text:
A method of pedestrian flow monitoring based on received signal strength
Zhiyong Yang1,
Jing Wen1 &
Kaide Huang ORCID: orcid.org/0000-0002-4826-87732
EURASIP Journal on Wireless Communications and Networking volume 2022, Article number: 2 (2022) Cite this article
There is a wide demand for people counting and pedestrian flow monitoring in large public places such as scenic tourist areas, shopping malls, stations, squares, and so on. Based on the feedback from the pedestrian flow monitoring system, resources can be optimally allocated to maximize social and economic benefits. Moreover, trampling accidents can be avoided because pedestrian guidance is carried out in time. In order to meet these requirements, we propose a method of pedestrian flow monitoring based on the received signal strength (RSS) of wireless sensor networks. This method mainly utilizes the shadow attenuation effect of pedestrians on radio frequency (RF) signals of effective links. In this paper, a deployment structure of RF wireless sensor network is firstly designed to monitor the pedestrians. Secondly, the features are extracted from the wavelet decomposition of RSS signal series with a short time. Lastly, the support vector machine (SVM) algorithm is trained by an experimental data set to distinguish the instantaneous number of pedestrian passing through the monitoring point. In the case of dense and sparse indoor personnel density, the accuracy of the SVM model is 88.9% and 94.5%, respectively. In the outdoor environment, the accuracy of the SVM model is 92.9%. The experimental results show that this method can realize the high precision monitoring of the flow of people in the context of real-time pedestrian flow monitoring.
Pedestrian flow monitoring is a research hotspot in the field of computer vision and intelligent monitoring [1, 2]. Pedestrian flow monitoring aims at mastering the accurate distribution of personnel density at any time, so as to create strategies for various emergencies and effectively avoid the loss of life and property of personnel [3]. Owing to the rapid growth of population, congestion and stampedes have taken place to different degrees around the world, resulting in huge economic losses and casualties. The worst was the stampede in 1990 during the Hajj to Mecca, Saudi Arabia, in which 1426 people were killed. Another example was the stampede in Ming Tong Primary School on September 26, 2014 in Yunnan Province, which killed 6 people and injured 26 students. These painful lessons are reminding us of the importance of pedestrian flow monitoring. With the great development of society, pedestrian flow monitoring has been playing an increasingly important role in security prevention, urban construction, and market decision-making, especially in crowded places such as squares, stations, and shopping malls. In addition, the realization of real-time and accurate monitoring of pedestrian flow is of great significance for commercial information collection, public security prevention and control, and rational allocation of social resources.
In recent years, with the advent of artificial intelligence, pedestrian flow monitoring has made some progress at home and abroad. For instance, Viola proposes a pedestrian flow monitoring method based on motion characteristics [4]. Antonini et al. [5] propose a track-based pedestrian flow estimation method. Meanwhile, Kong et al. [6] propose and design a pedestrian flow monitoring method based on neural network. The method extracts edge and grey level histograms as features and makes use of a feedforward neural network to establish the classification model of personnel density. Ali [7] provides a new idea for pedestrian flow monitoring by referring to particle dynamics. This method can detect and separate foreground objects in the optical flow field and carry out dynamic analysis and research on group targets. Zhou et al. [8] propose a pedestrian flow monitoring method that combines feature regression and detection, while Wu et al. [9] propose a SURF algorithm based on the linear interpolation perspective correction for large-scale personnel statistical monitoring. The performance of the above methods can be weakened under the conditions of overlapping objects and dim light. In addition, the use of cameras can also bring privacy issues. Furthermore, Li et al. [10] propose a pedestrian flow monitoring method based on smart phone. Mizutani et al. [11] propose a pedestrian flow monitoring by mobile devices. These methods require people to carry mobile devices, thus it may not be appropriate under certain circumstances.
Currently, wireless IntelliSense technology, which utilizes received signal strength (RSS) and channel state information (CSI), has been developing rapidly. The wireless IntelliSense technology does not need to configure any sensors, but only uses the link information between wireless devices for task awareness. Target tracking based on RSS information is studied in the university of Utah. Yang and Ramezani propose CSI-based systems for indoor human tracking and fall detection, respectively [12, 13]. This paper is inspired by the above research results. Therefore, we hope to find a pedestrian flow monitoring method with strong environmental applicability, high accuracy, easy installation, and low computational cost.
We face two main challenges. First, according to the phenomenon of the fading change of the RSS value between nodes in the radio frequency (RF) sensor network when the physical human body passes through the RF sensor network. We need to observe the variation of RSS characteristics and find out the relationship between different number of people in unit time and area and RSS characteristics. Second, how to use support vector machine (SVM) to model, find the best kernel function, and conduct supervised learning and classification of data.
