry module can read and display an existing ASCII file and it also writes an ASCII file that can subsequently be used in the adjustment. The terrestrial observation files have a *.usr (user) file extension and the control file have a *.txt file extension.

Geodetic Calculator

The EzaPro’s geodetic calculator is independent of any adjustment. The calculator’s functionalities can be explored using the Coordinate Conversions, Plane Coordinates, and Geodetic Coordinates tabs (Figure 12). The input fields are color-coded, with yellow signifying an optional field, white a required field, and aqua a calculated field.

The calculation of plane coordinates using the geodetic calculator is shown in Figure 13; Figure 14 shows a similar calculation performed for geodetic coordinates. I have found the geodetic calculator to be an extremely useful tool in surveying programs.

Other useful features of the geodetic calculator are its ability to integrate the Geoid 2003 model, and input and output data from and to ASCII files.


The Ez-Adjust’s Eza module performs adjustments of level and 2D horizontal networks, which can include reduction of observations to State Plane Coordinates. The display format of the adjusted results is very similar to that of EzaPro. The input option is, however, slightly different (Figure 15); in essence, unlike in EzaPro there is no need in Eza for the control points to be in a separate file.

Data Entry

As stated earlier, all input to both EzaPro and Eza comes from ASCII files. The Two-D Data Entry (Figure 16) and the Level Network Data Entry (Figure 17) options provide convenient means of creating such files under program control.

Leica Digital Level Support

Ez-Adjust supports the processing of observations collected with Leica’s digital levels in Eza. The data can be imported by specifying the weighting criteria and instrument type (Figure 18).


The Ez-Adjust software package is designed for real-world applications in surveying, as well as for student use in academia. I have found the Geodetic Calculator to be a very useful tool for coordinate conversion, State Plane Coordinate application problems, as well as such geodetic calculations as the calculation of geodetic lines and their azimuths. The package can be used by students to check their solutions or to perform adjustment on large data sets where other software may fall short. Both adjustment modules of Ez-Adjust have step-by-step tutorials and example data sets. The context-sensitive on-line help and the ready-to-print documentation are excellent resources for anybody wishing to learn how to use the software.


NGS Website, June 2005. [http://www.ngs.noaa.gov/].

NGS Website, June 2005. [http://www.ngs.noaa.gov/GEOID/GEOIDO3/download.html].

Ez-Adjust Website, June 2005. [http://www.srhleastsquares.com/].

Sayed R. Hashimi, Professor, Surveying Engineering Department, Ferri’s State University. E-mail: .

Copyright American Congress on Surveying and Mapping Sep 2005

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