Novel Technique for Locating an Intruder in 3D Environments by Using a Cooperative System of Multistatic Radars

— the aim of this work is to present a new methodology, based on vector and geometrical techniques, for determining the position of an intruder in a residence (3D problem). Initially, modifications in the electromagnetic responses of the environment, caused by movements of the trespasser, are detected. It is worth mentioning that slight movements are detected by high frequency components of the used pulse. The differences between the signals (before and after any movement) are used to define a sphere and ellipsoids, which are used for estimating the position of the invader. In this work, multiple radars are used in a cooperative manner. The multiple estimates obtained are used to determine a mean position and its standard deviation, introducing the concept of sphere of estimates. The electromagnetic simulations were performed by using the FDTD method. Results were obtained for single and double floor residences.


I. INTRODUCTION
Considerable increase of the attention of researchers to indoor radar systems has been observed in last decade [1][2][3][4].This kind of system is able to detect and precisely locate intruders, even when they are positioned among walls and furniture.These radars use UltraWideBand (UWB) pulses [1] for detecting the presence of an intruder by measuring differences on electromagnetic responses when these pulses are propagated at different moments.These pulses are extremely narrow in time, what characterizes them as ultrawideband signals.This characteristic provides to the pulse enhanced immunity to selective attenuations of frequencies, which are inherent to scattering environments.Due to the fact that the UWB pulses are so narrow, they can use broad frequency spectra, allowing the signals to use low power, what minimizes the interference with other communication systems, such as cell phones, GPS, Bluetooth, W-LAN IEEE 802.11, among others [2].
The finite-difference time-domain method (FDTD), developed by Kane Yee [5], when applied to solve Maxwell's equations, allows the simulation of the propagation of electromagnetic waves in time domain, providing full-wave solutions.In this work, this technique was combined to the Uniaxial Novel Technique for Locating an Intruder in 3D Environments by Using a Cooperative System of Multistatic Radars Josivaldo de S. Araújo, Rodrigo M. S. de Oliveira and Carlos Leonidas da S. S. Sobrinho Universidade Federal do Pará (UFPA) -ICEN & ITEC -josivaldo@ufpa.br,rmso@ufpa.br,leonidas@ufpa.brPerfectly Matched Layer (UPML) formulation [6], in order to truncate the analysis region.In this way, this technique simulates an anechoic chamber.
Based on the ideas discussed above, the aim of this work is to present a methodology which estimates the position of an intruder in a tridimensional environment through detecting modifications in the transient responses of the environment about wideband (WB) pulses, caused by the movements of the intruder.Even if these movements are slight, the detection is possible due to the higher frequency components of the pulse.The estimate of the position will be held through a vector technique proposed in this work.This paper represents advance to previous works, because, besides approaching the problem in 3D, when previous works are limited to the 2D case [3,4], it introduces a simpler methodology.The power spectrum of the used wideband pulse ranges from 0.3 to 0.8 GHz.It is observed in this paper that pulses in this frequency range, associated to the developed methodology, can be used for properly estimate the intruder's position inside an ordinary indoor environment.The developed methodology was tested by using data obtained from the full-wave numerical simulations.

II. ENVIRONMENT DESCRIPTION AND SIMULATION PARAMETERS
In this work, tridimensional indoor environments are considered.Fig. 1 illustrates the first scenario simulated.In this environment, there are two distinct kinds of walls, characterized by different electrical parameters, which are: the relative electric permittivity of external walls is ε r = 5.0 and, for those of the interior, ε r = 4.2.The used conductivity is σ = 0.02 S/m for every wall [7].Everywhere else, the relative permittivity is equal to unity and σ = 0, except in the ground region, which penetrates the UPML.The thickness of walls is 30 (external) and 18 (internal) centimeters [7].Every media is modeled by using µ = µ 0 .In order to complete the environment description, the only missing item is the target.In order to represent the intruder, it was used the model presented in

