Localization of Multiple Unknown RF Sources by Combining a Power Monitoring Network and a Guided Moving Sensor Under Constraints Ioannis Kyriakides1 , Konstantinos A. Gotsis2 , John N. Sahalos1,2 1 University 2 Aristotle
of Nicosia: Department of Engineering, Nicosia, Cyprus,
[email protected] University of Thessaloniki: Department of Physics, Thessaloniki, Greece,
[email protected]
Abstract—This paper presents a Sequential Monte Carlo (SMC) method for the localization of an unknown number of RF sources with unknown transmit power. The proposed method uses Received Signal Strength (RSS) measurements taken by a network of static sensors and a guided moving sensor. A constraint is imposed on the number of trips that the moving sensor is allowed to make for the confirmation of the existence and the location of a new source. In order to identify sources of varying transmission power, the SMC algorithm incorporates an adaptive RSS threshold detection method. Simulations demonstrate the improvement in the performance of the proposed adaptive versus a fixed threshold algorithm, under the constraints of a limited number of sensor trips. Moreover, source identification performance is examined using different number of sensor trips and static sensors. Index Terms—wireless sensor network, localization, RSS, moving sensor, Monte Carlo.
I. I NTRODUCTION The continuous increase in mobile broadband traffic and the increasing demand of end users for high data rates, leads to the densification of the radio-access networks [1]. Thus, the problem of detection and identification of unknown RF transmissions in urban environments is becoming more intense. To the best of our knowledge there has not been targeted research dealing with this problem, although in the literature one can find many publications concerning the localization of electromagnetic, acoustic or other types of sources using Wireless Sensor Networks (WSN) [2]-[9]. A typical WSN consists of a big number of sensor nodes. The location of some nodes is known (anchor nodes), whereas the localization of the unknown nodes (sources) is needed. The most practical and useful localization approach uses the Received Signal Strength (RSS) measurements between the anchor nodes and the sources [2]. Most of the works found in the literature deal with the localization of a single unknown node. It is difficult for a sensor that simultaneously gets signals from multiple sources, to distinguish the contribution of each source. There are works that deal with the multiple source localization problem, but instead of the RSS measurements, they use the relatively complex Time of Arrival (ToA) measurements [9]. In other cases cooperative RSS-based localization is used [6]. In cooperative localization there is also the possibility of RSS measurements between the source
nodes, which means that after an unknown source has been found, this source can be used as an anchor node for the localization of other sources. In non-cooperative localization, the source nodes communicate only with the anchor nodes. Moreover, in some approaches a small number of unknown sources is considered as a priori known [7]. The localization of multiple unknown RF sources in an urban environment differs from a typical WSN localization problem, since the number of the unknown sources usually is big, variable and it is also an unknown. Moreover, cooperative techniques cannot be applied and there are restrictions and particularities due to the extent, the characteristics and the dynamic changes of the urban environment. In order to deal with the requirements and the dynamic state of this problem, the authors in [10] introduced a novel Sequential Monte Carlo (SMC) based method, which uses the RSS measurements from a network of static sensors, in conjunction with a moving sensor. An SMC method is able to accurately model the noisy nature of sources and the non-linear relationship between target state and measurements [11], [12]. In [10] the SMC method used the measurements of each static sensor to provide the probability distribution of the possible presence of sources in an area. This enabled the localization algorithm to focus sensing and computational resources in areas of high probability of new source existence and guide the moving sensor towards these areas, in order to verify source presence and give the final location estimation. In essence, the moving sensor is used to remove the ambiguity caused from the simultaneous signals received by a single sensor from multiple unknown sources. This paper adds a significant and realistic parameter to the problem, by assuming that the transmit power of the sources to be found is unknown. Moreover, an important restriction is imposed on the number of moving sensor trips in relation to the number of static sensors. This restriction is necessary, as a real life scenario would consider the cost of fuel and sensor deployment. Considering sources of unknown power, while imposing a constraint on moving sensor trips, increases the level of difficulty in source localization. Thus, an adaptive method is required to handle the decision to activate the moving sensor and confirm a new source. Therefore, unlike [10] that uses a fixed weight threshold to activate the moving sensor and a fixed RSS threshold for the final source
confirmation, this work introduces an adaptive RSS threshold to identify sources with varying transmit power, based on the constraint of a limited number of moving sensor trips and number of static sensors. Simulation results are given that demonstrate the performance of the method under various scenarios and constraints. Section II describes the system model, whereas the source detection and localization methodology is developed in Section III. Simulations results are presented in Section IV, and the paper is concluded in Section V. II. S YSTEM MODEL Consider an area with S randomly located RF sources, H−1 wireless static sensors and one moving sensor. Sources indexed by i = 1, . . . , K are considered to have known states, while the indices i = K + 1, . . . , S represent the unknown sources. The proposed algorithm locates one unidentified source at a time. After a confirmation of a source as a true one, the procedure goes on to the next source to be detected. The power received by sensor h at each time step τ is given by rh,τ =
S X
F(xi,τ , ψ h,τ ) + ητ
(1)
i=1
where xi,τ = [xi,τ , yi,τ , zi,τ ], i = 1, . . . , S
(2)
ψ h,τ = [¯ xh,τ , y¯h,τ , z¯h,τ ], h = 1, . . . , H
(3)
n For the first unknown source, the measured signal density rh,τ at each sensor h is calculated by n rh,τ =
K X
F(xi,τ , ψ h,τ ) + F(xnK+1,τ , ψ h,τ ).
