Modeling and Understanding the Localization Performance With Network Signatures

With the continuous development of wireless network technology, more and more mobile devices are connected to the network, and the location information of these devices is becoming one of the important basis for analyzing other geographic data in the net. Location is an important problem in spatial information sensing, and the theoretical basis of location is the free space fading feature of wireless signals. In this paper, we proposes WiLocWare, which is a middle ware to understand and modeling the performance of the state-of-the-art and to be proposed algorithms. We evaluated and characterized the correlation between localization accuracy and networks parameters such as signal propagation model, the coverage of wireless radios, the distributions of wireless devices and the density of the anchor nodes. The experimental results show the localization accuracies under different wireless signatures, WiLocWare is also scalable for the performance evaluation for the to be proposed algorithms.


I. INTRODUCTION
With the continuous development of wireless network technologies, nearly six hundred and fifty million mobile devices added in networks according to the forecast by Cisco [1]. The location information of these devices is becoming one of the important information for analyzing geographic data in both indoor [2] and outdoor [3] scenarios. The accurate location information could enable variety of applications such as pedestrian trajectory prediction [4], human behavior prediction [5], navigation systems [6], group recommendation [7] and other IoT-based applications [8]. Therefore, modeling and understanding the localization performance in different scenarios is significant for proposing accurate localization algorithms.
The location estimation methods can be classified into target/source method and node self-localization method. The target/source localization algorithms are mainly energybased methods, while self-localization methods could enable node estimate its own location by wireless signatures such The associate editor coordinating the review of this manuscript and approving it for publication was Rongbo Zhu. as received signal strength (RSS), channel state information (CSI), hops, topologies, radio coverages and other readable networks signatures.
However, it is hard to get the detailed correlations between localization performances with different network signatures and settings. The performance comparisons among different algorithms are also hard since the diversity of evaluation platforms and settings. Therefore, localization performance evaluation in wireless network have several challenges: i) The evaluation model should be scalable since the rapid development of location algorithm, the input parameters of different location algorithm is slightly different, leading to different performance of the location algorithm is also different. Therefore, the model should improve the scalability of the input parameters, algorithms and the evaluation index of the algorithm; ii) Traditional range-free location algorithms don't take the influence of free space fading characteristics into account on the performance of the algorithm, and the scalability evaluation model should focus on the evaluation and iii) In addition to the fading characteristics of free space, location algorithm is also affected by other parameters of node distribution, the density of anchor node, the communication radius of node, in the process of model design it should give full consideration and evaluation on the effects of these factors on different location algorithm.
In order to solve these three challenges, the main contributions WiLocWare proposed in this paper are as follows: • The scalable location system is divided into four scalable modules, which are node deployment module, topology module, location algorithm module and performance evaluation module.
• In order to reduce the coupling of the four modules, three data structures are designed for scalable architecture, they are coordinate data structure, neighbor relational data structure and localization result data structure respectively. The three data structures could reduce the coupling degree of four the modules, which could improve the scalability of the middleware.
• We evaluated WiLocWare with Matlab, four kinds of deployment methods, four kinds of signal propagation methods, four classical localization algorithms were implemented to test the scalability and reliability of WiLocWare, and three kinds of performance matrix were test under WiLocWare. The simulation and experimental results show the scalability and reliability of WiLocWare. The remainder of this paper is organized as follows, Section II introduce related works, Section III describe the WiLocWare model, and Section IV shows the evaluation results and Section V concludes the paper.