III. TEMPLATE
The relative permittivity considered [10], which represent average parameters.The simulations are performed by using the 3D-FDTD method for nondispersive isotropic media (analysis region), based on the Yee's formulation [5].Here, a mesh with 384 × 352 × 120 cells was ∆s = 3.0 cm ( s x y z ∆ = ∆ = ∆ = ∆ ) were used.tenth of the minimum free-space wavelength of the excitation pulse reduce numerical dispersion effects.The time increment ∆t was obtained from ∆ the numerical stability of the method.In this paper, 70% of the Courant's limit were optimized in order to reduce undesired reflections cells, maximum attenuation conductivity σ max = 15 S/m, and the order of the attenuation Here, a Beowulf cluster with 16 cores was used for generating the transient signals.
The waveform used as an excitation source, in order to scan the environment, is the Gaussian .This type of pulse is used, for example, by the PulsON system [ The Gaussian monocycle is the first derivative of Gaussian function with respect to time , τ = 0.255 ns and t 0 = 1.8 ns.This function is plotted in Graphical representation of the wideband excitation pulse (time domain) o complete the environment description, the only missing item is the target.In order to ed the model presented in Fig. 3, with approximately 1.70 m The relative permittivity considered for the intruder is ε r = 50 and its conductivity ], which represent average parameters.FDTD method for nondispersive isotropic media .Here, a mesh with 384 × 352 × 120 cells was were used.∆s is equivalent to space wavelength of the excitation pulse, in order to s ∆ , in order to assure limit is used [6][7][8].The were optimized in order to reduce undesired reflections: thickness of 10 attenuation polynomial was used for generating the transient signals.
order to scan the environment, is the Gaussian PulsON system [9].with respect to time, which is  The radar system was also simulated by using t a cuboid conductor, with dimensions h = 9 cm, w = c = 6 cm and d = 3 cm, with p = 30 cm.The distance from the ground plane to the vertical rectangular radiator is 3 cm.This monopole's bandwidth is approximately 500 MHz he transceiver antennas used for this work is a wideband dipole with the dimensions .The antenna dimensions are c = 12 cm, w = 6 cm, h = 6 cm and , modeled by thin wire [11].This dipole's bandwidth is approximately 300 MHz . Diagram of the dipole antenna used as transceiver.
The radar system was also simulated by using the monopole antenna shown by , with dimensions h = 9 cm, w = c = 6 cm and d = 3 cm, with p = 30 cm.The distance from the ground plane to the vertical rectangular radiator is 3 cm.This monopole's bandwidth is approximately 500 MHz (50 Ω feeding impedance).
Diagram of the monopole antenna used as transceiver.
Feeding Gap In order to determine the position of the intruder in the simulated environment, for the case of the residence presented in Fig. 1 (by using the origin of the system of coordinates as reference), two mathematical methods were used: the FDTD method, for generating electromagnetic field data; and the concept of propagating ray [8,12], for obtaining the parameters of the sphere and ellipsoids used for localization.When a two dimensional case is analyzed, two aspects related to propagating rays are considered: 1) the transceiver antenna transmits the pulse, which reflects at the target and returns to the transceiver.The time the wave needs to complete this path is used to define a circumference, centered at the transceiver, in which the trespasser may be positioned on any of its points.2) the transceiver transmits the pulse, which reflects at the intruder and reaches a receiver.The time the signal needs to complete this path is used to define an ellipse, in which the trespasser may be positioned on any of its points [7].The second case is also valid for other receivers.This defines a system of equations which solution is an estimate of the position of the undesired visitor.If the wave propagates in free space, the system's solution is the exact position of the man, as long as the propagating speed would be that of free space, everywhere.When three-dimensions are considered, this idea is still valid.However, a sphere and ellipsoids must be considered.
The cooperative system used to determine the position of the intruder is presented by Fig. 6, where four transceiver antennas can be observed, numbered from 1 to 4, as well as their positions in space.
