**8.2. Stationary target detection in an unknown indoor environment**

Indoor stationary object detection in an unknown environment is important for many civilian and military applications, such as indoor surveillance, search and rescue operations, logistics, security and so on. Compared with target detection in a known environment, it presents some challenges:


### *8.2.1. Signal enhancement*

Due to the challenges mentioned above, a possible detection scheme is given in Fig. 53. In the scheme, the objective of the first step, "signal enhancement" which is realized by a "*time-shift* & *accumulation*" operation, is to raise the SINR of system, and to transform the unknown environment into a Gaussian clutter and noise environment so that the detector could be

**Figure 52.** Measurement configuration. *T*1...*Tn*...*TN* are different transmission positions on the track **L***l*. "*R*1...*RM*" are sparsely spaced receivers with different reception angles. The dashed curve is an ellipse segment with the foci *Rm* and *Tn*.

**Figure 53.** Flow chart of the algorithm .

48 Will-be-set-by-IN-TECH

is situated and even traces of these ellipses make the interpretation of the image difficult. Figure 51 (b) illustrates the image of the same scenario obtained by the cross-correlated algorithm. The color scaling of both images in Fig. 51 (a) and (b) is the same. The reduction of image artifacts by means of the cross-correlated algorithm is evident. Elliptical traces were significantly reduced. This helps to identify the inspected environment in this figure more clearly. A more detailed discussion on the cross-correlated imaging with measurement

Y−direction [m]

X−direction [m]

(b) Cross-correlated imaging

0 1 2 3 4 5 6 7 8

examples is given in [74] and [75].

Y−direction [m]

**Figure 51.** Imaging in sensor networks.

challenges:

*8.2.1. Signal enhancement*

X−direction [m]

(a) Range migration

**8.2. Stationary target detection in an unknown indoor environment**

unknown, leading to further complications in the detector design.

cancellation) between sequence snapshots, etc [58].

Indoor stationary object detection in an unknown environment is important for many civilian and military applications, such as indoor surveillance, search and rescue operations, logistics, security and so on. Compared with target detection in a known environment, it presents some

• *The detection takes place in an unknown environment (e.g. an environment after disaster).* Thus, it is not possible to probe the environment before the presence of target. A range of techniques based on "*a priori*" information of the background cannot be utilized (e.g. [41, 64]). Additionally, the statistical distributions of clutter and noise are sometimes

• *The targets concerned are stationary with respect to the background.* There is no distinct speed difference between the targets and the background. Hence, it prevents the application of the motion-based detection techniques, such as Doppler based approaches, subtraction (or

• *It is a highly cluttered environment.* The targets (objects of interest) are typically surrounded by clutter (objects, which are not of interest, as shown in Fig. 52). In this case, the response of targets is not always stronger than clutter. In other words, the Signal to Interference and Noise Ratio (SINR) of the system is not always high enough to ensure a reliable detection.

Due to the challenges mentioned above, a possible detection scheme is given in Fig. 53. In the scheme, the objective of the first step, "signal enhancement" which is realized by a "*time-shift* & *accumulation*" operation, is to raise the SINR of system, and to transform the unknown environment into a Gaussian clutter and noise environment so that the detector could be

0 1 2 3 4 5 6 7 8

designed based on Gaussian clutter and noise. Mathematically, the "*time-shift* & *accumulation*" operation is described as

$$\sum\_{m=1}^{N} s\_{Rm,Tn}(t + t\_{Tn,T1}^{diff})\tag{19}$$

where *sRm*,*Tn*(*t*) is the signal received by the receiver *Rm* with respect to the transmission position *Tn*, and *t di f f Tn*,*T*<sup>1</sup> = |**T***<sup>n</sup>* − **T**1| /*c* is the time-delay to be compensated for. **T***<sup>n</sup>* and **T**<sup>1</sup> are the position vectors of *Tn* and reference transmission position *T*<sup>1</sup> , respectively. In the operation,


