**3.4. Surface estimation and subsurface localization algorithms**

In this section we present algorithms which can be applied for the localization of actively transmitting beacons inside of the human body. The targeted application is the tracking of catheters equiped with UWB transmitters. In this context, the use of active transmitters would mitigate the challenges related to the high attenuation of electromagnetic waves in human tissue, which makes purely passive localization extremely difficult [3].

A similar approach has been investigated in the field of ultrasonics, where catheter-mounted ultrasound transducers in combination with external arrays of imaging transducers are used to track the catheter position [25]. The advantage of UWB catheter localization is a contactless measurement setup with receivers placed in air around the patient while ultrasound transducers have to be placed directly on the body.

In subsurface imaging and localization problems, where sensors are not directly in contact with the medium, the permittivity contrast between air and the medium cannot be neglected as it leads to a different wave propagation velocity inside of the material. In case of medical applications, a relative permittivity of human tissue between 30 and 50 in the FCC UWB frequency range has to be considered [13]. UWB signals are therefore strongly reflected at the air-to-body interface. These reflections are beneficial to surface estimation applications using UWB pulse radars. For in-body localization, however, they constrain a signal emission from inside of the body. In order to overcome the strong reflection losses, we therefore propose a system that combines an active transmitter inside of the body with an array of radar transceivers outside of the body. The sensor array acts as both a surface scanner and a receiver recording the time of arrival (ToA) of a signal transmitted from inside of the body. A determination of the exact body shape prior to localization is necessary to cope with refraction effects at its surface and the change of wave propagation speed from air to tissue. This distiguishes the proposed in-body localization method from most through-dielectric localization problems like through-the-wall imaging where a plane boundary between air and the target medium is assumed [1].

**Figure 36.** Proposed localization procedure of a transmitter buried in a dielectric medium. In the first step the sensor array is used to scan the surface (left), in the second step it only receives the signal transmitted from inside of the medium (right).

Fig. 36 summarizes the proposed localization approach of a transmitter placed in a dielectric medium. In a first step, the array of radar sensors is used to measure the distance to the boundary surface. These measured distances together with the known antenna positions are the input of the surface estimation algorithm which returns a model of the boundary surface. In the second step, the transmitter inside of the dielectric is switched on and the radar sensors operate in receive mode recording the time of flight of the transmitted signal. Finally, we analyze all the acquired data and determine the position of the transmitter.

Several methods to estimate the surface of a highly reflective medium using UWB pulse radar sensors have been investigated in recent years [17, 29]. Some of these imaging algorithms, however, need extensive preprocessing of the measurement data or suffer from high complexity and computation time. In the first part of this section, we derive a simple and easy to implement 3D surface estimation algorithm based on trilateration. In the second part, building on this surface estimation method, we present an approach for the localization of transmitters inside an arbitrarily shaped dielectric medium taking into account its surface profile.

### *3.4.1. Surface estimation algorithm based on trilateration*

30 Will-be-set-by-IN-TECH

particle filtering in parallel with conventional methods and exchange information between

In this section we present algorithms which can be applied for the localization of actively transmitting beacons inside of the human body. The targeted application is the tracking of catheters equiped with UWB transmitters. In this context, the use of active transmitters would mitigate the challenges related to the high attenuation of electromagnetic waves in human

A similar approach has been investigated in the field of ultrasonics, where catheter-mounted ultrasound transducers in combination with external arrays of imaging transducers are used to track the catheter position [25]. The advantage of UWB catheter localization is a contactless measurement setup with receivers placed in air around the patient while

In subsurface imaging and localization problems, where sensors are not directly in contact with the medium, the permittivity contrast between air and the medium cannot be neglected as it leads to a different wave propagation velocity inside of the material. In case of medical applications, a relative permittivity of human tissue between 30 and 50 in the FCC UWB frequency range has to be considered [13]. UWB signals are therefore strongly reflected at the air-to-body interface. These reflections are beneficial to surface estimation applications using UWB pulse radars. For in-body localization, however, they constrain a signal emission from inside of the body. In order to overcome the strong reflection losses, we therefore propose a system that combines an active transmitter inside of the body with an array of radar transceivers outside of the body. The sensor array acts as both a surface scanner and a receiver recording the time of arrival (ToA) of a signal transmitted from inside of the body. A determination of the exact body shape prior to localization is necessary to cope with refraction effects at its surface and the change of wave propagation speed from air to tissue. This distiguishes the proposed in-body localization method from most through-dielectric localization problems like through-the-wall imaging where a plane boundary between air and