The contributions of this paper are as follows:
We propose a pedestrian flow monitoring method that does not require wearable equipment and protects the privacy of pedestrians. It uses the shadow attenuation effect of pedestrians on RF signals to achieve pedestrian monitoring.
We use the SVM algorithm to build a model and achieve statistical classification of the number of people.
The rest of the paper is organized as follows. The second section reviews the related work briefly. The third section introduces the principle of the RSS-based pedestrian flow monitoring system. The fourth section introduces the process of data acquisition and preprocessing, wavelet analysis and SVM classification algorithm. The fifth section describes the conducted experiments and classification result. Finally, the sixth section draws conclusion.
At present, the methods of pedestrian flow monitoring and statistics mainly include gate statistics, infrared detection and machine vision, etc. These methods can be divided into two categories: contact methods and non-contact methods.
The contact methods mainly include two approaches: installing mechanical gate or pressure sensitive pedal at the monitoring point [14]. The mechanical gate device is convenient and the count is accurate, but the equipment installation and operation and maintenance cost of this method are high, and the pedestrians are very slow, which is easy to cause congestion, and it will also bring a very unfriendly experience and impression to pedestrians. The pressure sensitive pedal approach needs to install the pressure sensor under the floor. This approach is simple and has a higher pass efficiency, but the pressure sensitive pedal is easy to damage after long-term use, and there are obvious limitations when many people pass at the same time.
Non-contact methods mainly include infrared-based approach and vision-based approach. Lv [15] and Xu et al. [16] design a statistical scheme for the number of people in construction elevator cages based on the principle that the visual distance path of infrared optoelectronic tube will change the signal output state of the receiver after being blocked by a human body. Infrared optoelectronic tube technology has a very high accuracy for single-person detection, but when multiple people or pedestrians carry objects such as large pieces of luggage through the detection point, the statistical accuracy of the number of people will be greatly reduced.
With the rapid development of image processing and machine learning, pedestrian flow monitoring based on machine vision has become a hot research branch. A large number of research results have sprung up in recent years, most of them mainly using individual characteristics such as shape, color, outline, or population characteristics to achieve pedestrian flow monitoring through a combination of SVMs, BP neural networks, CNNs [17, 18], and other machine learning algorithms [19,20,21]. Although domestic and foreign experts and scholars have put forward many ingenious methods for the monitoring of pedestrian flow, there are still some problems and deficiencies. In real life, the accuracy of judgment will also change with differences in the environment, which greatly increases the difficulty of the monitoring of pedestrian flow. The above methods often need to carry out pedestrian estimation based on a large number of data in pedestrian flow monitoring, which greatly increases the computational complexity, consumes more computing resources, and reduces monitoring efficiency. Furthermore, it is difficult to overcome the disadvantages of vision-based methods, such as high cost, pedestrian privacy, and susceptibility to light or smoke.
In this paper, we propose a method of pedestrian flow monitoring based on RSS of RF signal. RF signal is a kind of high-frequency electromagnetic wave with long-distance transmission and see-through abilities. It is now widely applied to the fields of transportation, medical care, anti-counterfeit technology, logistics, and security protection [22,23,24]. Our method utilizes the influence of the human body on RF signals to judge and monitor pedestrian flow. By processing the received RSS data and using the SVM algorithm for classification modeling, real-time pedestrian flow monitoring can be achieved. The method does not need to touch a human's body, and there is no requirement for pedestrians to carry equipment. It does not have an impact on people's normal activities, nor does it affect the passage efficiency of monitoring points. Since there is no need to take photos and videos, the privacy of pedestrians is not be involved. In addition, this method has a simple requirement for equipment and cost, and it is easy to operate and has a satisfying performance. The feasibility and credibility of the method are proved by the real-time verification of the system.
System principle
The pedestrian flow monitoring system proposed in this paper is based on the shadow attenuation effect of the human body on RF signals. The attenuation strength of RSS signals of different links is different when different numbers of people pass through the monitoring gate. Therefore, the attenuation value of RSS of all effective wireless links is used as the classification feature to establish a classification model when different numbers of people pass through the gate so as to realize judgment of the number of pedestrians at certain time points and also obtain statistics of the pedestrian flow over given time periods. This section will elaborate the principle of the RSS-based pedestrian flow monitoring system.
The basic block diagram of the proposed system method is shown in Fig. 1. Firstly, sufficient RSS data are collected. In the data preprocessing phase, wavelet filtering is carried out, then the output need wavelet decomposition, and the data are extracted after decomposition. Finally, the SVM model is trained to get the number of people passing through the monitoring gate.
