**7.5. Short range imaging algorithm**

In [28] , an imaging algorithm called Range Point Migration (RPM) was proposed that utilizes fuzzy estimation for the Direction Of Arrival (DoA). It extracts a direct mapping by combining the measured distance of the wavefront with its DoA. It realizes a stable imaging of even complex objects and requires no pre-processing like clustering or connecting discontinuous wavefronts. The 2D RPM was introduced in [28] for a planar sensor track nearby the object which allows either only a limited image of the lateral region of the object or requires huge scan distances. Consistently, the back region of the object is not scanned and, hence, not imaged. In [28] the RPM was extended to 3D where the sensors are placed on a planar surface in front of the 3D object. However, this 2D sensor track, too, is not capable of a full perspective of all stereoscopically distributed voxels (volume pixel) of 3D objects.

The set of angles *α*1*<sup>n</sup>* with its *n* neighboring wavefronts are called crisp set in terms of Fuzzy logic. Each of these scalar values could be regarded as one Dirac delta function at the corresponding angle value and is used for further processing. However, this would only make sense in the case of ideal point scatterers. Once the dimensions of the object are expanded or if the object consists of additional complex structures (e.g. edges and corners), it would result in erroneous image points. Fuzzy technology is applied here to compensate such influences and to still use a kind of convergence of nearby wavefronts. Therefore, each angle of the discrete crisp set is Fuzzyfied by a Gaussian membership function. Hence, the result does not only

Cooperative Localization and Object Recognition in Autonomous UWB Sensor Networks 217

A scaling/clipping operation of the amplitude of the neighboring reflection point is performed to focus on strong reflections and scattering. Additional weighting is performed which scales the fuzzy sets as a function of the distance between the neighboring position and the one under test. Thus, it is ensured that the influence of sensors being further away is minimized. Afterwards, an accumulation of these differently weighted fuzzy sets

Within CoLOR it was investigated whether the standard deviation of the Gaussian membership functions are crucial parameters for the image processing. Depending on these parameters, the algorithm either extracts straight parts of the contour of the object, if it is larger than several wavelengths, or it extracts object features, i.e. scattering centers (edges and corners). A strong echo, i.e. a specular reflection is received only when the main lobe of the antenna is aligned to the normal of a smooth surface of the object. However, in the case of a circular track this occurs very rarely, if the cross-section of the object is not a circle. Scattering and diffraction effects overbalance immensely within a circular track, even more if the scan track is spread over a large circular arc. To overcome this problem, weak echoes which spread spherically from the edges can be recorded from any line of sight position. For detailed information, an extensive discussion, as well as the extension to 3D imaging see [49].

is performed. The DoA can be estimated by a maximum defuzzyfication operator.

h

−0.2

−0.1

Distance [m]

**Figure 39.** Radargram with extracted wavefronts on the left side and corresponding object on the right

On the right side of Fig. 39 the object under test is depicted in blue. This object was scanned on a circular track with 1◦ grid resulting in the radargram shown on the left side. The wavefronts which are extracted with the DCM are also plotted in the radargram. With the previously

discussed Fuzzy imaging the red image points shown on the right side are extracted.

0

0.1

0.2

0.3

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norm [V]

depend on one scalar but on a Fuzzy set around each scalar.

<sup>0</sup> <sup>100</sup> <sup>200</sup> <sup>300</sup> 1.6

with extracted image points.

Angle [°]

1.7 1.8 1.9 2 2.1 2.2

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In CoLOR, the RPM was extensively analyzed, validated with numerous measurements in different scenarios and further improved [49]. For a full perspective of the object, the sensor track and the antenna alignment need circumnavigation to extract entirely all stereoscopically distributed voxels. In order to reconstruct a full 3D object contour, the scan pattern of the sensors was modified and extended to a spatial scanning including the z-axis. Experimental validations were carried out based on complex test objects with small shape variations relative to the wavelength used (for results see Fig. 40).