TX/RX RX

**Figure 36.** Proposed localization procedure of a transmitter buried in a dielectric medium. In the first step the sensor array is used to scan the surface (left), in the second step it only receives the signal

Fig. 36 summarizes the proposed localization approach of a transmitter placed in a dielectric medium. In a first step, the array of radar sensors is used to measure the distance to the boundary surface. These measured distances together with the known antenna positions are the input of the surface estimation algorithm which returns a model of the boundary surface.

Measurement of transmit signal ToA

transmitter position Estimation of

of boundary surface

Radar measurements

model using surface

Creation of surface estimation algorithm

TX

both methods can also help to reduce complexity.

**3.4. Surface estimation and subsurface localization algorithms**

tissue, which makes purely passive localization extremely difficult [3].

ultrasound transducers have to be placed directly on the body.

the target medium is assumed [1].

transmitted from inside of the medium (right).

Radar measurements with quasi-omnidirectional antennas only provide information about the target distance, but not about its direction. This makes surface imaging an inverse problem which can only be solved by combining measurement results from different antenna positions. In this context, target ranging using trilateration means determining the intersections of spheres, the radii of which correspond to measured target distances. The underlying assumption for using trilateration as a surface estimation method is that two neighboring antennas are "seeing" the same scattering center. As with other imaging algorithms this assumption can lead to inaccuracies of estimated target points.

The imaging principle shall first be explained using a two-dimensional example. Fig. 37(a) shows the measurement scenario of a linear array of monostatic radar transceivers arranged along the *x*-axis scanning the surface of a target in *z*-direction. Each array element measures the distance to the closest point on the target. Two exemplary measurement points *Xn* and *Xn*+<sup>1</sup> are picked out, and semi circles with radii corresponding to the measured target distances are plotted around the antennas. The estimated surface point is the intersection of the two circles.

**Figure 37.** Cross section of a 2D imaging problem using a linear array of monostatic radar transceivers along the *x*-axis (a) and top view of a 3D imaging setup showing three measuring points of an antenna array in the *x*-*y*-plane (b).

Three-dimensional imaging demands for a third antenna position located in a different dimension. This setup is shown as a top view in Fig. 37(b). At each of the three positions a target distance *ri* is measured which leads to a set of spheres with radius *ri* around the respective antenna position A*i*, as defined by the system of equations

$$r\_1^2 = \quad x^2 \quad \quad + \quad y^2 \quad +z^2 \tag{11}$$

*3.4.2. Subsurface localization algorithm*

between the respective antenna position *n* and surface point *i*:

2D case because of simpler graphical representations.

0 1 2 3 45

(a) Determination of single wavefront

/ arbitrary unit

rays pi,4 antenna position =4 <sup>n</sup>

x

surface points =1,2,3,... i

z

/ arbitrary unit

air

location at (3,5) (b).

medium

*ri*,*<sup>n</sup>* <sup>=</sup> <sup>1</sup> <sup>√</sup>*ε*<sup>r</sup> 

secondary wavefronts

The given parameters of the localization problem are the shape of the dielectric medium containing the transmitter, its distance to the antenna array and the ToA of the localization signal at each array element. Since all the wave propagation effects are reciprocal, our problem can also be regarded in a reverse way: At each receiver position the transmission of a short pulse with a delay corresponding to the respective previously measured ToA is assumed. In order to get the original beacon position we have to find the spot where all these virtual pulses would superimpose, i.e. the intersection of the impulse wavefronts inside of the medium [27]. According to the Huygens-Fresnel principle a refracted wavefront can be represented by an infinite number of spherical waves which originate from points on the boundary surface reached by the incoming wave. This is shown in Fig. 38(a) for a pulse transmitted from an antenna at position (3,0) towards a dielectric half space. In this 2D example, 20 source points of radial waves on the dielectric surface are considered. The radii *ri*,*<sup>n</sup>* of the secondary waves are calculated from the measured ToA at the receiving antenna and the length of the ray *pi*,*<sup>n</sup>*

