**6.4. Simulations**

The algorithm was first tested with simulated data. The ray tracing algorithm described in Section 3 was used to calculate the impulse response function of a room. The outline of the room is shown in Fig. 3, alongside with 78 measurement points. At each point, 120 measurements were made by turning the bat-type antenna array in steps of 3 degrees. The simulated environment consisted of a rectangular room with the size of 8 m by 9 m, with a rectangular column the size of 1.5 m by 1.5 m roughly in the middle. Between the walls and the column, six complex objects used to test the object recognition algorithm from Section 7 were placed. Walls, objects and the column were assumed to be of metal. The frequency response function was calculated from 4.5 GHz to 13.4 GHz for an antenna array with three double-ridged horn antennas in the bat-type configuration. The distance between the antennas was set to 0.5 m.

Figure 21 shows the complete radargram for one whole rotation of the antenna array at point 16. In this example, it can be seen that for every angle, there are clear peaks in the impulse response that connect to peaks in the next measurement step, so data association in measurement space is possible. Mapping the whole room just from this position is not possible, because some features simply cannot be seen from there. To map the whole room, measurements from all 78 points were used. The result can be seen in Fig. 23. Walls, shown as solid and dotted lines, and corners, shown as triangles, are mapped at an accuracy of approximately 20 cm. Due to their small size, the placed objects are detected as point scatteres which are depicted as stars. Their positions correspond to the object locations shown in Fig. 3. At this point, a separate object recognition algorithm as described in Section 7 could be used to identify and distinguish them. Note that the origin of the coordinate system is set arbitrarily at the point of the first measurements.

**Figure 21.** Radargram at position 16 of the simulated room.

**Figure 22.** Impulse responses at position 16 of the simulated room, facing 0 degrees.

Figure 22 shows the impulse responses for the left and right channel at point 16 of the scenario described in Section 2.2. On the x-axis, the time *t* times the speed of light *c* indicates the distance the pulse has travelled. Peaks reflected or scattered from different room characteristics can easily be separated.

### **6.5. Measurements**

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One problem that arises in using a particle filter is that due to the probabilistic nature of the algorithm the number of particles can grow considerably high. This is because the number of possible data associations increases with every measurement step. Using more particles or

To reduce the necessary number of particles, we use a second approach: Measurements are not directly associated to landmarks. Instead, they are first grouped in the measurement space. To do this, the fact is used that the antenna array moves only in small steps between consecutive measurements, so measurements originating from the same feature also change only slightly. This correlation can be exploited. By employing a simple Kalman Filter in the measurement space, it is possible to predict and group measurements that belong to the same feature. Only whole groups of measurements are passed to the particle filter, which greatly reduces the number of hypotheses needed and therefore the number of particles necessary. Figure 20 shows a simulation of this process. In the left figure, measurements are taken as the robot travels through the environment. Dots indicate extracted time-of-flights. The measurements are cluttered, but almost continuous echoes originating from room features can be made out.

The disadvantage of this procedure is that the grouping introduces a time delay in the system. Moreover, it requires measurements to be made more frequently, and so partly weakens one

The algorithm was first tested with simulated data. The ray tracing algorithm described in Section 3 was used to calculate the impulse response function of a room. The outline of the room is shown in Fig. 3, alongside with 78 measurement points. At each point, 120 measurements were made by turning the bat-type antenna array in steps of 3 degrees. The simulated environment consisted of a rectangular room with the size of 8 m by 9 m, with a rectangular column the size of 1.5 m by 1.5 m roughly in the middle. Between the walls and the column, six complex objects used to test the object recognition algorithm from Section 7 were placed. Walls, objects and the column were assumed to be of metal. The frequency response function was calculated from 4.5 GHz to 13.4 GHz for an antenna array with three double-ridged horn antennas in the bat-type configuration. The distance between

Figure 21 shows the complete radargram for one whole rotation of the antenna array at point 16. In this example, it can be seen that for every angle, there are clear peaks in the impulse response that connect to peaks in the next measurement step, so data association in measurement space is possible. Mapping the whole room just from this position is not possible, because some features simply cannot be seen from there. To map the whole room, measurements from all 78 points were used. The result can be seen in Fig. 23. Walls, shown as solid and dotted lines, and corners, shown as triangles, are mapped at an accuracy of approximately 20 cm. Due to their small size, the placed objects are detected as point scatteres which are depicted as stars. Their positions correspond to the object locations shown in Fig. 3. At this point, a separate object recognition algorithm as described in Section 7 could be used to identify and distinguish them. Note that the origin of the coordinate system is set arbitrarily

discarding unlikely hypotheses by resampling can only partially solve this problem.