The system works as a cooperative multistatic radar.It is also observed from Fig. 6 that there are two x-polarized (transceiver) dipoles and two y-polarized dipoles (for the cooperative system based on the dipole antenna).The goal is to avoid that the intruder gets to be simultaneously positioned at a null of two or more (transceiver) antennas' radiating patterns, what could make the pinpointing of the position difficult.A system based on z-polarized cuboid monopole antennas (Fig. 5) was also tested.
In order to determine the position of the intruder, the wideband pulse defined by ( 1) is transmitted.
Then, the temporal evolution of the electric field is registered in several points (receivers) and stored as reference.The pulse is then retransmitted and the transient electric field is once more registered by the receivers.Any movement performed by the intruder inside the house, as for example, a little movement of his head distorts the signals captured, which are compared to the transient responses previously obtained.After processing these data, the radii of the ellipsoids (each with foci positioned at a transceiver and a receiver positions) and the radii of spheres (each centered at a transceiver's position) [3] are obtained.A transceiver and two receivers define a multistatic radar system, which produces an estimation of the position of the intruder.This way, the combination of this transceiver with other pair of receivers produces a different estimate, as it also happens when other transceiver is considered.In this case, and a statistic analysis is performed.For each transceiver, deviation are calculated, and a sphere of estimates (centered at the mean position with radius identical to the calculated standard deviation) is defined.This the intruder is possibly positioned when that transceiver is considered.
way, four spheres of estimates are determined.In order to decide which transceiver produces more , the smaller radius (standard deviation) sphere is considered.
IV. THE PROPOSED METHODOLOGY oriented from point A (x A , y A , z A ) to point B (x B , y B , z B ), oint A defines the position of a transceiver and point B defines the position of can be written as ( , , ) ( , , ).
, which are defined for sake of simplicity, are, this way, given by .A transceiver and two receivers define a multistatic radar system, which produces an estimation of e combination of this transceiver with other pair of receivers produces a different estimate, as it also happens when other transceiver is considered.In this case, and a statistic analysis is performed.For each transceiver, the mean centered at the mean is defined.This sphere encloses a when that transceiver is considered.This transceiver produces more ), such as indicated by and point B defines the position of a receiver.
Finally, the unit vector , k is obtained by using ( 12), as follows , , , In order to perform the transformation of coordinates around the origin, by using the former coordinate system as reference, the equation is solved, in which 1 1 1 2 2 2 3 3 3 ( , , , , , , , , ) l m n l m n l m n are the direction cosines related to x, y and z, respectively.From (13), the equations ˆ. ; . ; .; ˆ. ; . ; .; ˆˆˆ.
After performing the transformation of coordinates, it is necessary to rotate the ellipse, so that points of an ellipsoid (aligned to , î ) are calculated.In a general way, an arbitrary unit vector L =(l x , l y , l z ) is used to define rotation.The coordinates x R , y R and z R , obtained by performing the rotation of (x, y, z) around L by an angle α, are given by (1 (1 ) (1 ) ( 1) , (1 ) (1 ) (1 ) in which [R] is the rotation matrix, c = cos(α) and s = sin(α).
In order to obtain the rotation around the axis x', (17) is used in (16).
x y z l l l In synthesis: a) initially one generates a ellipse (Fig. 8a) on the coordinate system of reference (x,y,z) (the radii of the ellipse are obtained by using the difference of the transient signals obtained at the associated receiver [3] and z=0); b) one defines a new coordinate system by using ( 2)-( 12) and performs the transformation of coordinates around the origin by using ( 13)-(15) (Fig. 8b); c) ellipse in 3D space is then rotated by using ( 16)-( 19), generating this way the corresponding ellipsoid (Fig. 8c); d) finally, the multistatic radar's geometry is defined by considering a transceiver (sphere) and two receivers (Fig. 8d).The estimate of the trespasser's position is defined by the point equidistant to the three surfaces, such as it is illustrated by Fig. 8d.

