Políticas de reducción de la oferta de drogas en Colombia

As indicated in Fig. 4.1, the target moves within a 2 D indoor environment and is monitored using a CRN. As discussed in works like [37,106,119], a 2 D environment is used to simplify the tracking problem under consideration. The height or the azimuth information of the target is irrelevant to the radar scene under consideration, since we are interested to locate the target within the 2D indoor map. This type of approach is used for ground targets in which the radar units employ beam-steering techniques to illuminate the radar scene in a direction parallel to the ground plane. This greatly simplifies the problem since the spatial discretization need not be carried out in a 3 D space. Each radar unit in the CRN is fixed at a known location and transmits UWB pulses at fixed time intervals to probe the surroundings. The service area under surveillance is divided into a number of Voronoi regions, where the radars distributed in the region form the Voronoi centers as shown in Fig. 4.1. The locations of the object are classified into discrete “states” following the Voronoi regions where

−15 −10 −5 0 5 10 15 −15 −10 −5 0 5 10 15 (m) (m) Radar unit Target 1 2 3 4 5 6 ₇ 8 9 10

Figure 4.1: 10 Voronoi regions formed based on the distribution of 10 radars in the CRN. The target locations are classified into discrete “states” corresponding to the Voronoi regions where the target is located. In the above plot, the sequence of target states is 6 → 8 → 9.

Figure 4.2: System architecture of the HMM-enabled CRN.

the object is located. We further assume that the target states in consecutive time instants are correlated.

A block diagram of the system architecture is illustrated in Fig. 4.2. Each radar

transmitter probes the environment to obtain a radar scene by sending UWB wave-

forms. The signals reflected from the target are sampled and the RSS/TOA profiles are extracted, which are relayed to a central data fusion center. Subsequently, the data fusion center stores the measurements recorded by all radars and constructs a global RSS/TOA map. The global RSS/TOA map comprises the first arrived pulse of the backscatter signal at each radar unit as well as the corresponding TOA lag. It then identifies the nearest set of radars based upon this profile at the current time instant to facilitate triangulation of the object. The index of the nearest radar (or equivalently, the Voronoi region in which the target is located) is identified as the state of the target to establish the HMM. Next, the data fusion center forwards this information to the estimation and tracking module, which then estimates the required HMM parameters. This process is repeated until the convergence of the parameters is achieved. The estimation and tracking module then computes the target position, which is fed back to the data fusion center and is subsequently used for activating the appropriate group of radars in the vicinity of the object in the next time interval. This operation facilitates adaptive illumination of the radar scene and essentially leads to a CRN featuring the following two properties described in [34,35]: (i) intelligent signal processing, which builds on real-time learning through contin- uous interactions of the CRN with the surroundings; and (ii) feedback from the

receiver to the transmitter, which is a facilitator of intelligence.

We consider a monostatic radar configuration, where the transmitter and the receiver are collocated. The radar channel comprises a forward connection and a backward connection. The former describes signal propagation from the transmitter to the target, while the latter characterizes the target-to-receiver link. Each radar measures the RSS and TOA of the backscatter signal from the object. The method of least square is then applied for location estimation from the noisy set of mea- surements. To solve the multimodal optimization problem due to the nonlinearity of the relationship between RSS/TOA and target position, the Taylor-series expan- sion method is used to linearize the measurement model following the procedures in [108, 109]. It is worth noting that a radio frequency identification (RFID) tag could be attached to the object to enhance its radar cross section [37, 120, 121]. In this case, a radar unit also serves as a RFID reader, and the RFID tag could facili- tate boosting of the backscatter signal (e.g., enhanced RSS, more recognizable target signature) from the target, potentially leading to improved localization accuracy.

It is assumed that each LOS path has been extracted through some preprocess- ing steps. For example, each radar may employ beam-steering [37, 122] and delay windowing [101] to suppress undesirable clutter interference. As a result, we focus on the direct path in the subsequent analysis. The TOA is equal to the round-trip propagation time τ = 2d/c, where d is the one-way propagation distance and c is the speed of the electromagnetic wave. To account for the dependence of RSS on d, the received power can be expressed as [120]

PR = −10α log τ + ̺, (4.1)

where α is the two way path loss exponent, and ̺ = 10 log PT+ K is a constant that

depends on the power PT of the transmit antenna and a propagation constant K

that depends on the indoor path loss model that we adopt. The value of α = 4.8 and K = −25 dB is as shown in [123]. Thus (4.1) represents the log-normal shadowing and fast fading effect for the received signal power. The received signal could also be represented as where PT represents the transmission power, and α denotes the one-

way path loss exponent. The extension to noisy LOS data due to channel shadowing and fading, imperfect LOS acquisition, and measurement errors can be realized by modeling PR and τ as log-normal random variables as discussed in the subsequent

analysis.