(7)
i=1
Then, the measurement likelihood and the weight wτn of the nth particle are calculated [10]. Particles with higher values of weight, it is more likely to be closer to the actual location of the unknown source. The static sensors which are closest to the location indicated by the highest particle weight are found. If the RSS measurement of one of these sensors is higher than the activation threshold Ta , the moving sensor is activated and guided towards this static sensor to detect a possible unknown source. Then, the RSS confirmation threshold Tc confirms or not the existence of an unknown source and through an optimization procedure the final location estimate is provided. The source that has just been confirmed is considered as known in (7), and the procedure is repeated to find the next unknown source. The RSS thresholds are dynamically adjusted by the localization process as explained next. A high threshold allows the detection of stronger emitting sources with a limited number of moving sensor trips, however may miss the weaker sources. If there is a sufficient number of remaining sensor trips, the algorithm is then able to reduce the threshold and localize weak sources.
and denote the Cartesian coordinates of the ith source and the hth sensor, whereas ητ is a zero mean gaussian noise with variance σ 2 . The function F is used to represent the power intensity contribution from source i to sensor h, !α c (4) F(xi , ψ h ) = Pi Gt Gr 4πdi,h f where q di,h =
2
2
2
(xi − x ¯h ) + (yi − y¯h ) + (zi − z¯h )
(5)
is the distance between the source i and the sensor h, c is the speed of light in vacuum, Pi is the transmit power of the ith source, Gt is the transmitter gain, Gr is the sensor gain, f is the frequency and α is a constant that depends on the electromagnetic radiation propagation model. III. S OURCE D ETECTION AND L OCALIZATION M ETHOD A. SIR with static sensors The area under test is divided into subareas. The Sampling Importance Resampling (SIR) particle filter [11] is applied to each subarea to estimate the probability distribution of an unknown source location. According to the SIR, N random hypotheses on the j th unknown source location are proposed and each particle n is represented as n n xnK+j,τ = [xnK+j,τ , yK+j,τ , zK+j,τ ]
(6)
B. Threshold Adaptation In this section the threshold adaptation technique and its benefits are explained. We define as a trip, each departure of the moving sensor in order to confirm the existence and the location of a new source. The amount of total trips is the addition of trips that lead to a successful source localization and unsuccessful trips triggered by false alarms. The ratio of successful trips over the total number of trips is expected to increase by increasing the probability of detection Pd . Similarly, the unsuccessful trips would be reduced if the probability of false alarm Pf a reduces. Therefore, the goal is to increase Pd and reduce Pf a . The parameters on which the two probabilities depend in the context of this work are next considered. The probability of detection is given by [13] √ (8) Pd = Q (Ta − F(xi , ψ h ))/ σ 2 where σ 2 is the sensor noise variance, Q is the right-tail probability [13], and F(xi , ψ h ) is given in (4). Thus, the probability of detection Pd will be higher for sources with higher values of F(xi , ψ h ), which result at higher SNR at the sensors. Assuming that the noise variance is the same for all sensors, the SNR depends on the unknown transmitted power of the source Pi and the unknown source-sensor distance di,h . Also, √ Pf a = Q Ta / σ 2 , (9)
IV. S IMULATION R ESULTS Independent runs were used to test the proposed methodology for different simulation scenarios. At each run, 40 known and 10 unknown sources are randomly located in an area with dimension 1000 × 1000m2 . The height of the sources is also randomly chosen between 25 ± 10m. The static sensors are uniformly located throughout the entire area and their configuration remains constant for all simulation runs. For the purposes of the simulation, we consider a Nominal Signal to
Misidentified sources (%)
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Fig. 1. The percentage of misidentified sources versus NSNR using adaptive threshold. 10 unknown sources, 11 moving sensor trips and three different numbers of static sensors: 3, 9, and 16.