II. RELATED WORKS
Currently, there are many localization algorithms using network signatures especially in wireless sensor networks, such as the approaches proposed in paper [9]- [12]. However, the uniform middleware for the performance evaluation of localization algorithms are rare. Different research team use relatively independent platform with different parameters to evaluate the performance of localization algorithms. The diversity evaluation methods make other researchers unable to quantify the performance of base-lines with the change of parameters. In the practice application process, it is also difficult to choose the appropriate algorithm according to the parameters of the sensors and their deployments. Table 1 shows the diversity of the platforms and parameters used by the current localization performance evaluation works.
In Table 1, the parameters include: ND (Node Density), AH (Anchors Heard), ANR (Anchor to Node Range Ratio), AP (Anchor Percentage), GPS errors, deployments and topologies of the networks. The main performances of the localization algorithms include localization error rate, localization coverage and localization energy-cost. The additional overhead of algorithms can be evaluated according to additional communications or energy consumptions. Therefore, the experimental platform and the evaluation parameters are the important components of the performance evaluation model. Table 1 lists several evaluation platforms and settings of classical localization algorithms such as DV-Hop [19] algorithm, Amorphous algorithm [20] and APIT algorithm [10] and etc., besides the experimental platform and experimental parameters used in the latest location algorithms in recent years are also showed in Table 1. For example, the experimental platform and settings used in paper [13], [15]- [17], and [14]. The examples show in Table 1 demonstrate that the experimental platforms and experimental parameters of the location algorithms are diversity, and it is difficult to compare the performances among different algorithms under the same or similar conditions.
In summary, the evaluation methods of localization algorithms have diverse characteristics, the platform and settings are quite different in individual works which leads to the uncertainty in algorithm evaluation, and it is difficult to choose the appropriate algorithm according to the actual application. In order to solve this problem, this paper proposes WiLocWare, which is a middleware for model and understanding the localization performance in a scalability, reliability and uniformly way. Section III introduces the design overview and the structures of WiLocWare.

III. DESIGN
This section introduces the model and overall structure of WiLocWare for modeling and understanding localization performance evaluation, including scalable structure model design, node deployment model design, signal propagation model design and localization performance evaluation model design. The overall structure is shown as Figure 1. In order to increase the scalability of WiLocWare, we separate the data and the operations according to the input parameters of localization algorithms.
The WiLocWare model consists of four sub-modules, which are node deployment module, free space fading module, location algorithm adding module and performance analysis module. The main data structures of WiLocWare model are coordinate information data structure (Coordinates.mat in Figure 1), neighbor information data structure (neighbor.mat in Figure 1) and results structure (Results.mat in Figure 1). The relationships among the four modules and the three data structures are shown in Table 2.   The scalability of WiLocWare model can be summarized as follows: • Researchers could add or change the node deployment module in a scalable way without modifing another modules.
• Researchers could add or change the signal propagation module in a scalable way without modifing any other modules by changing the ''free space fading model''.
• Researchers could add the developed new algorithms under different deployments and signal propagation models in ''location aware algorithm model''; • Researchers could use the existing performance matrix or design new performance matrix and add them to ''performance analysis module'' without any changing of other modules and data structures.

A. NODE DEPLOYMENT MODEL
The parameters of nodes deployments could be summarized as Table 3.
In order to implement the scalable localization middleware, this section implements four kinds of deployments which is shown as Figure 2. Figure 2(a) shows an example of random distribution in a square area assumes GPS error are 0, Figure 2(b) shows an example of random distribution in a ''C'' shape area, Figure 2(c) shows an regular distribution in a square shape area, and Figure 2(d) shows an regular distribution in a ''C'' shape area. Other parameter are shown in Table 4.
As shown in table 4, the node density and anchor node ratio of the four distributions are the same (the error is not more than 0.1%), and the communication radius is the same (10m), assuming that the error rate of GPS is 0.
Generally, GPS has errors which results in the localization error rate when nodes using anchors to estimate their locations. Figure 3 shows two deployment examples when GPS error rate is 0.1. While, Figure 3(a) is an example of random distribution in square shape area and Figure 3(b) is an example of Regular distribution in square shape area.    Figure 3 show that users could customize node deployment to evaluate localization performance in different scenarios by using WiLocWare. Users also could adjust their distribution area, the number of unknown nodes, node number, communication radius and GPS error rate according to practical applications. In addition, users could develop their own node distribution methods according to their own application senarios under the WiLocWare model.

B. SIGNAL PROPAGATION MODEL
The free space fading model mainly refers to the signal strength varies with the distance between the transmitter  and receiver. The free space fading feature is an important theoretical basis for location and also an important factor that affecting the accuracy of location algorithms. In fact, the fading of the signal is also related to the actual deployment. This section implements four free space fading models, they are DOI model, Regular model, Logarithmic Attenuation model and RIM model. The definitions of each model are shown as follows.