*c*<sup>0</sup> · ToA*<sup>n</sup>* − *pi*,*<sup>n</sup>*

0

/ arbitrary unit

z

**Figure 38.** Determination of the 2D wavefront shape inside a medium with *ε*<sup>r</sup> = 30 for a signal transmitted in air at position (3,0) by evaluating the envelope of radial secondary wavefronts (a). Intersections of wavefronts corresponding to six different antenna positions indicate the transmitter

The wavefront shapes in Fig. 38(b) agree with the hyperbolic approximation of wavefronts in dielectric half spaces [28]. With more complex boundaries, however, the analytical calculation of refracted wavefronts is no longer practical, while the approach presented here is independent of the surface shape. An example of a transmitter placed behind a more complex

medium air

where *<sup>c</sup>*<sup>0</sup> is the speed of light. The division by <sup>√</sup>*ε*<sup>r</sup> accounts for the different wave propagation speed in the dielectric medium. The envelope of all radial waves corresponds to the wavefront we are looking for. By repeating the procedure for every antenna element of the receiver array we get a set of wavefronts as illustrated in Fig. 38(b). Finally, we determine the intersection of these wavefronts to obtain the transmitter position inside of the medium. A 3D localization problem is solved in an analog way with envelopes of spheres leading to intersecting 3D wavefronts. Here, however, the derivation of the localization procedure shall be limited to the

, (18)

UWB in Medicine – High Performance UWB Systems for Biomedical Diagnostics and Short Range Communications

471

0 1 2 3 54

(b) Localization by intersecting wavefronts

x / arbitrary unit

transmitter position

$$r\_2^2 = (\mathbf{x} - d)^2 + \quad y^2 \quad +z^2 \,. \tag{12}$$

$$r\_3^2 = \quad x^2 \quad \quad + (y-j)^2 + z^2 \tag{13}$$

where *d* and *j* are the distances between two antennas in *x*- and *y*-direction, respectively. For simplicity, the first antenna position A1 shall be at the center of the coordinate system. The above equation system is valid for a planar antenna array. In case of a curved antenna array an offset *z*-value has to be inserted.

The initial assumption that all three antennas are "seeing" the same target has to be assured by comparing the measured target distances *r*1-3. If the difference between these distances is small enough, the assumption can be considered valid. For the above equations this precondition can be formulated as follows:

$$|r\_1 - r\_2| \le T\_{\rm s,x} \quad \text{and} \quad |r\_1 - r\_3| \le T\_{\rm s,y} \tag{14}$$

A threshold *T*s in the range of about half the antenna distance has shown good results.

If the conditions in (14) are fulfilled, the target surface point of interest can be calculated by intersecting the three spheres. The coordinates (*x*, *y*, *z*) of the intersection are

$$\alpha = \frac{r\_1^2 - r\_2^2 + d^2}{2d},\tag{15}$$

$$y = \frac{r\_1^2 - r\_3^2 + j^2}{2j},\tag{16}$$

$$z = \pm \sqrt{r\_1^2 - x^2 - y^2}.\tag{17}$$

These coordinates are offsets refering to the position of the first antenna A1. The sign in (17) depends on the arrangement of the radar transceivers. Here, we assume that the antennas are oriented towards positive *z*-values.

The necessary steps of the presented trilateration algorithm can be summarized as follows:


### *3.4.2. Subsurface localization algorithm*

32 Will-be-set-by-IN-TECH

a target distance *ri* is measured which leads to a set of spheres with radius *ri* around the

where *d* and *j* are the distances between two antennas in *x*- and *y*-direction, respectively. For simplicity, the first antenna position A1 shall be at the center of the coordinate system. The above equation system is valid for a planar antenna array. In case of a curved antenna array

The initial assumption that all three antennas are "seeing" the same target has to be assured by comparing the measured target distances *r*1-3. If the difference between these distances is small enough, the assumption can be considered valid. For the above equations this

A threshold *T*s in the range of about half the antenna distance has shown good results.