The basic block diagram of the proposed system method
Human impact on RSS
When people pass by the wireless line-of-sight links consisting of transmitting nodes and receiving nodes, the RSS value of receiving nodes will be significantly decreased because of the human body's absorption, reflection, and refraction of the RF signal. As shown in Fig. 2, the transmitting nodes and the receiving nodes are 2.4 m apart. When there is no person in the line-of-sight path, the mean value of RSS from receiving nodes is \(-57.5\,\hbox{dBm}\). When an adult stand in the middle of the line-of-sight path, the mean value of RSS is \(-70.0\,\hbox{dBm}\). It can be seen that the human body has a significant attenuation effect on the RSS of wireless links.
Influence of human body on received signal strength. a Experimental setup and b comparison of RSS values
Pedestrian flow impact on RSS
If L wireless sensor network nodes are installed on a gate-shaped bracket, these L nodes will form \(L(L - 1)/2\) wireless links. Figure 3 is a schematic diagram of a monitoring gate composed of 18 nodes and their wireless links. There are 153 wireless links in total, 105 of which go through the gate.
We find that when different people pass through the monitoring area through experiments, the RSS value of each wireless link will undergo different changes due to different links being blocked by the human body. For example, when different numbers of people walk through the monitoring gate shown in Fig. 3, the RSS values of the 70th wireless link (composed of nodes 5 and 14) and the 100th wireless link (composed of nodes 6 and 18) are as shown in Fig. 4. The RSS of each wireless link varies with different numbers of people passing through the monitoring area. This verifies the feasibility of pedestrian flow monitoring by using wireless link RSS based on a wireless sensor network. Therefore, different changes in RSS of links can be used as the classificational feature to estimate the number of instantaneous people.
Schematic diagram of node deployment and effective wireless link distribution
a RSS comparison diagram of the 70th wireless link and b RSS comparison diagram of the 100th wireless link
In this paper, the RSS value is utilized to monitor the pedestrian flow, and the number of people passing through is obtained by the RSS value of the link composed by the wireless sensor network. From the perspective of machine learning, this problem is a supervised multi-classification problem [25,26,27]. In the case of small data volume, the SVM can handle multiple classification problem well [28, 29]. Compared with other more complex machine learning algorithms, such as KNN, CNN, and RNN, SVM algorithm has many advantages, the most prominent two are suitable for small sample data classification and low computational complexity. This feature is especially suitable for the application of people flow monitoring based on RSS. Therefore, we adopt the SVM for obtaining the classification model of this system.
RSS data acquisition and preprocessing
The monitoring algorithm in this paper is shown in Fig. 5. In order to ensure the collection frequency of RSS values of each wireless link, the node software uses IAR to design an RSS collection program for nodes to broadcast messages according to their ID. When a sensing node receives a message packet, it must obtain the source node ID, read and calculate the RSS value of this communication wireless link, and write the RSS value to the element position corresponding to the source node ID in the RSS array. When it is the node's turn to send a message, the saved array of RSS values are put into the message packet and broadcast. During RSS data sampling, 18 nodes constitute a polling broadcast network, and a Sink node listens and receives all the broadcasted packets, which are transmitted to the computer through the serial port and saved in TXT files.
Algorithm diagram
In the data preprocessing stage, we specify a sampling period from the start of first sensing network node sending packets to the end of the last node sending packets. Due to the dynamic changes in the environment, pedestrian interference and other factors, the data collected by the PC may be incomplete, that is, the data of a sensing node may be missing for a certain sampling period. In this paper, the algorithm designed to deal with the missing period uses the data of the previous sampling period to fill in the missing data of the current sampling period, thus improving the robustness of the algorithm in real-time pedestrian flow monitoring. We examine the received data and fill in the incomplete sampling period. Because the received RSS data are expressed in hexadecimal, it first needs to be converted to decimal for ease of processing. Then we can subtract an offset from the decimal number to get the real RSS value in dBm. After obtaining the real RSS value of each link in the wireless sensor network, the feature matrix of the effective links is obtained through feature extraction. The RSS measurement value on link i is expressed as \(y_i\), and the RSS vector of all links can be written as \({\mathrm{Y}} = {\left[ {{y_1},{y_2},{y_3}, \ldots {y_m}} \right] ^T}.\) Then the wavelet filtering is adopted to further extract precise features of RSS data of effective links.
Wavelet analysis
We use a series of low-pass filters and high-pass filters to filter the collected signal data. Low-pass filtering and high-pass filtering are both filtering methods in data processing. The rule of low-pass filtering is that the low-frequency signal can pass, and the high-frequency signal that exceeds the critical value set by the system is blocked and weakened. High-pass filtering is the opposite. Therefore, different filtering methods can be used according to different requirements. And then carry out wavelet decomposition of the output. The decomposition produces two parts whose lengths are halved: one is the approximate component of the original signal produced by the low-pass filter, and the other is the detailed component of the original signal produced by the high-pass filter. An RSS signal of length W is down sampled through a low-pass filter and a high-pass filter, the corresponding approximate component coefficient cA1 and detailed component coefficient cD1 are obtained, and the length of both component coefficients is W/2. Then, the same method is applied to cA1 for obtaining the approximate component cA2 and detailed component cD2 of the second layer. We repeat this process until we reach the preset decomposition level [30]. The decomposition process is shown in Fig. 6.