The right figure shows the result of the grouping algorithm.

advantage of the room reconstruction algorithm.

**6.4. Simulations**

the antennas was set to 0.5 m.

at the point of the first measurements.

To further verify the results, measurements were made in a laboratory room. The room included furniture, some metal pipes on the walls, and was filled with assorted laboratory equipment at one end of the room. The sensor array consisted of three double ridged horn antennas 0.46 m apart, similar to the simulation.

The antenna array was placed in the middle of the room and rotated manually. Pictures of the room can be seen in Fig. 25. As in the simulation, no information about the current angle of

**Figure 24.** Impulse response showing the features of the room

**Figure 25.** Room used for measurements

**6.6. Optimized antenna design for SLAM**

additional sensor data.

(a) Tidy side of the room (b) Chaotic side of the room

Cooperative Localization and Object Recognition in Autonomous UWB Sensor Networks 207

The results in Fig. 27 show that the algorithm is able to recognize the outline of the room using only these few measurements, although a higher number of measurements still improves the quality of the reconstruction. There is also a trade-off between the different data association methods. While grouping in measurement space is only possible if the measurements are taken frequently, data association in state space can cope with few measurements, but rely on

To further optimize the results of the SLAM algorithm described in this section, antennas with a broader 3 dB beam-width (>60◦) than for the object recognition in section 7 are needed.

Apart from the broad frequency band of 3.5 to 10.5 GHz in order to meet further conditions the antenna also has to be dual-orthogonally polarized. The radiation phase center should be constant over frequency, and the two polarizations should have identical radiation conditions. In literature several types of UWB antennas can be found. Most of them are either biconical

**Figure 23.** Reconstructed room.

the array was passed to the algorithm. The algorithm only used the UWB measurements to reconstruct the room. Figure 24 shows a sample of a recorded impulse response.

In a first test, the array was rotated only by 180◦, illuminating the tidy side of the room. In this case, results similar to those of the simulation could be produced; walls and corners could be mapped with 10-20 cm accuracy. A reconstruction of the whole room was not possible. Many objects on the other, chaotic side of the room produced a large number of echoes and made it impossible to associate the measurements reliably. Here, the algorithm reached its limits.

In a second scenario, measurements were made at 15 positions in an L-shaped corridor, as depicted in Fig. 26. The array was rotated in 3 degree steps at every position, resulting in 1800 measurements.

To test the ability of the algorithm to cope with sparse measurements, only 24 measurements at 5 positions (station 1, 4, 6, 8 and 12 of the scenario) were used, resulting in a total of only 120 measurements. Here, additional information about the position of the robot had to be used, in this case odometry data about the way the robot traveled and the direction the antenna faced. The use of inertial measurement units is also possible.

**Figure 24.** Impulse response showing the features of the room

(a) Tidy side of the room (b) Chaotic side of the room

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distance in m

the array was passed to the algorithm. The algorithm only used the UWB measurements to

In a first test, the array was rotated only by 180◦, illuminating the tidy side of the room. In this case, results similar to those of the simulation could be produced; walls and corners could be mapped with 10-20 cm accuracy. A reconstruction of the whole room was not possible. Many objects on the other, chaotic side of the room produced a large number of echoes and made it impossible to associate the measurements reliably. Here, the algorithm reached its limits.

In a second scenario, measurements were made at 15 positions in an L-shaped corridor, as depicted in Fig. 26. The array was rotated in 3 degree steps at every position, resulting in 1800

To test the ability of the algorithm to cope with sparse measurements, only 24 measurements at 5 positions (station 1, 4, 6, 8 and 12 of the scenario) were used, resulting in a total of only 120 measurements. Here, additional information about the position of the robot had to be used, in this case odometry data about the way the robot traveled and the direction the antenna faced.

reconstruct the room. Figure 24 shows a sample of a recorded impulse response.

The use of inertial measurement units is also possible.

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**Figure 23.** Reconstructed room.

measurements.

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−1

0

1

2

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The results in Fig. 27 show that the algorithm is able to recognize the outline of the room using only these few measurements, although a higher number of measurements still improves the quality of the reconstruction. There is also a trade-off between the different data association methods. While grouping in measurement space is only possible if the measurements are taken frequently, data association in state space can cope with few measurements, but rely on additional sensor data.
