ARTICLE Year : 2012  Volume : 2  Issue : 2  Page : 6974 A Censoring and Quantization Scheme for EnergyBased Target Localization in Wireless Sensor Networks Zhenxing Luo Department of Electrical and Computer Engineering, The University of Alabama at Birmingham, Birmingham, AL, USA Correspondence Address: This article presents a censoring and quantization scheme for energybased target localization in wireless sensor networks (WSNs). This scheme can save energy and communication bandwidth. Moreover, a multiobjective optimization method is used to balance the energy consumption and target localization performance of the energybased target localization method using this scheme. Results show that the root square mean (RMS) errors provided by the energybased target localization method using this scheme were close to the CramerRao lower bound (CRLB). Moreover, the Paretofronts provided by the multiobjective optimization method can guide practical applications.
1. Introduction Wireless sensor networks (WSNs) have been successfully applied to solve many problems, such as, environmental monitoring, medical asset tracking, and fire rescue [1 7]. Typically, a WSN is comprised of a large number of widely distributed sensors, which are of lowcost and are resourceconstrained [8]. After gathering environmental information, the sensors will send information back to the fusion center, which has a greater computational capacity to further process the information from the sensors. In the energybased target localization method, based on the information from the sensors, the fusion center estimates the target position [8]. Usually, sensors can send either uncompressed data, such as analog data, or compressed data, such as quantized data, to the fusion center [8]. However, sending compressed data is better for resourceconstrained sensors, for two reasons. One reason is that sensors are powered by irreplaceable batteries, and therefore, energy is a precious resource for sensors. Sending compressed data will save sensor energy [8]. The second reason is that the bandwidths of communication channels between sensors and the fusion center are limited [8]. Sending compressed data uses less of the communication bandwidths. A target localization method in which sensors send analog data to the fusion center was presented in [3]. This method was improved by a target localization method, using quantized data in [8]. In recent times, another scheme to save sensor resources, which was called the 'censoring scheme', was presented in [9], for the distributed detection problem. The censoring scheme was further discussed in [1012]. A scheme to combine the censoring scheme and the quantization scheme for the distributed detection problem was presented in [13]. Moreover, a scheme to combine the censoring scheme and the quantization scheme was presented for estimation, based on a linear estimation model in [14]. This article presents a censoring and quantization scheme for the energybased target localization method based on a nonlinear estimation model, the energy decay model. Following this, a modern multiobjective optimization method, the nondominated sorting genetic algorithm (NSGAII), will be used to balance the energy consumption and the estimation performance for the energybased target localization method, using the quantization and censoring scheme. The NSGAII is a modern multiobjective optimization algorithm, with low computational complexity [15]. In most applications, it can find a good spread of solutions near the true Paretofront. Although the energy function and performance function for the energybased target localization method, using only the quantization scheme, has been presented in [16], the energy function and the performance function have not been presented for the energybased target localization method, which used the quantization and censoring schemes. The main contribution of this article is a quantization and censoring scheme for the energybased target localization method, and a multiobjective optimization approach to balance energy consumption and the target localization performance. Section 2 presents a censoring and quantization scheme for the energybased target localization method, followed by the performance function and energy function in WSNs, with onedimensional sensor array in Section 3. The energy function and performance function in WSNs with twodimensional sensor arrays are presented in Section 4. Section 5 discusses the simulation setup, and Section 6 presents results and analysis. The concluding remarks are presented in Section 7. 2. A Censoring and Quantization Scheme for the EnergyBased Target Localization Method The signal emitting from a target received at the ith sensor can be determined by the decay model originally presented in [8] [INLINE:1] in which G i is the gain of the ith sensor and P 0 is the power of the target, measured at a reference distance d0 . The distance between the ith sensor at (xi ,y i0) and a target at (xt ,y t) can be defined as [INLINE:2] A typical area of the sensor field used in the simulations is shown in [Figure 1], and our simulations for twodimensional sensor arrays were based on this sensor field with sensors in the range of (90 90), (90, 90), (90, 90), and (90 90).