<sup>1</sup> <sup>−</sup> *<sup>r</sup>*<sup>2</sup>

<sup>1</sup> <sup>−</sup> *<sup>r</sup>*<sup>2</sup> <sup>3</sup> + *j* 2

These coordinates are offsets refering to the position of the first antenna A1. The sign in (17) depends on the arrangement of the radar transceivers. Here, we assume that the antennas are

The necessary steps of the presented trilateration algorithm can be summarized as follows:

1. Pick three neighboring measurement points in two different dimensions (here: along the

2. Extract the target distance from the recorded radar measurement data at each antenna

3. Check if the differences between the measured distances satisfy the trilateration condition

4. If the previous condition is fulfilled, calculate the target coordinates using eq. (15)-(17). 5. Repeat the two previous steps if higher order reflections exist, or otherwise start over with

intersecting the three spheres. The coordinates (*x*, *y*, *z*) of the intersection are

*<sup>x</sup>* <sup>=</sup> *<sup>r</sup>*<sup>2</sup>

*<sup>y</sup>* <sup>=</sup> *<sup>r</sup>*<sup>2</sup>

*z* = ± *r*2

position. Multiple target responses per measurement are possible.

If the conditions in (14) are fulfilled, the target surface point of interest can be calculated by

<sup>2</sup> <sup>+</sup> *<sup>d</sup>*<sup>2</sup>

<sup>1</sup> <sup>=</sup> *<sup>x</sup>*<sup>2</sup> <sup>+</sup> *<sup>y</sup>*<sup>2</sup> <sup>+</sup> *<sup>z</sup>*2, (11)

<sup>2</sup> = (*<sup>x</sup>* <sup>−</sup> *<sup>d</sup>*)<sup>2</sup> <sup>+</sup> *<sup>y</sup>*<sup>2</sup> <sup>+</sup> *<sup>z</sup>*2, (12)

<sup>3</sup> <sup>=</sup> *<sup>x</sup>*<sup>2</sup> + (*<sup>y</sup>* <sup>−</sup> *<sup>j</sup>*)<sup>2</sup> <sup>+</sup> *<sup>z</sup>*2, (13)


<sup>2</sup>*<sup>d</sup>* , (15)

<sup>2</sup>*<sup>j</sup>* , (16)

<sup>1</sup> − *<sup>x</sup>*<sup>2</sup> − *<sup>y</sup>*2. (17)

respective antenna position A*i*, as defined by the system of equations

*r* 2

*r* 2

*r* 2

an offset *z*-value has to be inserted.

oriented towards positive *z*-values.

the next three measurement positions.

*x*- and *y*-axis).

in eq. (14).

precondition can be formulated as follows:

The given parameters of the localization problem are the shape of the dielectric medium containing the transmitter, its distance to the antenna array and the ToA of the localization signal at each array element. Since all the wave propagation effects are reciprocal, our problem can also be regarded in a reverse way: At each receiver position the transmission of a short pulse with a delay corresponding to the respective previously measured ToA is assumed. In order to get the original beacon position we have to find the spot where all these virtual pulses would superimpose, i.e. the intersection of the impulse wavefronts inside of the medium [27].

According to the Huygens-Fresnel principle a refracted wavefront can be represented by an infinite number of spherical waves which originate from points on the boundary surface reached by the incoming wave. This is shown in Fig. 38(a) for a pulse transmitted from an antenna at position (3,0) towards a dielectric half space. In this 2D example, 20 source points of radial waves on the dielectric surface are considered. The radii *ri*,*<sup>n</sup>* of the secondary waves are calculated from the measured ToA at the receiving antenna and the length of the ray *pi*,*<sup>n</sup>* between the respective antenna position *n* and surface point *i*:

$$r\_{i,n} = \frac{1}{\sqrt{\mathcal{E}\_\mathbf{r}}} \left( \mathbf{c}\_0 \cdot \text{ToA}\_n - p\_{i,n} \right),\tag{18}$$