Schematic diagram of four-layer wavelet decomposition
The above process of wavelet decomposition can be expressed as the following equation:
$$\begin{aligned} \left\{ \begin{array}{l} {\mathrm{c}}_{j + 1,k} = \sum \limits _{n = - \infty }^{ + \infty } h_{n-2k}{c_{j,n}} \\ d_{j + 1,k} = \sum \limits _{n = - \infty }^{ + \infty } g_{n - 2k}c_{j,n} \end{array} \right. \end{aligned}$$
where \({j \in \left\{ {0,1,2, \ldots } \right\} }\) is the levels of decomposition, k and n are translation coefficients, \({\mathrm{c}}_{j + 1,k}\) and \(d_{j + 1,k}\) are low-frequency approximate component coefficients and high-frequency detail component coefficients at \(2^{j}\) resolution, respectively, and \(h_{n - 2k}\) and \(g_{n - 2k}\) are low-pass filtering coefficients and high-pass filtering coefficients, respectively.
In this paper, the DB4 wavelet is adopted to carry out wavelet decomposition on received RSS measurement data. The threshold filtering method is also used to carry out signal filtering, and the threshold is set to 0.1. In this paper, if one person goes through the "gate," the filtered waveform of the RSS value of one of the effective links can be obtained through 15-layer decomposition, as shown in Fig. 7. In the case of the same number of people passing through the gate, the same effective links have, theoretically, a small change in RF. Because the environment changes over time, the RF signal will fluctuate greatly. As can be seen from the waveform after wavelet filtering, the RSS fluctuation of the same effective link under the same condition tends to be stable, which is conducive to the establishment of the later model.
Wavelet filtering of effective link RSS value
SVM classification
The SVM is a method proposed by Vapnik et al. [31] on the basis of statistical learning theory. The SVM aims at ensuring the learning machine's generalization ability by using the principle of structural risk minimization. Based on the statistical learning theory, the model base is established using the principle of structural risk minimization. The decision rules can still achieve lower expected risks for independent test datasets with a limited number of samples. The training process of the SVM involves finding an optimal hyperplane to partition data in high-dimensional space. The optimal hyperplane is defined as maximizing the distance from the nearest sample points to the hyperplane, and these sample points are called support vectors. SVMs have received considerable attention and have been successfully applied to many classification tasks due to their good generalization ability.
We assume that \({\mathbf{x }_i}\in {\mathbb {R}}^{n}\, \left( i = 1,2, \ldots ,N\right)\) are the input vectors, where each point \(\mathbf{x }_{i}\) belongs to one of the two classes denoted by a label \({y_i} \in \left\{ - 1, + 1 \right\}\). In the linearly separable case, the input vectors can be classified by the separating hyperplane, \(\mathbf{w }^T\mathbf{x } + b = 0\), which satisfying the condition of \({\mathrm{y}}_{i}\left( \mathbf{w }^{T}\mathbf{x }_{i} + b \right) >0\), where \(\mathbf{w }\) is the normal vector that determines the direction of the hyperplane, and b determines the distance between the hyperplane and the origin. There may exist many hyperplanes which meet this condition. In order to construct a optimal hyperplane to separate the two classes, by scaling w and b, we set \({\mathrm{y}}_{i}\left( \mathbf{w }^{T}\mathbf{x }_{i} + b\right) \ge 1\) for \(i = 1,2, \ldots ,N\). The distance from the closest point to the hyperplane is \({1 /{\left\| \mathbf{w } \right\| }}\) so that finding the optimal separating hyperplane needs maximize \(1/\Vert \mathbf{w }\Vert\) which can be converted to minimize \(\frac{1}{2}{\left\| \mathbf{w } \right\| ^2}\). The original support vector machines solved the following optimality problem:
$$\begin{aligned} \begin{array}{l} \mathop {\min }\limits _{w,b} \frac{1}{2}{\left\| w \right\| ^2}\\ \hbox{s.t.}\,\,\,\hbox{y}_{i} \left( {{w^{\mathrm{T}}}{x_i} + b} \right) \ge 1,\quad i = 1,2, \ldots ,N \end{array} \end{aligned}$$