50 Will-be-set-by-IN-TECH 228 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Cooperative Localization and Object Recognition in Autonomous UWB Sensor Networks <sup>51</sup>

where, *θRi* and *θRj* are the reflection angles of the receiver *Ri* and *Rj*,respectively. **V***bi* is the bisector of the angle *RiXT*1. *θbi* is the reflection angle of **V***bi*. According to this principle,

Cooperative Localization and Object Recognition in Autonomous UWB Sensor Networks 229

In practice, (20) is demonstrated in Fig. 55, where the spectra of receivers *R*1-*R*4 are

According to the principle discussed above, if we take the observation of *R*1, *s*¯*R*1,*Tn*(*τ*), as a reference signal, the observation of receiver *Rj* can be given by *s*¯*Rj*,*Tn*(*τ*) ≈ *s*¯*R*1,*Tn*(*τ*) exp(−*jγj*,1*τ*), where *γj*,1 is determined by the illuminating geometry according to (20). Based on this relationship, if we consider the effects of unwanted contributions due to

where **y** is an *NMN* × 1 vector. *NMN* = *M* × *N*, where *M* and *N* are the numbers of receivers

According to the Central Limit Theorem (CLT) of the probability theory, if a large number of clutter from different sources (scattered from different objects) is accumulated, the statistical distribution of the sum will approach a Gaussian distribution. As the scenario concerned takes place in a cluttered indoor environment which has many scatterers, we assume that the clutter **c** and the noise **n** can approach a Gaussian distribution due to the "*time-delay* & *accumulation*" operations given by (19). Hence, our detection problem simplifies to searching targets in Gaussian clutter and noise. We assume that the noise **n** and the clutter **c** are *NMN* × 1 independent zero-mean complex Gaussians with *NMN* × *NMN* known covariance matrices **M***c*+*<sup>n</sup>* = *E*[(**c** + **n**)(**c** + **n**)*H*]. **M***c*+*<sup>n</sup>* is a positive semidefinite and Hermitian symmetric matrix [63]. The superscript *H* indicates conjugate transpose of a matrix. Based on the signal model

*<sup>c</sup>*+*n***<sup>x</sup>** <sup>=</sup> **<sup>M</sup>**−<sup>1</sup>

In terms of the Neyman-Pearson criterion, the threshold *kth* could be set as *kth* = *D*Φ(1 − *Pf*),

*<sup>c</sup>*+*n*(**¯s**

, *fRj* ∈ [ *fR*<sup>1</sup> , *fR*<sup>2</sup> , *fR*<sup>3</sup> , *fR*<sup>4</sup> ] are the frequencies at which the maximum amplitudes are located. The differences between *fR*1-*fR*<sup>4</sup> indicate the spectrum shifts between *R*1, *R*2, *R*<sup>3</sup>

*fRj*−*fR*<sup>1</sup> <sup>≈</sup> *<sup>γ</sup>i*,1−<sup>1</sup>

*ref <sup>T</sup>*<sup>1</sup> , *s*¯ *ref Tn* , ...,*s*¯

*ref* <sup>⊗</sup> **<sup>K</sup>**) (22)

*<sup>D</sup>* ). Here, *kth* is the threshold for a likelihood

2/2*dt*. The parameter *D* is defined as *D*<sup>2</sup> = **x***H***M**−<sup>1</sup>

*av* is the average signal power of **<sup>x</sup>**. Generally, *<sup>x</sup>*<sup>2</sup>

*<sup>D</sup>* ), and the probability of

*<sup>c</sup>*+*n***x** =

*av E*[(*y*−*x*)*<sup>H</sup>* (*y*−*x*)]

*<sup>T</sup>*. The symbol <sup>⊗</sup> denotes the

*ref* <sup>⊗</sup> **<sup>K</sup>** <sup>+</sup> **<sup>c</sup>** <sup>+</sup> **<sup>n</sup>** <sup>=</sup> **<sup>x</sup>** <sup>+</sup> **<sup>c</sup>** <sup>+</sup> **<sup>n</sup>** (21)