where *<sup>c</sup>*<sup>0</sup> is the speed of light. The division by <sup>√</sup>*ε*<sup>r</sup> accounts for the different wave propagation speed in the dielectric medium. The envelope of all radial waves corresponds to the wavefront we are looking for. By repeating the procedure for every antenna element of the receiver array we get a set of wavefronts as illustrated in Fig. 38(b). Finally, we determine the intersection of these wavefronts to obtain the transmitter position inside of the medium. A 3D localization problem is solved in an analog way with envelopes of spheres leading to intersecting 3D wavefronts. Here, however, the derivation of the localization procedure shall be limited to the 2D case because of simpler graphical representations.

**Figure 38.** Determination of the 2D wavefront shape inside a medium with *ε*<sup>r</sup> = 30 for a signal transmitted in air at position (3,0) by evaluating the envelope of radial secondary wavefronts (a). Intersections of wavefronts corresponding to six different antenna positions indicate the transmitter location at (3,5) (b).

The wavefront shapes in Fig. 38(b) agree with the hyperbolic approximation of wavefronts in dielectric half spaces [28]. With more complex boundaries, however, the analytical calculation of refracted wavefronts is no longer practical, while the approach presented here is independent of the surface shape. An example of a transmitter placed behind a more complex surface is presented in Fig. 39. The times of flight between the transmitter at (5 cm,5 cm) and the individual elements of the receiver array at *z* = -20 cm are calculated using electromagnetic field simulation software [6].

**Figure 39.** Calculated wavefronts in a medium with *ε*r=10 based on EM field simulations. The receiving antennas are placed along the *x*-axis at *z*=-20, the transmitter is positioned at (5 cm,5 cm).

**Figure 40.** Block diagram of the single-ended bistatic radar system.

direct and non-inversed coupling between the antennas.

receive antenna with correlator IC and baseband circuit.

the 3.1-10.6 GHz UWB spectral mask allocated by the FCC in the United States and has a voltage amplitude of 600 mV peak-to-peak [8]. The impulse generator radiates an impulse at every rising slope of an input trigger signal. Here a sinusoidal signal is used to trigger the impulse generator, so at every rising edge of the sinusoidal signal an impulse is emitted which results in a continuous impulse train. The sinusoidal signal is supplied from one source of the direct-digital-synthesizer (DDS) AD9959. All four clock sources of the AD9959 (three are used) are synchronized among each other to allow a phase and frequency stable operation between the signals. The transmitter is adjusted to generate an impulse train with a repetition rate of *frep* = 200 MHz. To reduce impulse-to-impulse jitter, spurious emissions of the 200 MHz sinusoidal trigger signal are filtered by a narrowband helix filter. The generated impulse train is continuously radiated by the antennas, is reflected at the desired object and enters the receiver. The reflection at the object causes a phase inversion to the impulses, therefore it is received with inverted amplitude. Additionally the impulse train is fed to the receiver by a

473

UWB in Medicine – High Performance UWB Systems for Biomedical Diagnostics and Short Range Communications

(a) (b)

**Figure 41.** Picture of (a) Vivaldi transmit antenna with mounted impulse generator IC and (b) Vivaldi

These signals are processed in the receiver by a monolithic correlator IC, which consist of a UWB LNA, a four-quadrant multiplier, a template impulse generator generating a fifth Gaussian derivative impulse corresponding to the transmit impulse, and a first integrating low-pass filter with a cut-off frequency of 800 MHz [9]. The template impulse generator is driven by a second clock source of the AD9959 at a repetition rate of

The above mentioned 2D localization procedure leads to a belt of refracted wavefronts with a focussing point where the receiver has been placed in the simulation. To decrease calculation time it is also possible to search for the narrowest point in the wavefront belt instead of calculating the intersections. This leads to an estimated transmitter position of (4.60 cm,4.94 cm), having an error of about 4 mm.

It is obvious that in the example of Fig. 39 a smaller number of wavefronts and thus less receiving antennas would be sufficient for a successful localization of the transmitter. But in practical applications this high number of antennas might still be required as a dense sensor array is rather needed for surface estimation than for solving the localization problem.