1) REGULAR MODEL
Regular model assumes that the propagation range of the signal is a circular, and the received signal strength (RSS) varies with distance between sender and receiver, The RSS is calculated by Equation 1, in which the P t is the transmission energy, PL d 0 is the reference path loss when the distance between sender and receiver is d 0 , and η is the constant of the channel loss. Figure 4 as shown in Equation 1. Among them, is the transmit energy; is the reference path loss when the distance between the transmitter and receiver is, and is the channel loss constant. Figure 4(a) is an example of Regular Model.
The DOI model introduces irregular characteristics of signals on the basis of Regular Model, and the irregular feature is defined as the maximum fluctuation in the range of the propagation direction of the wireless signal. In DOI model, the received signal strength is calculated by Equation 2. DOI is the irregular degree feature value which set by the user according to the network. Figure 4(b) is an example of wireless signal path loss when DOI= 0.01.

4) LOGARITHMIC ATTENUATION MODEL
Logarithmic Attenuation model is a special case of RIM model. It does not take into account the irregular characteristics of signals, only considers the propagation losses caused by temperature and humidity of the wireless signals. The calculation method is shown as Equation 4. Figure 4(d) is an VOLUME 8, 2020 example of Logarithmic attnuation model.
In summary, users could choose the wireless signal attenuation model according to the actual network deployment, and also could develop new attenuation model that matches the actual network in real-word applications.

C. PERFORMANCE INDEX MODEL
The performance matrix of localization algorithm in this paper includes location error rate, location cover rate, and energy consumption. Their specific definitions are as follows.

1) LOCALIZATION ERROR RATE
Location error rate is the difference between the estimated coordinates and the actual coordinates of the node i, which is calculated by Equation 5. N represents the total number of unknown nodes, L(N ) is the number of nodes that can be located by localization algorithm, R is the communication radius of the unknown node, (x ie ,y ie ) is the actual coordinates of the unknown nodes, (x it ,y it )is the coordinates estimated by the localization algorithm.

2) LOCATION COVER RATE
Localization cover rate of location algorithms is the ratio of the number of nodes that can be located by localization algorithm and the total number of nodes to be located, it is calculated by Equation 6.

3) LOCATION ENERGY CONSUMPTION
Energy consumption is another important performance for evaluating localization algorithms. However, the energy consumption of location algorithms varies greatly with the experimental platform and devices. Therefore, the WiLocWare model proposed uses the execution time of the location algorithm in the Matlab simulator to measure the energy consumptions of localization algorithms.

IV. SIMULATION AND EVALUATIONS
In order to evaluate the localization performance of different algorithms under different platforms and settings of network signatures. We take the traditional DV-Hop algorithm, Amorphous algorithm, Centroid algorithm and APIT algorithm as examples to evaluate the scalability and reliability of WiLocWare. We evaluated the correlations between localization performances including localization error rate, localization cover rate and energy consumptions with different free space fading model, different node deployment methods, different node communication radius, different density of the anchor nodes.

A. CORRELATIONS BETWEEN LOCALIZATION PERFORMANCE AND SIGNAL PROPAGATION FEATURES
In order to investigate the correlations between localization performance and free space fading model, we deploy the nodes as Figure 2(a) with parameters shown in Table 5. The experimental results are shown in Figure 5, Figure 6 and Figure 7. Figure 5 shows that the localization error rate of DV-Hop algorithm, Amorphous algorithm and Centroid algorithm don't change severely with fading model; APIT algorithm is greatly affected by the fading model, the localization error rate of APIT algorithm is minimum when using Regular Model, in LA (Logarithmic Attenuation) model, the APIT algorithm has large error. However, under the same conditions, the localization error rate of the APIT algorithm is significantly lower than the other three algorithms.     Figure 6 shows that the localization cover rate of DV-Hop, Amorphous algorithm, APIT algorithm change little when we use different free space fading models. While the cover rate of Centroid algorithm when using Regular Model and DOI Model is higher than those using LA and RIM Mode. Figure 7 shows the energy consumption(as measured by the running time) of different free fading model for localization algorithms. The energy consumption of DV-Hop algorithm, Amorphous algorithm have not significant changes with the free space fading models. The energy consumption of APIT algorithm has minor changes with the free space models. Centroid algorithm is affected by the attenuation model is large in the DOI model, and in RIM model, the energy consumption of the Centroid algorithm is larger 100 − 1000 times than the other algorithms.

