Surveying Network Simulation¶
Purpose of Survey Layout Simulation¶
Survey layout simulation is performed to assess the quality you can expect from the network before conducting field measurements. Through this process, you may discover that you do not need to measure as extensively as originally planned, saving both time and resources. Alternatively, calculations may show that additional measurements are necessary to achieve the desired network quality. Without simulation, you risk having to return to the field for additional measurements.
In simulated calculations, the final coordinate values for the unknowns are of no interest since the observations are planned, not actual. However, we need the left side of the reduced normal equation matrix to calculate standard deviations, error ellipses, and internal and external reliability.
Standard Deviations and Error Ellipses¶
In ordinary adjustment, standard deviations for the unknowns are calculated by multiplying the square root of the weight coefficients \(Q_{xx}\) with the estimated standard deviation of the unit weight. In simulation, the estimated standard deviation of the unit weight is replaced with the assumed value.
The same principle applies to the calculation of error ellipses. The assumed standard deviation of the unit weight is used instead of the estimated value.
Internal Reliability¶
Redundancy depends only on the network geometry and observation weights. Simulation of redundancy is therefore performed in the same way as ordinary calculation.
For Largest Remaining Gross Error (in multiples of the standard deviation), the situation is more complex. In ordinary calculation, the gross error is estimated and a confidence interval is calculated around the estimated value. The confidence limit indicates the largest remaining gross error. In simulation, we cannot perform gross error detection to estimate gross errors, but instead use the statistical expectation value of the absolute value of the gross error parameter.
Info
The assumed standard deviation of the unit weight is used to calculate the confidence interval in simulation.
With support from the figure under Theoretical Description of the Method, we see that the Largest Remaining Gross Error becomes \(m_{\nabla}\), where \(0.8 \cdot m_{\nabla}+ m_{\nabla}T_\alpha /2\) is the standard deviation of the gross error estimate based on the assumed standard deviation of the unit weight.
External Reliability¶
External reliability is calculated as maximum deformation in the usual way, but Largest Remaining Gross Error is based on expectation values as described for internal reliability.
Theoretical Description of the Method¶
Calculation of standard deviations, error ellipses, and redundancy has been described previously. Here we address how Largest Remaining Gross Error can be estimated by simulation.
Figure: Calculation of the expectation of the absolute value of measurement error
The starting point is the estimated gross error. We assume that the observation error is random and normally distributed, and look at the expectation value of the absolute value of the error.
As the calculation in the figure shows, the expectation value becomes 0.80. The expected gross error therefore has the numerical value \(0.8 \cdot m_{\nabla}\), where \(m_{\nabla}\) is the standard deviation of the gross error estimate based on the assumed standard deviation of the unit weight.
Calculation of confidence intervals is covered under Reliability. In simulation, the same method is applied, but estimated \(m_0\) is replaced with assumed \(m_0\).
Creation of Simulated Survey Data¶
The simulated data is entered as project data through the lists for coordinates, conventional observations, and leveled height differences.
Coordinates¶
Start by registering the coordinate values for the known points in the area in the point list. Use the Survey Point icon for this.
Then supplement with new points with approximate coordinates. It is advantageous to have all relevant information in the model - plan data, map data, known 3D constructions, etc. This makes it easier to find good station points that will not disappear during the construction period.
Important
All new points must have STATUS=Unknown.
From the entered points, relevant observations are registered - conventional observations and/or leveled height differences.
Tip
When observations are registered, the calculation of standard deviations will be based on the instrument parameters for the selected instrument. Always check these parameters before starting the registration of survey data.
Conventional Observations¶
Simulated surveying observations are entered into the project via the station list for conventional observations.
Procedure
- First create a station by pointing to the station point
- Then add observations by selecting New observation and pointing to the target point
- Repeat this for all relevant target points
Note
You can create the station point at the same time as you create the station. Instead of pointing to an existing station point, you point to the desired location on the map. The program suggests a Point-ID for the new point, which you can change if needed.
The observations entered in this way are calculated from the coordinates of the station and target points. During calculation, the adjustment corrections become 0 for all observations since there are no contradictions between the coordinates and the observations, or between the observations themselves.
Direction, zenith, and distance are shown in the parameter window if both the station and target points are defined in plan and elevation.
Important
The instrument code is decisive for which standard deviations the observations receive.
Leveled Height Differences¶
Leveled height differences are entered via the station list for leveling. You can then point to the station point and target point respectively.
The observations entered in this way are calculated from the elevations of the station and target points.
Activation and Deactivation of Simulation¶
Calculation of standard deviations, error ellipses, and internal and external reliability is performed in the same way as with real observations, using the same menus and functions. The only thing you must remember is to specify that you want simulated calculation.
Note
Gross error detection and testing of the basis (global test) is not relevant since the observations are planned and not real.
The function to activate simulation is found on the calculation tab.
Simulation Activated¶
When simulation is activated, the following premises are set for the network calculation:
- Assumed standard deviation is used instead of the estimated
- Expected measurement error is used instead of the estimated
- On the application layer it is shown that simulation is active
Simulation Deactivated¶
When simulation is deactivated, ordinary calculations are returned to. All premises that were defined are removed, and normal calculation can be performed.
Important
Any simulated observations still remain in the lists and must be removed from there if the observation files contain both measured and simulated data!