{Figure 1} To avoid numerical problems, the target is assumed to be at least d0 meters away from any sensor. To simplify the model (1), it is further assumed that Gi = 1 and d0 = 1. Then, model (1) can be expressed as [INLINE:3] On account of the presence of environmental noises, the signal received at sensor i can be expressed as [INLINE:4] where wiis a Gaussian noise with zero mean and variance σ 2. In the censoring and quantization scheme, two thresholds are used: A high threshold si0 and a low threshold γ 2. If the received signal si is greater than the low threshold, sensors will quantize si0 and send the decisions to the fusion center. Otherwise, the sensors will not send any decision. This is called the censoring process. In the quantization process, if si is higher than the high threshold γ 1, the decision is 1. If si0 is less than the high threshold γ 1, the decision is 1. The censoring and quantization scheme can be denoted by: [INLINE:5] The probability that mi takes value m is [INLINE:6] Based on decision vector M = [m 1 m 2 ... m N ] T received at the fusion center, the fusion center finds θ = [P 0 x t y t ] T that can maximize [INLINE:7] The maximum likelihood estimator tries to find the θ value to maximize [INLINE:8] If an unbiased estimate of θ exists, the CramerRao lower bound (CRLB) can be derived by [INLINE:9] The derivation of the CRLB matrix is similar to the process in [8]. Therefore, the detailed procedures to derive the CRLB will not be presented here. 3. The Performance Function and Energy Function in WSNS with One Dimensional Sensor Array For onedimensional sensor arrays, as shown in [Figure 2], the energy and performance functions are defined here.{Figure 2} 3.1 The energy function The energy used by sensors can be divided into three parts: Energy to keep sensors awake, energy sensors used to measure the environmental phenomena, and energy sensors used to send decisions to the fusion center. Energy to keep sensors awake and energy sensors used to measure the environmental phenomena are assumed to be constant. Then, only the energy sensors used to send decisions to the fusion center are defined. According to [16,17], the energy consumption (in Joules) for sensor i to send m bits of information to the fusion center can be determined by [INLINE:10] In (12), E elec = 50 nJ/bit, εamp = 100 pJ/bit/m 2 , and d f,i 0is the distance between sensor i and the fusion center. The overall energy required by the sensors to transmit the decision vector M to the fusion center is the sum of the energy used by each sensor to transmit mi [INLINE:11] where mi0 is the ith element of decision vector M. For a onedimensional sensor array with a specific target location and parallel decision transmission scheme, if it is assumed that the target is always present, it is easy to have [16,17]. [INLINE:12] where M is the decision vector made by the sensors and ui is the decision made by sensor i. If a target is located at (x t ,y t), the probability that sensor i has decision mi 0is p(m i/x t,y t). In (14), E T is the average energy needed for sensors to send the decision vector M to the fusion center. In determining the p(m i/x t,y t) value, high threshold γ 1 and the low threshold γ 2 are used. A detailed method to calculate p(m i/x t,y t) can be found in [17]. Throughout this article, it is assumed that the sensing cycle time is one microsecond. If A is the energy required to keep a sensor awake plus the energy needed for a sensor to sense the environment in one microsecond, the overall energy consumption by all sensors in one microsecond is [INLINE:13] where N is the total number of sensors in the WSN. The energy consumption function is ƒ 1 = E a (γ 2 ) and the only input is the low threshold γ 2. However, the computation of E T using (14) increases exponentially with N [16,17]. Therefore, this approach can only be used for a sensor network with a small number of sensors. 3.2 The performance function Similar to the setup in [16], if the target power is known, then for a onedimensional sensor array, only one variable θ = x t is estimated. As the maximum likelihood estimation is unbiased, the variance of estimation errors is an important indicator of estimation performance. The CRLB is a lower boundary of the variance of the estimation errors, and therefore, can be used and the CRLB is the inverse of the J matrix. Then the performance function is defined as [INLINE:14] The details of the method used to calculate the J matrix can be found in [8]. Now that the energy function (15) and the performance function (17) have been defined, the multiobjective optimization method can be used to balance (15) and (17). 