TerraPos is utilized for post-processing of the navigation solution. The processed solutions are then exported as a text file (ASCII-format) and imported in MAT- LAB for further analysis.
4.5.1
Generating XML files of various amount of tie points
An efficient selection of tie points involved reducing the dataset by half its size, recursively, until an interval by a certain amount of points was detected. The aim is to locate the least amount of tie points necessary to preserve the required accuracy.
In large datasets, such as this, it is necessary to utilize an efficient time-saving method for the detection of a significant amount of points, without having to search through the entire dataset. Searching through every possible combination would be unnecessary and time-consuming.
The halving method used corresponds to a bi-sectioning procedure, and would much faster located the interval of interest. Every combination are hence not evaluated, but as later argued, would be of no use either.
The selection of edited XML-files was post-processed in TerraPos to locate the minimum amount of tie points needed. Calculation of the 95 percentile of the po- sition errors was used to detect the significant threshold. This is further explained in the following RTP analysis section.
Findings from this procedure are plotted in Figure 4.9 and 4.10, presented in the subsequent section.
4.5.2
Post-processing in TerraPos
The necessary processed solutions for the analysis include the reference trajectory, the non-aided trajectory and several versions of RTP aided trajectories, for the purpose of the hypotheses testing.
Generating the reference trajectory To assess the absolute accuracy, ex- pressed by true errors, a reference is necessary. The reference trajectory is based upon all possible information available, including all the available adjustment
points and tie points, the base station reference, in addition to the INS and odome- ter data. The accuracy of the adjustment points is about 2 centimetres, and the points are evenly spread apart by a distance of 10 or 20 meter throughout the tunnel.
As previously emphasized, the DGNSS aiding only contribute with information outside the tunnel. Still, GNSS data are used to derived the estimate of the complete trajectory. The reference solution will therefore have the best available position aiding, and will involve the least amount of accumulated error for each tunnel run.
It is to be expected that the quality of the reference trajectory is dominated by the accuracy of the adjustment points, and therefore be at the level of a few cm.
Minimal-aided solution The non-aided solution only include the inertial nav- igation sensor and the odometer measurements. Hence this solution is based on nearly free-inertial properties. The generated solution represents the abso- lute worst case scenario, due to inclusion of the minimum amount of information. Since the positioning solution based on the IMU will tend do drift over time, when lacking proper positioning aid, this solution will have the largest accumulation of errors for each tunnel run. The drift in position is due to the error propagation in the integration of the IMU sensor outputs, noise in the odometer data, and imperfect knowledge of the navigation states at each end of the outage.
RTP aided solutions In addition to RTP solutions including all available tie points or no tie points at all, solutions are also generated for various amounts of tie points. The applied bi-sectioning method for editing XML-files explained previously is used to process the corresponding RTP aided processed solutions in TerraPos. The solutions will serve as the basis of the hypotheses testing and analysis in the following section.
Export from TerraPos For the export, a predefined format file was first gen- erated. This simplifies the process of export, as every export will turn out exactly the same. Since the object of research are the tunnels, the export include the use of a so called ”event file” containing the 1 Hz rate time events in GPS time for the tunnels only. The event files where generated in MATLAB, corresponding to a simple vector n-dimensions saved as a text-file output in ASCII format. By utilizing these event files in the export from TerraPos, the result is data only for the tunnels of interest. This is how the various solutions in terms of speed and number of runs are generated.
Number of tie points The table below states how many tie points the various XML-files used for the RTP position aided in the post-processing.
1d points 2d points Tie points total
Solution for 11 m/s 26 73 99
Solution* for 20 m/s 26 61 87
Solution** for 20 m/s 30 57 87 Both * and ** for 20 m/s 41 81 122 For all six solution 47 85 132
Table 4.1: Number of tie points in the respective XML-files used in post-processing.
The notation * and ** denotes two distinct combinations of runs sampled by speed of 20 m/s. In total there are four runs sampled at this velocity, and the first two and the last two of these four are implied by the asterisk notations. Hence it only implies two different combinations of runs, not containing the same processed solutions.
MATLAB computation
MATLAB is used for the purpose of generating the statistics from the TerraPos exported solutions, resulting in plots and tables for further analysis. The results are given in the analysis and discussion section that follows.