However, most data sets in the real world cannot be completely linearly separated. Therefore, in this paper, the soft margin SVM is used to establish a pedestrian classification model. It is implemented by introducing slack variables, \({{\xi _i} \ge 0}\). This improved method allows for errors in some samples. The optimal classification hyperplane can be obtained by solving the following convex quadratic programming problem:
$$\begin{aligned} &\mathop {\min }\limits _{w,b,{\xi _i}} \frac{1}{2}{\left\| \mathbf{w } \right\| ^2} + C\sum \limits _{i = 1}^N {{\xi _i}} \\ &\hbox{s.t.}\,\,\,\hbox{y}_{i}\left( {{\mathbf{w }^T}{\mathbf{x }_i} + b} \right) \ge 1 - {\xi _i},\quad {\xi _i} \ge 0,\quad i = 1,2, \ldots ,N \end{aligned}$$
where \({{\xi _i}}\) are positive slack variables and C is the penalty factor controlling the tradeoff between the maximal margin and the minimal classification error. The parameter C affects the generalization ability of the SVM. If the value of C is large, it will cause overfitting to the training data. On the contrary, if it is set too small, the classifier will cause underfitting. Formula (1) can obtain its dual problem by using Lagrange multiplier method and then obtain the estimated decision function by solving the dual problem:
$$\begin{aligned} &{\mathop {\mathrm{max}}\limits _\alpha } \sum \limits _{i = 1}^{\mathrm{N}} {\alpha _i} - \frac{1}{2}\sum \limits _{i=1}^N \sum \limits _{j = 1}^N {\alpha _i}{\alpha _j}{y_i}{y_j}\mathbf{x }_i^T{\mathbf{x }_j}\\ &\hbox{s.t.}\,\, \sum \limits _{i = 1}^{\mathrm{N}} {\alpha _i}{y_i} = 0,\quad 0 \le {\alpha _i} \le C \end{aligned}$$
where \({{\alpha _i}}\left( {i = 1,2, \ldots ,N} \right)\) are the nonnegative Lagrangian multipliers. By solving the above problems, the decision function is obtained as follows:
$$\begin{aligned} f\left( x \right) = {\mathrm{sgn}} \left\{ {{\mathbf{w }^T}\mathbf{x } + b} \right\} = {\mathrm{sgn}} \left\{ {\sum \limits _{i = 1}^N {{\alpha _i}{y_i}\mathbf{x }_i^T\mathbf{x } + b} } \right\} \end{aligned}$$
When the input vectors are not linearly separable, we cannot process the vectors with linear classification. We need to utilize the kernel function to map input vectors to a higher-dimensional space, which turns the problem of nonlinear separability in low-dimensional space into the problem of linear separability in high-dimensional space. Then, the purpose of classification by finding the classification hyperplane can be achieved. The kernel function is as follows:
$$\begin{aligned} K\left\langle {{\mathbf{x }_i},\mathbf{y }_j} \right\rangle = \left\langle {\phi \left( {{\mathbf{x }_i}} \right) \cdot \phi \left( {{\mathbf{y }_j}} \right) } \right\rangle \end{aligned}$$
\(\phi\) is a mapping from X to the inner product feature space. Any function that satisfies Mercer's condition can be considered as a kernel function. In the SVM, different kernel functions are selected to generate different models, and the selection of kernel functions directly determines the classification results and machine learning ability of the SVM. There are four main types of common kernel functions including linear, polynomial, gaussian, sigmoid kernel function. By using the appropriate kernel function \({\mathrm{K}}\left( \mathbf{x }_{i},\mathbf{x }_{j} \right)\) to achieve classification, the decision function is obtained as follows:
$$\begin{aligned} f\left( \mathbf{x } \right) = {\mathrm{sgn}}\left\{ \mathbf{w }^{T}\phi \left( \mathbf{x } \right) + b \right\} = {\mathrm{sgn}} \left\{ \sum \limits _{i = 1}^N \alpha _{i}y_{i}{\mathrm{K}}\left( \mathbf{x }_{i},\mathbf{x } \right) + b \right\} \end{aligned}$$
In this study, this paper chooses the linear kernel function as the kernel function of SVM to classify the experimental data. The linear kernel function is defined as follows:
$$\begin{aligned} {\mathrm{K}}\left( {{\mathbf{x }_i},{\mathbf{x }_j}} \right) = {\mathbf{x }_i^T} \cdot {\mathbf{x }_j} \end{aligned}$$
SVM was originally designed for two classification problem, but since the pedestrian flow monitoring in this paper is a multi-class problem. There are roughly two implementations of SVM multi-class classification methods:
Modifying the algorithm of support vector machine so that multiple classification problem is realized by solving the optimization problem "at one time".