The main principle of the improved RPM, which is called Fuzzy imaging henceforth, shall briefly be described on the basis of the following illustration of a simple scenario with 3 measurements.

**Figure 38.** Measurement scenario to illustrate the principle of Fuzzy imaging

In the 1*st* scenario on the left side of Fig. 38, an object under test is measured at two antenna positions which are separated from each other by a distance *d*<sup>1</sup> which equals *c*. Both positions provide the time of flight and the distances *a* and *b*, respectively. With a geometric approach (law of cosines), the intersection points of the wavefronts as well as the angle *α*<sup>12</sup> are extracted. Afterwards, shown on the right side of Fig. 38 a 3*rd* measurement is performed at a distance of *d*<sup>2</sup> < *d*<sup>1</sup> and provides the new angle *α*13. Evidently, for *d*<sup>2</sup> → 0, the antenna configuration converges to a mono-static configuration. In that case, *α*<sup>13</sup> → *αideal* which would result in an exact image point when combined with the corresponding time of flight measurement.

The set of angles *α*1*<sup>n</sup>* with its *n* neighboring wavefronts are called crisp set in terms of Fuzzy logic. Each of these scalar values could be regarded as one Dirac delta function at the corresponding angle value and is used for further processing. However, this would only make sense in the case of ideal point scatterers. Once the dimensions of the object are expanded or if the object consists of additional complex structures (e.g. edges and corners), it would result in erroneous image points. Fuzzy technology is applied here to compensate such influences and to still use a kind of convergence of nearby wavefronts. Therefore, each angle of the discrete crisp set is Fuzzyfied by a Gaussian membership function. Hence, the result does not only depend on one scalar but on a Fuzzy set around each scalar.

38 Will-be-set-by-IN-TECH

In [28] , an imaging algorithm called Range Point Migration (RPM) was proposed that utilizes fuzzy estimation for the Direction Of Arrival (DoA). It extracts a direct mapping by combining the measured distance of the wavefront with its DoA. It realizes a stable imaging of even complex objects and requires no pre-processing like clustering or connecting discontinuous wavefronts. The 2D RPM was introduced in [28] for a planar sensor track nearby the object which allows either only a limited image of the lateral region of the object or requires huge scan distances. Consistently, the back region of the object is not scanned and, hence, not imaged. In [28] the RPM was extended to 3D where the sensors are placed on a planar surface in front of the 3D object. However, this 2D sensor track, too, is not capable of a full perspective

In CoLOR, the RPM was extensively analyzed, validated with numerous measurements in different scenarios and further improved [49]. For a full perspective of the object, the sensor track and the antenna alignment need circumnavigation to extract entirely all stereoscopically distributed voxels. In order to reconstruct a full 3D object contour, the scan pattern of the sensors was modified and extended to a spatial scanning including the z-axis. Experimental validations were carried out based on complex test objects with small shape variations relative

The main principle of the improved RPM, which is called Fuzzy imaging henceforth, shall briefly be described on the basis of the following illustration of a simple scenario with 3

 

of all stereoscopically distributed voxels (volume pixel) of 3D objects.

**7.5. Short range imaging algorithm**

to the wavelength used (for results see Fig. 40).

*-*


 

 

**Figure 38.** Measurement scenario to illustrate the principle of Fuzzy imaging

 



**-**

In the 1*st* scenario on the left side of Fig. 38, an object under test is measured at two antenna positions which are separated from each other by a distance *d*<sup>1</sup> which equals *c*. Both positions provide the time of flight and the distances *a* and *b*, respectively. With a geometric approach (law of cosines), the intersection points of the wavefronts as well as the angle *α*<sup>12</sup> are extracted. Afterwards, shown on the right side of Fig. 38 a 3*rd* measurement is performed at a distance of *d*<sup>2</sup> < *d*<sup>1</sup> and provides the new angle *α*13. Evidently, for *d*<sup>2</sup> → 0, the antenna configuration converges to a mono-static configuration. In that case, *α*<sup>13</sup> → *αideal* which would result in an exact image point when combined with the corresponding time of flight measurement.

measurements.



