Systra is an adjustment program which computes unique coordinates from redundant inconsistent observations. It distinguishes itself in particular by concepts of automated analysis and a very high computing performance. The program sequence is subdivided in the parts proximity value calculation, strict adjustment with statistical analysis and homogenization. Each part can be switched on or switched off separately.

  • Observation types
  • Results
  • Hardware and computing performance
  • Proximity value calculation
  • Strict adjustment and statistical analysis
  • Homogenization (proximity fitting)
  • Data interface

Observation Types

The following observation types are processed by Systra:

  • Reference coordinates
  • Digitized coordinates
  • GPS coordinates
  • Point identity
  • Rectangularity
  • Rectlinearity (3 points)
  • Alignment (n points)
  • Parallelism
  • Parallelism with distance
  • Distance point-line
  • Aligning base (abscissas and ordinates also seperately)
  • Total station measured values (directions and distances also seperately)
  • Range distance
  • Straight line intersection
  • Circle (radius, sag, angle at centre, peripheral points)


The results of the adjustment calculation are saved in a protocol file Systra. OUT and for the subsequent process in ASCII files. In detail following values are putted out:

  • Adjusted coordinates
  • Empirical standard deviations of the coordinates
  • Error ellipses
  • Adjusted transformation parameters
  • Residuals
  • Parts of redundancy
  • Normalized residuals
  • Displacement vectors of the homogenization
  • List of the 10 largest normalized residuals
  • Variance components and parts of redundancy grouped by observation types

Hardware and Computing Performance

The standard design is laid out for 50,000 points and 50,000 observations and runs on customary PCs or notebooks. The number of points and observations to be processed depends only on the available RAM of the computer. If necessary a version with an arbitrary number of points can be delivered. Nevertheless, from a technical point of view a project size of more than 250,000 points does not make sense any more. An adjustment calculation with Systra needs on a customary PC with a project size of 50,000 points approx. 10 seconds.

Proximity Value Calculation

The observation equations used in Systra are non-linear generally. Because the least squares method is defined only for linear problems, these observation equations have first to be linearized. For the linearization proximity values of the unknown coordinates and transformation parameters are required.

Systra don’t need any externally introduced proximity values. Rather these are automatically generated whereby it is not necessary to give an arithmetic way. By use of the very robust solution approach of conjugated gradient this calculation step leads to a result even if the data contain blunders.

In an iterative process recognized blunders are eliminated stochastically. Results of this first calculation step are the proximity values in request as well as the observations corrected by blunders.

Strict Adjustment and Statistical Analysis

In this step the actual adjustment problem is strictly solved by the least squares method. The calculation proceeds in several iteration steps in whose course the non-linear problem is solved using Newton's method. After achieving the solution point analysis values are determined for the observations and the calculated coordinates. The results are in detail:

  • Adjusted coordinates
  • Transformation parameters
  • Error ellipses and empirical standard deviations of the coordinates
  • Residuals, parts of redundancy and normalized residuals of the observations
  • The results are logged in a standard conform analysis protocol and as well machine readable in ASCII-Files.


Each observation can be weighted individually or by association with an observation group. In this manner the different accuracy of the observations is modeled.

Treatment of Reference Points

For analysis purposes reference point coordinates can be introduced in the adjustment calculation as observations. On this way identity errors in reference points can easily be recognized and be eliminated, while the normalized residuals are used as test values.

Homogenization (proximity fitting)

The observation type digitized coordinates a specific feature shows compared with other observation types: The coordinates are subjects of distance-dependent correlations. The calculation step homogenization realizes the modeling just of those correlations. For this purpose the original digitized coordinate observations are exchanged by neighborhood observations. All the other observations remain unchanged in the adjustment model.

By some digitized objects (e.g. houses) geometrical constraints are known like rectangularity, rectlinearity or parallelism. These constraints are introduced in the homogenization model as observations.

The neighborhood observations are automatically generated from the digitized coordinates. For this a Delaunay triangulation is carried out over all points of a digitized system. Along the originating triangular sides coordinate difference observations are introduced. The observed values of these observations are derived from the digitized coordinates of the involved points.

The stochastical model of these observations works in a way that the originating triangular net shows under distortion the behavior of an elastic membrane. It should be pointed out to the fact that all observations, also constraints and geodetic measured values, equally take part in this adjustment step. Therefore it does not come for violations of the neighborhood geometry as they appear with the usually usual sequential calculation approach.

Data Interface

The adjustment module Systra is a pure arithmetic kernel which is controlled by ASCII-Files and also generates those as result. This robust and transparent kind of  data exchange allows integrating the module into already existing software architectures. Also the other modules of the program system communicate via this interface with the adjustment kernel.

Input files


project information


control parameters


reference coordinates


locale coordinates


range distances, point identities


additional observations

Output files


adjusted coordinates


adjusted transformation parameters


results of statistical analysis

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