V. RESULTS
In order to pinpoint the intruder's position, nine receivers and four transceiver dipole antennas were set up in different parts of the house (Fig. 6).The cooperative multistatic system was tested for four different cases.For the first and second cases, a single-floor residence is considered and the intruder was positioned at different rooms.His head was displaced by a single Yee's cell.For the third case, the intruder moves one of his legs.Finally, it is considered a double-floor residence in the fourth case.
For the first case (Fig. 9), the center of the head of the intruder is located at x = 2.48 m, y = 2.53m, z = 1.70m and the intruder is located at bedroom 1.The sphere of estimates (which encloses the region of space with higher probability of finding the man), depicted in Fig. 9, is fully contained in the room where the intruder is located.It was obtained by using the system shown in Fig. 6.A sphere of estimates was determined for each transmission antenna.The region enclosed by the sphere with the smaller radius (estimate with the less significant standard deviation) was considered to be the radar's estimate (Table I).This sphere is represented in Fig. 9 and it is clearly seen that the intruder's head is inside the estimated region.

Journal of Microwaves, Optoelectronics
Brazilian Microwave and Optoelectronics Society Brazilian Society of Electromagnetism-SBMag  As it has been described in section III, the electromagnetic pulse is transmitted twice (after a certain period of time), in such way that movements of the person can be detected by the system.The detection is performed by computing the point to point difference between the two sign the receivers and at the transceiver points.For two different receivers, both signals received are plotted in Figs.10a and 10b.As it can be seen in Fig. 10, there is a slight difference between the signals.This small discrepancy is due to the fact that the intruder performed a minor movement (of 3 cm) of his head.Despite this slight difference between the signatures, the system is able to properly locate the intruder.For the second case (Fig. 11), the trespasser is at the kitchen.In this case, the intruder is placed near to TX2 (Fig. 6).The head of the intruder is centered at x = 6.08 m, y = 3.44 m, z = 1.70 m.In Fig. 11, a side view (x-z plane) of the intruder placed in the kitchen is presented.The sphere of estimates depicted in Fig. 11 (the sphere with the shortest radius) correctly indicates the room where the intruder is located.The information related to the spheres of estimates, for this case, is available in Table II.) the new leg's position.

Journal of Microwaves, Optoelectronics
Brazilian Microwave and Optoelectronics Society Brazilian Society of Electromagnetism-SBMag As it can be seen in Fig. 13, there is a slight difference between the signals.This small discrepancy is due to the fact that the intruder performed a minor movement (of 3 cm) of his leg.Despite this slight difference between the signatures, the system is able to properly locate the intruder.In the fourth case, a second floor is added to the house considered in the previous simulations (Fig. 14).In this case, all the transceiver by Fig. 6) and half of quantity of the receivers was moved to the second floor.
performs the same movement considered in the first case, Fig. 14, it is also depicted the smallest radius sphere encloses contains the intruder's head  As it can be seen in Fig. 13, there is a slight difference between the signals.This small discrepancy is due to the fact that the intruder performed a minor movement (of 3 cm) of his leg.Despite this signatures, the system is able to properly locate the intruder.performs the same movement considered in the first case, was also placed at the smallest radius sphere of estimates (see Table IV).The region of space it head.Here, only dipole antennas were employed.As it can be seen in Fig. 13, there is a slight difference between the signals.This small discrepancy is due to the fact that the intruder performed a minor movement (of 3 cm) of his leg.Despite this signatures, the system is able to properly locate the intruder.

Fig. 5 .Fig. 3 .
Fig.5.Diagram of t with the dimensions , h = 6 cm and d = p = 3 cm.The dwidth is approximately 300 MHz shown by Fig.5.It consists on , with dimensions h = 9 cm, w = c = 6 cm and d = 3 cm, with p = 30 cm.The distance from the ground plane to the vertical rectangular radiator is 3 cm.This monopole's III.RADAR APPLICATION

Fig. 6 .Fig. 7 .
Fig.6.Representation of the Environment of Simulation and Position of the Transceiver Antennas

.
Representation of the Environment of Simulation and Position of the Transceiver Antennas.
Fig.7.: The vector in which the direction cosines are given by , , ,

Fig. 8 .
Fig. 8. Steps necessary for defining the multistatic radar's geometry: (a) a ellipse on the coordinates (ellipse in 3D space), (c) rotation of the ellipse around to AB and (d) the multistatic radar's geometry associated to the ellipsoids).