Constructing and combining multiple binary classifiers. The second method mainly includes one-against-rest and one-against-one. If one-against-rest method is used, M SVMs are required for M classification problems. For the ith SVM, all the samples of the ith class are labeled as positive class, and the rest samples are labeled as negative class. A test sample is labeled according to maximum output among the M classifiers. If one-against-one method is used, \(M(M - 1)/2\) SVMs are required for M classification problems. It constructs a SVM between each pair of classes and chooses the class with the most votes as the final class of the test sample.
This paper uses one-against-rest method to construct multi-classification SVM to solve the multi-class problem. The advantage of this method is that for M classification problems, only M two-class classifiers support vector machines need to be trained and the classification speed is relatively fast.
Experiments and results
Experimental setup
The experimental environment is set up as shown in Fig. 8. This experiment utilized 18 CC2530 nodes and a metal door frame to form a 5–8–5 gate frame. Five sensor nodes were arranged at equal intervals on both sides of the gate frame, and the receiving antennas were upward. Ten sensor nodes were distributed at equal intervals above the gate frame, and the receiving antennas were uniformly downward. This constitutes the wireless sensor network. The gate frame selected in this experiment was 2.4 m wide and 2.0 m high. It was divided into three virtual pedestrian channels (A, B, and C), each of which was 60 cm wide to ensure the normal passage of three people. During the experiment, the distance between the experimenter and the nodes on both sides was not less than 30 cm because if the experimenter was too close to the nodes on the sides, it would block the radio frequency signal and affect the normal communication between nodes, thus greatly impacting the experiment. The Sink node was placed about 5 m away from the gate frame and was connected to a laptop for uploading raw data. The SVM tool used in this experiment was the LIBSVM package running under the Windows 10 operating system.
The experimental scene (A):indoor environment
Experimental data processing
The feature vectors of wavelet domain can be obtained from original data of RSS by basic processing of the method described in the previous section. In fact, we only use the feature vectors of the effective links for model building and pedestrian flow monitoring. We need to use SVM to train an optimized classification model, and then use this model for real-time pedestrian flow monitoring. In other words, the processing of pedestrian flow monitoring based on RSS was divided into two steps:
Offline stage. The purpose of this stage was mainly data collection and data processing. First, the signal strength values of nobody, 1 person, 2 people, and 3 people passing through the experimental gate frame were collected as experimental samples. The RSS values of different numbers of pedestrians were calculated from received data and taken as the feature vectors. Second, the SVM algorithm was utilized to establish the classification model. Finally, we optimized the classification model. In order to reduce the impact of random interference in the experiment, multiple groups of data were collected in each case, and the collection time was as random as possible.
Online stage. In this stage, real-time monitoring was carried out to estimate the number of people that pass through the gate. We received the RSS values of the system nodes when pedestrians passed through the gate, and conducted data processing. Then, the processed real-time received data were taken as input to determine the number of pedestrians using the classification model. We utilized the error rate of manually derived statistics and system statistics to judge the performance of this monitoring algorithm. The formula for error rate is
$$\begin{aligned} \frac{\left| \hbox{num}_{\mathrm{actual}} - \hbox{num}_{\mathrm{system}}\right| }{\hbox{num}_{\mathrm{actual}}}*100\% \end{aligned}$$
\(\hbox{num}_{\mathrm{actual}}\) and \(\hbox{num}_{\mathrm{system}}\) represent the actual number of people manually counted and the number of people automatically estimated by our designed system, respectively.
In order to train the classification model, we design four off-line experiments to obtain a small data set. In the four experiments, the number of people passing through the monitoring gate at the same time was 0, 1, 2 and 3, respectively. We collected a total of 360 sets of source data, the detail of which were as follows:
When nobody passed through, 90 sets of data were collected. Each set lasted for 10 s to obtain about 50 cycles of sampling data.
Only one person passed through the monitoring gate at a time. Total 30 people took part in this experiments. The experimenter passed through one of the three virtual pedestrian channels at normal speed successively. A total of 90 groups of data were collected.
There were two people who passed through the monitoring point at the same time. Total 15 groups of pairs participated in the experiments. A total of 90 groups of RSS data were collected.
When three people passed through at the same time, 15 groups of three people participated in the experiments. Also a total of 90 groups of RSS data were collected.
The received data were utilized to extract feature vectors through data processing and established classification labels. The obtained feature vectors were used as input to establish the classification model. In this paper, the identification tool was mainly LIBSVM. The selection of kernel function was determined by the accuracy(acc) of the model with different kernel functions:
$$\begin{aligned} \hbox{acc} = \frac{a}{s}*100\% \end{aligned}$$
where a represents the experimental data correctly classified and s represents the experimental data of all classifications. Cross validation (CV) is used to find the optimal kernel function. Table 1 shows the corresponding relationship between different kernel functions in the experiment and the accuracy of the model. As can be seen from Table 1, the linear kernel has the highest accuracy among the four commonly used kernel functions. Thus, we choose the linear kernel as the kernel function of the SVM to classify the number of people passing through the monitoring point instantaneously.