B. THE CORRELATION BETWEEN LOCALIZATION PERFORMANCE AND NODE DEPLOYMENT METHODS
In order to validate the influence of node distribution on the performance of localization algorithms, we assume the free space fading model is LA Model. The parameters setting under each distribution is shown in Table 5. The parameter settings in Table 5 show that the rest of the parameters are consistent except for the different distributions. The experimental results were showed in Figure 8, Figure 9 and Figure 10 respectively. The ''Square Random'' label represents the random distribution in a square area (distribution in Figure 2(a), ''Square Regular'' represents the regular distribution in a square area (distribution in Figure 2(b),'' C Random'' represents the random distribution in a ''C'' area (distribution in Figure 2(c) ), ''C Regular'' represents the regular distribution in a ''C'' area (distribution in Figure 2(d). Figure 8 shows the relationship between the localization error rate and node distribution for different localization algorithms, the experimental results show that the error rate of DV-Hop algorithm and Amorphous algorithm do not change a lot when we use different distributions. While the error rate of Centroid and APIT algorithm change greatly with different distributions. Figure 9 shows the influence of different node distribution on the error rate of node location algorithm, the experimental results show that DV-Hop algorithm, Amorphous algorithm, APIT algorithm are affected by different distribution is small.   But Centroid algorithm is greatly affected by the different distribution. Figure 10 shows the energy consumptions of different localization algorithms with different distributions. The experimental results show that the energy consumption (run time in Matlab Simulation) of DV-Hop algorithm, Amorphous algorithm, Centroid algorithm do not change much with the changing of distributions, while the energy consumptions of APIT algorithm changes a lot with different distributions.

C. CORRELATIONS BETWEEN LOCALIZATION PERFORMANCE AND COMMUNICATION RADIUS
In order to investigate the correlations between communication radius and localization performance, this section tests localization error rates with different communication radius, the parameters are showed in Table 6, the distribution is random in square area, the attenuation model is LA, the number of unknown node, the number of anchor node density and anchor node proportion are shown in Table 6, in order to simulate the real-word scenarios, the GPS error rate is set to 0.06. The radius of communication varies from 20m to 210m. Where 20m is more consistent with the actual settings of node (e.g., MacZ motes and TelB nodes), 210m assumes that the communication radius is larger than the distribution area and is used to test the performance of the algorithm in the limit case.
The experimental results under the settings of Table 6 are shown in Figure 11. The localization error rate is shown in Figure 11(a), the localization cover rate is shown in Figure 11(b) and the energy consumptions are shown in Figure 11(c). Figure 11(a) shows the localization error rate changing trend with the radius of communication. The experimental VOLUME 8, 2020  results show that the location error rate of different algorithms has different distribution characteristics with the change of communication radius R. In general, the change in the location error rate is roughly divided into two zones. When the communication radius R = [20,30,. . . ,90]m, the location error rate of DV-Hop algorithm and Amorphous algorithm is larger, and the localization error rate of Centroid algorithm and APIT algorithm is smaller. However, with the increasing of communication radius, the location error rate of DV-Hop algorithm and Amorphous algorithm continues to decrease, but the location error rate of Centroid algorithm and APIT algorithm will increase with the increase of communication radius. Figure 11(b) shows the change of localization cover rate as the radius of communication varies. It can be seen from Figure 11(b) that the localization cover rate of different algorithms present different distribution characteristics with the change of communication radius R. When the communication radius R < 100m, the location cover rate of the Centroid algorithm and the APIT algorithm increases with the increase of the communication radius. When R > 100m, the location error rate of the Centroid algorithm and the APIT algorithm can reach 100%. However, when the communication radius varies from 20m to 210m, the location cover rate of DV-Hop algorithm and the Amorphous algorithm can reach 100% Figure 11(c) shows the relationship between the running time of the algorithm (energy consumption) and the radius of communication. The results in Figure 11(c) demonstrate that the energy consumptions of DV-Hop algorithm and Amorphous algorithm are minimum, and it changes with the communication radius. The energy consumptions of Centroid algorithm are slightly higher than the above two algorithms, but not changes with the communication radius. The energy consumption of APIT algorithm increases with communication radius increases.