Fig. 9 .
Fig.9.Side view (x-z plane) of the the intruder in bedroom 1

y
Optoelectronics and Electromagnetic Applications, Vol.10,No. 2 Microwave and Optoelectronics Society-SBMO received 8 Oct. 2010; for review11 Oct. 2010defining the multistatic radar's geometry: (a) a ellipse on the xy-plane, (b) transformation of coordinates (ellipse in 3D space), (c) rotation of the ellipse around ' î and translation of coordinates the multistatic radar's geometry (considering a transceiver associated to the sphere plane) of the the intruder in bedroom 1 and a sphere of estimates.Movement of head was considered.section III, the electromagnetic pulse is transmitted twice (after a certain period of time), in such way that movements of the person can be detected by the system.The detection is performed by computing the point to point difference between the two sign the receivers and at the transceiver points.For two different receivers, both signals received are x b) transformation of coordinates for aligning the ellipsoid associated to the sphere and two receivers ovement of head was considered.section III, the electromagnetic pulse is transmitted twice (after a certain period of time), in such way that movements of the person can be detected by the system.The detection is performed by computing the point to point difference between the two signals obtained at the receivers and at the transceiver points.For two different receivers, both signals received are

Fig. 10 .
Signatures obtained at two receivers considering the initial and final positions of the intruder's head.In (a) Dipole Antenna and (b) Monopole Antenna.

Fig. 11 .
Fig.11.Side View (x-z plane) of the the intruder in In the third case, the intruder is the position x= 2.50 m, y = 2.30 intruder in the bedroom 1 and the associated estimative sphere new position, after performing the located.Again, in order to determine the was considered, as it can be seen in TableIII.deviation, as in the first case.I estimates of the third case was formed closer to the men's leg, presented methodology.

Fig. 12 .
Fig.12.(a) Side View (x-z plane) of the Optoelectronics and Electromagnetic Applications, Vol. 10, No. 2 Microwave and Optoelectronics Society-SBMO received 8 Oct. 2010; for review 11 Oct. 2010; accepted SBMag © 2011 SBMO/SBMag plane) of the in the kitchen and a sphere of estimates.Movement of head was considered.the intruder is placed at bedroom 1 and the center of one of 2.30 m, z = 0.78 m.In Fig.12a, one has a side view ( and the associated estimative sphere.Fig 12b shows the intruder's leg at its new position, after performing the movement.The sphere defines the room where the intruder to determine the position of the intruder, the sphere with the shortest radius was considered, as it can be seen in Table III.Once more, TX4 produced the smallest statist t can be observed by comparing Figs. 9 and 12 was formed closer to the men's leg, implying in consistency of the (a) plane) of the intruder in the bedroom 1; (b) original leg's position; (c) the new leg's position.II.RADIUS RELATIVE TO EACH TRANSCEIVER (THIRD CASE).
319 ovement of head was considered.one of his legs is located at , one has a side view (x-z plane) of the b shows the intruder's leg at its The sphere defines the room where the intruder is of the intruder, the sphere with the shortest radius Once more, TX4 produced the smallest statistical 12a that the sphere of implying in consistency of the (b) (C)

Fig. 13 .
Fig.13.Signatures obtained at two receivers considering the initial and final positions of the intruder's leg.Antenna and (b) Dipole Antenna.

Fig. 14 .
Fig.14.Side View (plane x-z) of the intruder in the

Fig. 13 .
Fig.13.Signatures obtained at two receivers considering the initial and final positions of the intruder's leg.
the intruder in the second floor's bedroom 1. Head movement

Fig. 13 .
Fig.13.Signatures obtained at two receivers considering the initial and final positions of the intruder's leg.In (a) Monopole 10,No. 2tronics and Electromagnetic Applications, Vol.10,No. 2 Microwave and Optoelectronics Society-SBMO received 8 Oct. 2010; for review 11 Oct. 2010; accepted SBMag © 2011 SBMO/SBMag are the coordinates of P. The points A, B and P are used to define coordinate system, which has its x', y' and z' axes aligned to the following directions:: it is defined as the unit vector directed from A to B (which represent .It is obtained from vector ,x ( given by (2) ).This way, Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol.10, No. 2, December 2011 Brazilian Microwave and Optoelectronics Society-SBMOreceived8 Oct. 2010; for review 11 Oct. 2010; accepted 5 July 2011 Brazilian Society of Electromagnetism-SBMag © 2011 SBMO/SBMag ISSN 2179-1074

TABLE I .
SPHERES OF ESTIMATES' RADII (FIRST CASE).

TABLE II .
ESTIMATIVE SPHERE'S RADIUS RELATIVE TO EACH TRANSCEIVER (SECOND CASE).