Table 1 Relationship between kernel and accuracy
In this paper, experiments were carried out at two different places. One place is corridor in the building as shown in Fig. 8. Because the first experiment was conducted in an indoor environment, and in order to make the results more rigorous, we conducted the second experiment outdoors. In the first experiment, the system framework was placed at the gate of the second floor of the building D, Nanchang Hangkong University. Data were collected in two cases, during class and after class, to compare the impact of personnel density on the experiments. In each case, the passage of personnel in 5 periods (5 min in each period) was collected in this experiment. During the experiment, both manual counting and system counting were used. Tables 2 and 3 show the experimental results in the cases of dense personnel density and sparse personnel density, respectively.
To evaluate the performance of the proposed RSS-based pedestrian flow monitoring method, we compare the performance of the system using SVM algorithm with the other two algorithms, the algorithm based on the model of Gaussian Mixture Model (GMM)–Hidden Markov Model (HMM) [32] and the gradient boosting decision tree (GBDT) algorithm.
It can be seen from Tables 2 and 3 that the statistical error rate of the two cases is 11.1% and 5.5%, respectively. By averaging the two accuracy values, we can get the overall accuracy of 91.7%. It also can be found that when the personnel density is sparse, the system's personnel statistics are relatively accurate; however, when the personnel density is relatively dense, the system's estimation has certain errors. When the density of people passing through is too high, the walls and pedestrians outside the experimental area will have an impact on the experiment because of the influence of multipath reflection.
Table 2 Comparison of dynamic monitoring results with dense personnel density
Table 3 Comparison of dynamic monitoring results with sparse personnel density
We conducted the second experiment in the corridor on the third floor between building D and building E, as shown in Fig. 9. In order to make the experimental scenario more consistent with the daily application scenario, this experiment collected a total of 6 periods (each period is a random period, ranging from 2 to 5 min). The first three groups had less people flow, while the last three groups had more people flow. During the experiment, both manual counting and system counting were used. The experimental results are shown in Table 4.
The experimental scene (B):outdoor experiment
Table 4 Dynamic monitoring results
It can be seen from Table 4 that the statistical mean error rate is 7.1%, that is, the average accuracy rate is 92.9%, which is obviously better than the compared algorithms GMM–HMM and GBDT. The six sets of data collected in this experiment all have relatively large numbers of pedestrians, however, the experimental results are satisfactory. Combining the results of the two groups of experiments, we can see that the proposed method can achieve good results, which achieves a high accuracy and can meet the needs of most pedestrian flow monitoring applications.
Conclusion and future work
In this paper, a pedestrian flow monitoring method based on radio frequency signals is proposed. This method mainly utilizes the shadow attenuation effect of pedestrians on RF signals of effective links, which may be blocked by pedestrians. The wavelet decomposition of RSS signal series of a short time is used as features. A SVM algorithm is trained by an experimental data set to distinguish the instantaneous number of pedestrian passing through the monitoring point. The performance of this method is verified by two online real-time experiments in indoor and outdoor, which can achieve approximate 92.9% accuracy of pedestrian flow counting. The proposed pedestrian flow monitoring method has the characteristics of strong environmental applicability, high accuracy, no privacy issues involved, easy installation, and low computational complexity. It can be a beneficial supplement to the traditional methods.
However, this method also has some limitations. For example, it can't distinguish the direction of pedestrians, and it is not clear about the impact of the people around the monitoring point. In addition, the proposed method can only allow up to three people to pass side by side. Our future research work will focus on these issues.