*<sup>γ</sup>j*,1−<sup>1</sup> , where

*ref TN*] *<sup>T</sup>* ,

measured based on the scenario of Fig. 54. It can be shown that *fRi*−*fR*<sup>1</sup>

clutter **c** and noise **n**, the signal model for detection can be given as

**y** = **¯s**

*Tn* = *s*¯*R*1,*Tn*(*τ*), and **K** = [1, exp(−*jγ*2,1*τ*), ..., exp(−*jγM*,1*τ*]

above, a matched filter detector is given as

false alarms can be given as *Pf* <sup>=</sup> <sup>1</sup> <sup>−</sup> <sup>Φ</sup>( *kth*

, where *x*<sup>2</sup>

1 2*π x* <sup>−</sup><sup>∞</sup> *<sup>e</sup>*−*<sup>t</sup>*

and transmission positions, respectively. **<sup>x</sup>** <sup>=</sup> **<sup>s</sup>**¯*ref* <sup>⊗</sup> **<sup>K</sup>**, where **<sup>s</sup>**¯*ref* = [*s*¯

**h** = **M**−<sup>1</sup>

and the detection probability can be given as *Pd* <sup>=</sup> <sup>1</sup> <sup>−</sup> <sup>Φ</sup>(Φ−1(<sup>1</sup> <sup>−</sup> *Pf*) <sup>−</sup> *<sup>D</sup>*).

The probability of detection can be given as *Pd* <sup>=</sup> <sup>1</sup> <sup>−</sup> <sup>Φ</sup>( *kth*−**h***<sup>H</sup>* **<sup>x</sup>**

can be regarded as the SINR at the output of the detector [43].

stationary plane-surface objects can be detected.

*fRi*

*s*¯ *ref*

and *R*4, correspondingly.

*8.2.3. Detection*

Kronecker product.

test and Φ(*x*) = √

*av E*[(**y**−**x**)*<sup>H</sup>* (**y**−**x**)]

*NMN <sup>x</sup>*<sup>2</sup>

**Figure 55.** Measured spectrum-shift

### *8.2.2. The detection principle*

For a detection problem, generally, detection algorithms are designed based on the differences (or deviations) between the targets and the background (clutter, noise). The ability to distinguish objects depends on how much their properties (e.g. electromagnetic properties, motion properties) deviate from the properties of the background. For the concerned stationary target which has no speed differences relative to the environment it can be detected based on the reflection characteristic deviations between the target and the background. Here, we take a planar-surface target as an example to illustrate the principle of indoor stationary target detection.

Consider a detection scenario as shown in Fig. 52 and Fig. 54. The transmitter moves along track **L***<sup>l</sup>* to probe the environment, and to enhance the signal. The target is a concrete brick-like object with a square plane-surface (50*cm* × 50*cm*). It is located at *x* = 24*cm* on the track **L***l*, with an orientation angle of 60◦. The receivers *R*1, *R*2, *R*<sup>3</sup> and *R*<sup>4</sup> receive the scattered signals from the surroundings. They are located at different directions with respect to the target. The transmitter-target-receiver angles are 13.9◦, 20.3◦, 26.3◦ and 31.7◦, respectively. The antennas of the transmitter and receivers are omnidirectional and horn antennas, respectively. The receivers *R*<sup>1</sup> and *R*<sup>2</sup> are in the same room with the target and the transmitter, while the receivers *R*<sup>3</sup> and *R*<sup>4</sup> are placed behind a 20cm-thick concrete wall.

Theoretically, it can be proved that if the target is a planar-surface object with diffuse reflections, after passing through the down-converter and certain mathematical transforms, the received signals from different directions would have a spectrum-shift, which is given by Ω*j*,*<sup>i</sup>* = *ωc*(*γj*,*<sup>i</sup>* − 1) under the illuminating geometry in Fig. 52. Here, the subscripts *i* and *j* are the indices of the receivers located at the different directions, *ω<sup>c</sup>* is the angular central frequency, and *γj*,*<sup>i</sup>* is a parameter associated with the reflection angles,

$$\gamma\_{j,i} \approx 1 + \left(\sin\theta\_{Rj} - \sin\theta\_{Ri}\right) / \left(|\mathbf{V}\_{bi}|\sin\theta\_{bi}\right) \tag{20}$$

where, *θRi* and *θRj* are the reflection angles of the receiver *Ri* and *Rj*,respectively. **V***bi* is the bisector of the angle *RiXT*1. *θbi* is the reflection angle of **V***bi*. According to this principle, stationary plane-surface objects can be detected.

