## 5 Results
Figure 19: (**a**) Red dashed line—reference path. Blue solid line—estimated path with a help of GPS receiver, inertial sensors, probability map, stereo camera and 3D model of the environment. The positioning is quite precise. The errors are mainly introduced by the error in estimating the heading direction. (**b**) Histograms of distance errors. Figure 20: (**a**) Red dashed line—reference path. Blue solid line—estimated path with a help of inertial sensors, probability map, stereo camera and 3D model of the environment. When the initial position is known, the filter can estimate the pedestrian location with smaller errors than the GPS receiver. (**b**) Histograms of distance errors. Figure 21: (**a**) Red dashed line—reference path. Blue solid line—estimated path with a help of GPS receiver, inertial sensors, probability map, stereo camera and 3D model of the environment. The error of estimating direction at (400 \(\mathrm{m}\), 120 \(\mathrm{m}\)) introduces big errors later on. The filter managed to recover at (240 \(\mathrm{m}\), 80 \(\mathrm{m}\)). (**b**) Histograms of distance errors. Figure 22: **(a)** Red dashed line—reference path. Blue solid line—estimated path with a help of the inertial sensors, _i.e._, gyroscope for estimating direction change and accelerometers for counting steps and their lengths. As times goes on, the errors accumulate due to angular random walk. **(b)** Histograms of distance errors. Conclusions  
The results were calculated based on _ca._ 1,900 GPS readouts, 3,400 particle filter estimates and 19,000 pictures from the stereo camera. The particle filter using all available data sources provides by far the best accuracy. For 99% of the time the accuracy is better than 4.5 m. This is still too large an error for safe navigation of visually impaired pedestrians. The main source of errors were introduced by misestimated direction, which is visible in Figure 22 at coordinates (410 \(\mathrm{m}\), 125 \(\mathrm{m}\)). The turn is misestimated by \(\approx\)20\({}^{\circ}\). This error is too large for the non-linearity error mentioned in Section 3.1.1 or any other gyroscope error. Possibly the sensors came adrift and did not change its direction accordingly. This error, when not corrected immediately, has a ripple effect. This can be, however, taken care of. Also, more accurate sensors are available on the market. It is surmised that an error of 3 m for 99% of time is achievable. It is interesting to note that when the initial position is known, the location of a pedestrian can be estimated without having to use a GPS receiver. The setup number 5 (see Table 1) gives best results after the setup number 4 and it is better than sole GPS readouts. Needless to say, this approach can be used in limited areas, e.g., inside buildings where GPS readouts are not available. The probability map concept limits the positioning error to the width of a street, _ca._ 10 m. Due to the imposed constraints on the pedestrian kinematics, the error dropped 3 times in terms of a root-mean-square error, which poses the best improvement from all other additional sources. As mentioned before, on the bases of GPS readouts and the probability map, a user's location can be estimated within _ca._ 10 m. A stereo camera can refine the user's position down to 2 m, providing there are no unexpected objects, or difficult objects like trees, whose crown's radius could differ from the assumed 2 m. GPS readouts complement nicely with the algorithm in which the depth images derived from terrain model and stereoscopy are compared. In the presence of high buildings, GPS readouts are compromised. Under these circumstances the image matching algorithm performs well as the walls of buildings are confidently detectable by a stereo camera. On the other hand, in an open space GPS readouts are accurate down to, _ca._ 2-3 m. Then in turn, the image matching algorithm has no reference points to perform a viable comparison. The presented algorithm works off-line. It is quite computationally demanding.