Misidentified sources (%)
which means that both the Pd and Pf a increase with a decrease of the threshold Ta and vice versa [13]. The usefulness of the adaptive threshold in improving the performance of unknown source detection is next explained. When a high threshold is used, (8) and (9) show that unknown sources resulting in high sensor SNR, will be most likely detected first, while maintaining a low Pf a . If these sources are identified with a low number of unsuccessful trips, then more trips remain available for identifying sources with lower RSS at their nearest sensors. For these low RSS sources, the threshold needs to be reduced to increase their probability of detection. However, reducing the threshold increases both the probability of false alarm and the number of unsuccessful trips. Another important reason for using an adaptive threshold is to avoid the costly trial and error procedure for the determination of the fixed threshold that works best in a given scenario. On the contrary, an adaptive threshold makes the source identification algorithm more versatile and widely applicable. Therefore, in this work the following simple adaptation mechanism is proposed: The algorithm starts with a high threshold to identify sources that give high sensor SNR. Then, if after a number of scans no detections are reported, the threshold is reduced to increase the probability of detection for sources that give lower sensor SNR. This process continues until the total number of trips is exhausted. Given that stronger sources will be most likely identified first, then the mechanism will gradually decrease the threshold, without manual interference, resulting to an automatic resource management. The adaptive method’s ability to identify sources of varying signal strengths is demonstrated using simulation results in Section IV. Starting values for the range of the adaptive activation threshold are selected based on a desired range of Pf a and Pd and the minimum and maximum values of the SNR at the sensors. The range of the SNR is calculated from (4), using minimum and maximum values of the transmitted power and a nominal distance between an unknown source and its closest static sensor. The nominal distance used to define the range for the activation threshold is taken as the distance between a static sensor and a point midway between the sensors. In order to calculate a range of values for the confirmation threshold, higher values of SNR are assumed, since the moving sensor moves in close proximity to the unknown sources. The proposed method may easily adapt to scenarios of varying transmitted power and SNR.
adaptive fixed optimized fixed low
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Fig. 2. The percentage of misidentified sources versus NSNR, for 10 unknown sources, 11 moving sensor trips and 9 static sensors. Adaptive threshold and two different values of fixed threshold are used for the detection and localization of the unknown sources.
Noise Ratio (NSNR) that comes from a nominal source-sensor distance of 100m and a transmit power of 40 Watts. The NSNR takes values of 6, 10, 14, 18 dB and it is used to calculate the values of noise variance, which are common for all sensors for the respective value of NSNR. The NSNR should not be confused with the actual SNR, which is different at each sensor and depends on the particular source-sensor distance. The transmit power of the unknown sources varies from 10 to 60 Watts, whereas Gt = 10dBi, Gr = 2dBi, and f = 942.5MHz. In all simulation results the number of misidentified sources is tested versus the different NSNR numbers. Misidentified sources are counted as the number of: a) sources for which estimates are located more than ds = 20m away from the true source locations, b) sources not identified, and c) any source identifications that exceed the number of true unknown sources. Figure 1 illustrates the percentage of misidentified unknown sources versus NSNR, for various numbers of static sensors. For this scenario, the moving sensor is allowed to make 11 trips in order to detect and localize 10 unknown sources using threshold adaptation. The results show that as the NSNR increases, the difference in the performance between the three configurations of static sensors becomes smaller (especially between the 9 and 16 sensors). In the following cases a setup of 9 static sensors is used.
Misidentified sources (%)
V. C ONCLUSION
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Fig. 3. The percentage of misidentified sources versus NSNR using adaptive threshold. 10 unknown sources, 9 static sensors and different number of sensor trips: 11, 12, 15, and 20. 10 11 trips 12 trips 15 trips 20 trips
RMSE (m)
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R EFERENCES
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This work considers the localization of an unknown number of multiple unknown RF sources in an urban environment. Compared to [10], the proposed SMC methodology has been extended to detect and localize RF sources with unknown transmit power and also to impose realistic constraints on the number of trips that the moving sensor is allowed to make. In order to deal with the above, an adaptive threshold technique has been introduced to control the moving sensor activation. Simulation results have shown that given an unknown number of multiple sources to be found with unknown transmit power, the proposed methodology is robust and accurate, given an adequate number of sensor trips and static sensors. In future work the theoretical framework and the practical implementation of the method will be further studied and developed.
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Fig. 4. The localization RMSE versus NSNR using adaptive threshold. 10 unknown sources, 9 static sensors and different number of sensor trips: 11, 12, 15, and 20.
In Figure 2 a comparison is provided between the use of a fixed threshold and the adaptive threshold method. The percentage of misidentified unknown sources versus NSNR is illustrated for 10 unknown sources and 11 moving sensor trips. The ’fixed low’ threshold value has been set equal to the lowest value of the adaptive threshold range. It is shown that for low NSNR the performance of the low threshold is much worse than the adaptive, since there are false alarms that spend the available number of moving sensor trips. For a fair comparison and after trials, the results for a higher, optimized threshold that gives improved performance are also given. The curve of the ’fixed optimized’ threshold converges with the adaptive one, as the NSNR increases. Results for even higher fixed thresholds are not demonstrated, since the performance significantly deteriorates due to the increased number of missed sources. Figure 3 illustrates that the percentage of misidentified unknown sources decreases as the number of moving sensor trips increases. Moreover, it is noted that the curves for various numbers of sensor trips, converge as the NSNR gets higher. Figure 4 shows the localization RMSE versus NSNR, which does not exceed 7 meters for any case. The RMSE performance is similar for the different number of sensor trips examined, since the RMSE is calculated for successfully detected sources, and thus, it does not include a penalty for misidentified sources.
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