A scaling/clipping operation of the amplitude of the neighboring reflection point is performed to focus on strong reflections and scattering. Additional weighting is performed which scales the fuzzy sets as a function of the distance between the neighboring position and the one under test. Thus, it is ensured that the influence of sensors being further away is minimized. Afterwards, an accumulation of these differently weighted fuzzy sets is performed. The DoA can be estimated by a maximum defuzzyfication operator.

Within CoLOR it was investigated whether the standard deviation of the Gaussian membership functions are crucial parameters for the image processing. Depending on these parameters, the algorithm either extracts straight parts of the contour of the object, if it is larger than several wavelengths, or it extracts object features, i.e. scattering centers (edges and corners). A strong echo, i.e. a specular reflection is received only when the main lobe of the antenna is aligned to the normal of a smooth surface of the object. However, in the case of a circular track this occurs very rarely, if the cross-section of the object is not a circle. Scattering and diffraction effects overbalance immensely within a circular track, even more if the scan track is spread over a large circular arc. To overcome this problem, weak echoes which spread spherically from the edges can be recorded from any line of sight position. For detailed information, an extensive discussion, as well as the extension to 3D imaging see [49].

**Figure 39.** Radargram with extracted wavefronts on the left side and corresponding object on the right with extracted image points.

On the right side of Fig. 39 the object under test is depicted in blue. This object was scanned on a circular track with 1◦ grid resulting in the radargram shown on the left side. The wavefronts which are extracted with the DCM are also plotted in the radargram. With the previously discussed Fuzzy imaging the red image points shown on the right side are extracted.

#### 40 Will-be-set-by-IN-TECH 218 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Cooperative Localization and Object Recognition in Autonomous UWB Sensor Networks <sup>41</sup>

(notation: the first index indicates the polarization of the transmitter, the second index the

Cooperative Localization and Object Recognition in Autonomous UWB Sensor Networks 219

Distance [m]

−0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25

**Figure 41.** Radargram of the object under test with cross-polarization and 45◦ rotated antennas on the

However, this object has more or less parts which imitate the scattering and reflection characteristic of flat plates or 0◦- dihedrals. In the field of polarization research it is well known that dihedrals have strong polarizing effects. For example, a 0◦-dihedral (the angle between the fold line of the dihedral and the vertical axis) has only co-polarized components, whereas a 45◦-dihedral has only cross-polarized components. Therefore, dihedrals are

In order to exploit polarimetric diversity gain a 45◦ shift is missing in the radar link [52]. As mentioned before, this would actually depolarize the wave. However, by rotating both antennas by 45◦, the scattering characteristic of the object edges are comparable to 45◦-dihedrals. Hence, in Fig. 42 both sensors are positioned diagonally. Using such a rotated

configuration a cross-polarized measurement was performed with cross polarization.

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0.5

1

norm [V]

Distance [m]

−0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25

**Figure 42.** Radargram of the object under test with cross-polarization and 45◦ rotated antennas on the

h

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Distance [m]

−0.2 −0.1 0 0.1 0.2 0.3

−0.2 −0.1 0 0.1 0.2 0.3

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Intensity

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one of the receiver).

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left and the extracted KM image from this radar data.

<sup>0</sup> <sup>50</sup> <sup>100</sup> <sup>150</sup> <sup>200</sup> <sup>250</sup> <sup>300</sup> <sup>350</sup> 1.6

left and the extracted KM image from this radar data.

especially suitable for calibration in polarimetric measurements.

<sup>0</sup> <sup>50</sup> <sup>100</sup> <sup>150</sup> <sup>200</sup> <sup>250</sup> <sup>300</sup> <sup>350</sup> 1.6

**Figure 40.** Photograph of an 3D test object on the left. Extracted 3D Radar image with Fuzzy imaging in the middle and top view on the right.