In practice, (20) is demonstrated in Fig. 55, where the spectra of receivers *R*1-*R*4 are measured based on the scenario of Fig. 54. It can be shown that *fRi*−*fR*<sup>1</sup> *fRj*−*fR*<sup>1</sup> <sup>≈</sup> *<sup>γ</sup>i*,1−<sup>1</sup> *<sup>γ</sup>j*,1−<sup>1</sup> , where *fRi* , *fRj* ∈ [ *fR*<sup>1</sup> , *fR*<sup>2</sup> , *fR*<sup>3</sup> , *fR*<sup>4</sup> ] are the frequencies at which the maximum amplitudes are located. The differences between *fR*1-*fR*<sup>4</sup> indicate the spectrum shifts between *R*1, *R*2, *R*<sup>3</sup> and *R*4, correspondingly.

### *8.2.3. Detection*

50 Will-be-set-by-IN-TECH

3900 4000 4100 4200 4300

*fR4 fR3 fR2 fR1*

R1 R2 R3 R4

Frequency Sampling Bins

For a detection problem, generally, detection algorithms are designed based on the differences (or deviations) between the targets and the background (clutter, noise). The ability to distinguish objects depends on how much their properties (e.g. electromagnetic properties, motion properties) deviate from the properties of the background. For the concerned stationary target which has no speed differences relative to the environment it can be detected based on the reflection characteristic deviations between the target and the background. Here, we take a planar-surface target as an example to illustrate the principle of indoor stationary

Consider a detection scenario as shown in Fig. 52 and Fig. 54. The transmitter moves along track **L***<sup>l</sup>* to probe the environment, and to enhance the signal. The target is a concrete brick-like object with a square plane-surface (50*cm* × 50*cm*). It is located at *x* = 24*cm* on the track **L***l*, with an orientation angle of 60◦. The receivers *R*1, *R*2, *R*<sup>3</sup> and *R*<sup>4</sup> receive the scattered signals from the surroundings. They are located at different directions with respect to the target. The transmitter-target-receiver angles are 13.9◦, 20.3◦, 26.3◦ and 31.7◦, respectively. The antennas of the transmitter and receivers are omnidirectional and horn antennas, respectively. The receivers *R*<sup>1</sup> and *R*<sup>2</sup> are in the same room with the target and the transmitter, while the

Theoretically, it can be proved that if the target is a planar-surface object with diffuse reflections, after passing through the down-converter and certain mathematical transforms, the received signals from different directions would have a spectrum-shift, which is given by Ω*j*,*<sup>i</sup>* = *ωc*(*γj*,*<sup>i</sup>* − 1) under the illuminating geometry in Fig. 52. Here, the subscripts *i* and *j* are the indices of the receivers located at the different directions, *ω<sup>c</sup>* is the angular central

sin*θRj* − sin*θRi*

/ (|**V***bi*| sin*θbi*) (20)

**Figure 54.** Measurement environment. *R*<sup>3</sup> and *R*<sup>4</sup> are placed behind the wall.

0.4 0.6 0.8 1

receivers *R*<sup>3</sup> and *R*<sup>4</sup> are placed behind a 20cm-thick concrete wall.

frequency, and *γj*,*<sup>i</sup>* is a parameter associated with the reflection angles,

*γj*,*<sup>i</sup>* ≈ 1 +

Normalized Amplititude

**Figure 55.** Measured spectrum-shift

*8.2.2. The detection principle*

target detection.

