## 5 Results  
The results are presented by plots of paths, a histogram and a cumulated histogram of errors and a table that summarizes the errors. An interesting question is how much a given data source improves the accuracy of the positioning. Table 1 provides the answer. Therefore, several off-line tests were run with different combination of data sources. It was though assumed that the starting location is known. Otherwise, a bigger number of particles would have been necessary to find a first approximate location. Once, a rough location is found the filter is convergent. The initial errors might have been large and therefore eclipse the key point of measurements. On one side, this assumption might be justified. A pedestrian, e.g., a blind user goes out from his home, so he knows his location. On the other hand, a blind pedestrian might use the system when lost. The aforementioned distance error \(r_{e}\) is used as a comparison criterion. The results are evaluated by the following measures:  
1. Root-mean-square value, denoted by RMS\({}_{e}\),
2. Mean error, denoted by \(\mu_{e}\),
3. CEP50--Circle of Error Probability 50%--the radius of a circle encompassing 50% of errors, _i.e._, a median value,
4. CEP90--the radius of a circle encompassing 90% of errors, _i.e._, ninth decile,
5. CEP95--the radius of a circle encompassing 95% of errors, _i.e._, 95 th percentile,
6. CEP99--the radius of a circle encompassing 99% of errors, _i.e._, 99 th percentile,
7. Maximal error--the maximum value of an error recorded during a trial, denoted by \(\max(r_{e})\) \begin{table}
\begin{tabular}{|r|c|c|c|c|c|c|c|} \hline Setup & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline GPS & + & + & + & + & & & \\ \hline Inertialsensors & & + & + & + & + & + & + \\ \hline Probability map & & & + & + & + & + & \\ \hline
3D matching algorithm & & & & + & + & & \\ \hline RMS\({}_{e}\) [m] & 5.23 & 4.96 & 2.10 & 1.26 & 1.65 & 4.39 & 107.5 \\ \hline \(\mu_{e}\) [m] & 3.27 & 3.45 & 1.56 & 0.87 & 0.95 & 2.94 & 86.4 \\ \hline CEP50 [m] & 2.19 & 2.47 & 1.24 & 0.57 & 0.55 & 1.89 & 76.4 \\ \hline CEP90 [m] & 6.54 & 6.79 & 3.39 & 2.03 & 2.13 & 6.92 & 182 \\ \hline CEP95 [m] & 10.7 & 12.0 & 4.28 & 2.90 & 3.19 & 9.09 & 210 \\ \hline CEP99 [m] & 23.3 & 18.2 & 6.41 & 4.50 & 7.02 & 16.0 & 261 \\ \hline \(\max(r_{e})\) [m] & 30.6 & 20.6 & 8.64 & 5.24 & 12.8 & 25.5 & 265 \\ \hline Figure & 16 & 17 & 18 & 19 & 20 & 21 & 22 \\ \hline \end{tabular}
\end{table} 
Table 1: Results of the trial at the University Campus. Seven setups of data sources were simulated. The sign ‘+’ in a column denotes that a given data source was included in the simulation. Otherwise the data source is not used. Setup number 4 was carried out with all data sources on. The results for this setup are best. Figure 16: **(a)** Red dashed line—reference path. Blue solid line—estimated path with a help of a GPS receiver. In the presence of buildings, the GPS readouts are \(\approx\)30\(\mathrm{\SIUnitSymbolMicro m}\) inaccurate. The errors depends also on the satellites configuration against a building. This can be noticed for coordinates (220\(\mathrm{\SIUnitSymbolMicro m}\), 80\(\mathrm{\SIUnitSymbolMicro m}\)). The same place was revisited after a couple of minutes and the positioning error was very different. **(b)** Histograms of distance errors. Figure 17: (**a**) Red dashed line—reference path. Blue solid line—estimated path with a help of GPS receiver and inertial sensors. The readouts from the inertial sensors enable to eliminate big errors. The accuracy improvement is not significant due to errors in estimating direction. (**b**) Histograms of distance errors. Figure 18: **(a)** Red dashed line—reference path. Blue solid line—estimated path with a help of GPS receiver, inertial sensors, probability map. The probability map eliminates direction errors, by pruning particles that diverge from a reference direction. Therefore errors are instantly eliminated and do not propagate. The positioning errors are then described by random walk with bounds. **(b)** Histograms of distance errors.