4. Energy Function and Performance Function in WSNS with TwoDimensional Sensor Arrays As the calculation of (14) involves the summation of E c (M) for all possible M, this method is not suitable for sensor networks with a large number of sensors [16,17]. In this section, an approximation method is used to calculate the energy used by all sensors. This method is similar to the method presented in [16]. In a noisefree case, which means w = 0 in (4), then it is easy to have si = ai, and the following steps can be used as an approximate approach to calculate the energy consumption. (1) It is assumed that all sensors employ the same low threshold γ 2. Then, under the quantization and censoring scheme, only sensors which receive signals higher than the low threshold γ 2 will send decisions to the fusion center. In the noisefree case, these sensors are located within the circular area centered at the target location. The radius R of this circular area can be determined by [INLINE:15] The total number of sensors within this circular area is N range. (2) For each of the sensors within the circular area, calculate the energy E TX (m i ,d f,i ) required for each sensor to transmit one bit of information to the fusion center using (14) (3) The total energy consumption consumed by all sensors in the circular area to send one bit of information to the fusion center can be calculated by using [INLINE:16] (4) The overall energy consumption of all sensors in one microsecond is [INLINE:17] The first part of (20) is the energy required to keep sensors awake and energy used by sensors to measure the environmental phenomena. The second part of (20) is the energy required for sensors in the circular area to send onebit information to the fusion center. The overall energy consumption function in (20) can be used as the energy function for a multiobjective optimization purpose. Similar to the setup in [16], for twodimensional sensor arrays, the CRLB is used as the performance function. However, for twodimensional sensor arrays, parameters θ = [P 0 x t y t ] T are estimated, and therefore, the CRLB matrix is a 3 × 3 matrix. As the estimation errors of x t and y t are the most important, the performance function can be set to the variance of the estimation errors for x t and y t [INLINE:18] Now, a multiobjective optimization algorithm can be used to jointly optimize the energy function (20) and the performance function (21). 5. Simulation Setup To verify the quantization and censoring scheme, the root square mean (RMS) errors given by the quantization and censoring scheme will be compared with the CRLB for twodimensional sensor arrays. The sensor layout in [Figure 1] is used, and set x t ,y t = (12,13), P 0 = 10,000, and γ 1 = 6 is used for all sensors. The low threshold γ 2 varied from 1 to 5. For each γ 2 value, the RMS error is based on 1000 Monte Carlo simulations. To balance the energy consumption and localization performance, the NSGAII algorithm is used. For onedimensional sensor array in [Figure 2], the fusion center is located at (100,0), A = 60e  9 joule, x t ,y t = (0,0), P0 = 100, and γ 1 = 2 for all sensors. The value of γ 2 was varied from 1 to 1.5. To generate the Paretofront corresponding to a onedimensional sensor array, the generation number was set to 30 and the population size of the NSGAII algorithm was set to 100. For twodimensional sensor arrays, the fusion center was located at (100,100), A = 60e  9 joule, γ 1 = 6 for all sensors, x t ,y t = (12,13), and P 0 = 10,000. The value of γ 2 was varied from 1 to 5. To generate the Paretofront corresponding to twodimensional sensor arrays, the generation number was set to 30 and the population size of the NSGAII algorithm was set to 100. 6. Results and Analysis The RMS errors given by the energybased target localization method using the censoring and quantization scheme were compared with the CRLB [Figure 3]. The low threshold γ 2 was varied from 1 to 5. The RMS errors were close to the CRLB [Figure 3]. It was also clear that the RMS errors varied for different values of the low threshold γ 2 [Figure 3]. It could be that a low threshold could give the lowest RMS errors.{Figure 3} The results of a multiobjective optimization algorithm are a Paretofront consisting of Pareto points. Pareto points are solutions to the multiobjective optimization problem. The NSGAII is a modern multiobjective optimization method, and, in most cases, it can generate uniformly spread Paretofront points [15]. The Paretofront corresponding to a onedimensional sensor array is shown in [Figure 4], and the Paretofront corresponding to twodimensional sensor arrays is shown in [Figure 5]. The points in [Figure 5] are sparser than the points in [Figure 4]. The reason is that many points in [Figure 5] overlap each other. Therefore, one point in [Figure 5] may actually be several identical points. In contrast, in [Figure 4], the points were spread out more uniformly. Therefore, it appears that [Figure 4] has more points, and the points in [Figure 4] are denser than the points in [Figure 5]. The Paretofront is useful because one can pinpoint a point on the Paretofront to choose the desired estimation performance and acceptable energy consumption [16].{Figure 4}{Figure 5} 7. Conclusion In this article, a censoring and quantization scheme for the energybased target localization method was presented. The results showed that the RMS errors given by the energybased target localization method using this scheme were close to the CRLB. Moreover, the energy functions and performance functions corresponding to the onedimensional sensor array and twodimensional sensor arrays were provided, respectively. The NSGAII algorithm was used to balance the energy consumption and target localization performance. The Paretofronts generated are useful in practice. References