According to the principle discussed above, if we take the observation of *R*1, *s*¯*R*1,*Tn*(*τ*), as a reference signal, the observation of receiver *Rj* can be given by *s*¯*Rj*,*Tn*(*τ*) ≈ *s*¯*R*1,*Tn*(*τ*) exp(−*jγj*,1*τ*), where *γj*,1 is determined by the illuminating geometry according to (20). Based on this relationship, if we consider the effects of unwanted contributions due to clutter **c** and noise **n**, the signal model for detection can be given as

$$\mathbf{y} = \mathbf{\bar{s}}^{ref} \otimes \mathbf{K} + \mathbf{c} + \mathbf{n} = \mathbf{x} + \mathbf{c} + \mathbf{n} \tag{21}$$

where **y** is an *NMN* × 1 vector. *NMN* = *M* × *N*, where *M* and *N* are the numbers of receivers and transmission positions, respectively. **<sup>x</sup>** <sup>=</sup> **<sup>s</sup>**¯*ref* <sup>⊗</sup> **<sup>K</sup>**, where **<sup>s</sup>**¯*ref* = [*s*¯ *ref <sup>T</sup>*<sup>1</sup> , *s*¯ *ref Tn* , ...,*s*¯ *ref TN*] *<sup>T</sup>* , *s*¯ *ref Tn* = *s*¯*R*1,*Tn*(*τ*), and **K** = [1, exp(−*jγ*2,1*τ*), ..., exp(−*jγM*,1*τ*] *<sup>T</sup>*. The symbol <sup>⊗</sup> denotes the Kronecker product.

According to the Central Limit Theorem (CLT) of the probability theory, if a large number of clutter from different sources (scattered from different objects) is accumulated, the statistical distribution of the sum will approach a Gaussian distribution. As the scenario concerned takes place in a cluttered indoor environment which has many scatterers, we assume that the clutter **c** and the noise **n** can approach a Gaussian distribution due to the "*time-delay* & *accumulation*" operations given by (19). Hence, our detection problem simplifies to searching targets in Gaussian clutter and noise. We assume that the noise **n** and the clutter **c** are *NMN* × 1 independent zero-mean complex Gaussians with *NMN* × *NMN* known covariance matrices **M***c*+*<sup>n</sup>* = *E*[(**c** + **n**)(**c** + **n**)*H*]. **M***c*+*<sup>n</sup>* is a positive semidefinite and Hermitian symmetric matrix [63]. The superscript *H* indicates conjugate transpose of a matrix. Based on the signal model above, a matched filter detector is given as

$$\mathbf{h} = \mathbf{M}\_{\mathbf{c}+\mathbf{n}}^{-1}\mathbf{x} = \mathbf{M}\_{\mathbf{c}+\mathbf{n}}^{-1}(\mathbf{\bar{s}}^{ref}\otimes\mathbf{K})\tag{22}$$

The probability of detection can be given as *Pd* <sup>=</sup> <sup>1</sup> <sup>−</sup> <sup>Φ</sup>( *kth*−**h***<sup>H</sup>* **<sup>x</sup>** *<sup>D</sup>* ), and the probability of false alarms can be given as *Pf* <sup>=</sup> <sup>1</sup> <sup>−</sup> <sup>Φ</sup>( *kth <sup>D</sup>* ). Here, *kth* is the threshold for a likelihood test and Φ(*x*) = √ 1 2*π x* <sup>−</sup><sup>∞</sup> *<sup>e</sup>*−*<sup>t</sup>* 2/2*dt*. The parameter *D* is defined as *D*<sup>2</sup> = **x***H***M**−<sup>1</sup> *<sup>c</sup>*+*n***x** = *NMN <sup>x</sup>*<sup>2</sup> *av E*[(**y**−**x**)*<sup>H</sup>* (**y**−**x**)] , where *x*<sup>2</sup> *av* is the average signal power of **<sup>x</sup>**. Generally, *<sup>x</sup>*<sup>2</sup> *av E*[(*y*−*x*)*<sup>H</sup>* (*y*−*x*)] can be regarded as the SINR at the output of the detector [43].

In terms of the Neyman-Pearson criterion, the threshold *kth* could be set as *kth* = *D*Φ(1 − *Pf*), and the detection probability can be given as *Pd* <sup>=</sup> <sup>1</sup> <sup>−</sup> <sup>Φ</sup>(Φ−1(<sup>1</sup> <sup>−</sup> *Pf*) <sup>−</sup> *<sup>D</sup>*).