D. INFLUENCE OF ANCHOR NODE DENSITY OF COMMUNICATION RADIUS ON ALGORITHM PERFORMANCE
In order to verify the influence of anchor node density on the performance of localization algorithm, the experimental parameters are shown in Table 7, the distribution type is random distribution in square area, communication model is LA model, the number of unknown nodes is 105, GPS error rate is 0.06, communication radius is 20m. The number of anchor nodes is vary from 10 to 400. The anchor node density is less than 1, which meets the cost performance requirements of the network. In this section, we test the limit of increasing density of anchor nodes. The experimental results are shown in Figure 12. Figure 12(a) shows the relationship between the localization error rate and the anchor node density. The experimental results show that when the proportion of anchor nodes and unknown nodes changes from 0.1 to 4, the location error rate of DV-Hop algorithm, Amorphous algorithm and APIT algorithm has stable fluctuation. The location error ratio of Centroid is decreased with increasing the number of anchors. Figure 12(b) shows the relationship between localization cover rate and anchor node density. The experimental results show that when the proportion of anchor nodes and unknown nodes changes from 0.1 to 4, DV-Hop algorithm, Amorphous algorithm can achieve 100%, with the increase of the density of anchor nodes, the the cover rate of Centroid location algorithm and APIT algorithm will continue to increase, when the number of anchor nodes is 2 times of the unknown node, the location cover rate of Centroid algorithm and APIT algorithm is close to 100%. Figure 12(c) shows the relationship between the location cover rate and anchor node density. The experimental results show that when the proportion of anchor nodes and unknown nodes changes from 0.1 to 4, the running time of the four classical location algorithms are significantly increased. The the speed of running time of DV-Hop algorithm and Amorphous algorithm increasing slowly, the running time of Centroid algorithm and APIT algorithm improves quickly.
We have the following conclusions according to the test for different localization algorithm by using WiLocWare.  algorithm and the Amorphous algorithm, and has a greater impact on the Centroid algorithm and the APIT algorithm.  Conclusion 3: running time of different algorithms varies with the communication radius has different distribution characteristics. The energy consumption of DV-Hop algorithm and Amorphous algorithm is minimum, and not change with the communication radius. The energy consumption of Centroid algorithm is slightly higher than the above two algorithms, but also not change with the communication radius. The energy consumption of APIT algorithm increases with increasing communication radius.
• Anchor node proportion selective characteristics of localization algorithm Conclusion 1: the localization error rate shows different characteristics with the density of anchor nodes in different algorithms, when the proportion of anchor nodes and unknown nodes changes from 0.1 to 4, the error rate of DV-Hop algorithm, Amorphous algorithm and APIT algorithm shows a steady fluctuation trend. The error rate of Centroid algorithm decreases with the increasing of anchors' number.
Conclusion 2: the localization cover rate shows different characteristics with the density of anchor nodes in different algorithms. When the proportion of anchor nodes and unknown nodes changes from 0.1 to 4, the coverage rate of DV-Hop algorithm and Amorphous algorithm can achieve 100%. With the increase of anchor nodes density, the cover rate of Centroid location algorithm will continue to increase. When the number of anchor nodes is 2 times the number of unknown nodes, the location cover rate of Centroid algorithm and APIT algorithm approaches 100%. Conclusion 3: different running time shows different characteristics with the density of anchor nodes. When the proportion of anchor nodes and unknown nodes changes from 0.1 to 4, the running time of the four kinds of classic algorithms are significantly increased, the running time of DV-Hop algorithm and Amorphous algorithm increases slower, the running time of Centroid algorithm, and APIT algorithm increases faster.

V. CONCLUSION
Location is an important problem in spatial information sensing, and the theoretical basis of location is the free space fading feature of wireless signals. In this paper, we propose WiLocWare which is a scalable middleware for modeling and understanding the performance of the localization algorithms with different network signatures. The main contributions of WiLocWare is the scalability, the data and operation separation design. Experimental results show that the middleware could help researchers investigate more insights of the localization algorithms.