Received signal strength
SVM:
Support vector machine
CSI:
Channel state information
RF:
RSSI:
Received signal strength indication
Cross validation
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G. Antonini, S.V. Martinez, M. Bierlaire, J.P. Thiran, Behavioral priors for detection and tracking of pedestrians in video sequences. Int. J. Comput. Vis. 69(2), 159–180 (2006). https://doi.org/10.1007/s11263-005-4797-0
D. Kong, D. Gray, H. Tao, A viewpoint invariant approach for crowd counting. in Proceedings of the 18th International Conference on Pattern Recognition (ICPR'06) vol. 3 (Hong Kong, China, 20–24 August 2006), pp. 1187–1190. https://doi.org/10.1109/ICPR.2006.197
S. Ali, M. Shah, A. Lagrangian, Particle dynamics approach for crowd flow segmentation and stability analysis. in Proceedings of the 2007 IEEE Conference on Computer Vision and Pattern Recognition (Minneapolis, MN, USA, 17–22 June 2007), pp. 1–6. https://doi.org/10.1109/CVPR.2007.382977
Z. Zhou, L. Xu, W. Li, People counting based on feature-regression and detection. J. Comput. Aided Des. Comput. Graph. 27, 425–432 (2015)
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H. Li, E.C.L. Chan, X. Guo, J. Xiao, K. Wu, L.M. Ni, Wi-counter: smartphone-based people counter using crowdsourced Wi-Fi signal data. IEEE Trans. Hum. Mach. Syst. 45(4), 442–452 (2015). https://doi.org/10.1109/THMS.2015.2401391
M. Mizutani, A. Uchiyama, T. Murakami, H. Abeysekera, T. Higashino, Towards people counting using Wi-Fi CSI of mobile devices. In 2020 IEEE International Conference on Pervasive Computing and Communications Workshops (PerCom Workshops) (23–27 March 2020), pp. 1–6. https://doi.org/10.1109/PerComWorkshops48775.2020.9156098
R. Ramezani, Y. Xiao, A. Naeim, Sensing-Fi: Wi-Fi CSI and accelerometer fusion system for fall detection. in 2018 IEEE EMBS International Conference on Biomedical Health Informatics (BHI) (Las Vegas, NV, USA, 4–7 March 2018), pp. 402–405. https://doi.org/10.1109/BHI.2018.8333453
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X. Xie, S. Sun, Multi-view support vector machines with the consensus and complementarity information. IEEE Trans. Knowl. Data Eng. 32(12), 2401–2413 (2020). https://doi.org/10.1109/TKDE.2019.2933511
L. Liu, W. Huang, C. Wang, Hyperspectral image classification with kernel-based least-squares support vector machines in sum space. IEEE J. Topics Appl. Earth Observ. 11(4), 1144–1157 (2018). https://doi.org/10.1109/JSTARS.2017.2768541
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V.N. Vapnik, Statistical Learning Theory (Wiley, New York, 1998)
M. Gao, Research of Human Traffic Monitoring Method Based on Radio Frequency Sensor Network. Thesis for Master Degree (Nanchang Hangkong University, Nanchang, China, 2018)
This research was funded by the National Natural Science Foundation of China, Grant Nos. 61501218 and 61906041.
School of Software, Nanchang Hangkong University, Nanchang, China
Zhiyong Yang & Jing Wen
School of Mathematics and Big Data, Foshan University, Foshan, China
Kaide Huang
Zhiyong Yang
Jing Wen
Conceptualization, ZY and KH; methodology, ZY and JW; software, JW; validation, ZY, JW and KH; formal analysis, JW; investigation, ZY; resources, JW; data curation, JW; writing–original draft preparation, ZY; writing–review and editing, ZY and KH; visualization, JW; supervision, KH; project administration, ZY; funding acquisition, KH. All authors have read and agreed to the published version of the manuscript. All authors read and approved the final manuscript.
Authors' information
Zhiyong Yang received the Ph.D. degree in communication and information system from Sun Yat-sen University, Guangzhou, China, in 2013. He is currently a Lecturer with the School of Software, Nanchang Hangkong University, Jiangxi, China. His research interests include compressed sensing, sensor-less sensing, and wireless sensor networks.
Jing Wen received the B.S. degree in software engineering from Gannan Normal University, Ganzhou, China, in 2020. Now she is currently working toward the M.S. degree with the School of Software in Nanchang Hangkong University, Jiangxi, China. Her research interests include sensor-less sensing and machine learning.
Kaide Huang received the B.S. and Ph.D. degrees from Sun Yat-sen University, Guangzhou, China, in 2011 and 2016, respectively. In 2016, he joined the Computer Network Information Center, Chinese Academy of Sciences, Guangzhou, where he was an Assistant Chief Engineer, from 2017 to 2018. He is currently an Associate Researcher with the School of Mathematics and Big Data, Foshan University, Guangdong, China. His research interests include compressed sensing, signal reconstruction, wireless sensor networks, and control systems.
Correspondence to Kaide Huang.
Yang, Z., Wen, J. & Huang, K. A method of pedestrian flow monitoring based on received signal strength. J Wireless Com Network 2022, 2 (2022). https://doi.org/10.1186/s13638-021-02079-y
Pedestrian flow monitoring


text:
"""Remove index from FileAttachment.repo_path.

Version Added:
    2.0
"""

from django_evolution.mutations import ChangeField

MUTATIONS = [
    ChangeField('FileAttachment', 'repo_path', initial=None, db_index=False)
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redpajama_set_name: RedPajamaGithub


text:
Posted on 10.11.2019 by Malagul
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9 thoughts on " Aint No Cure For Love - Jennifer Warnes - Famous Blue Raincoat (CD, Album) "
Zulurisar says:
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Nelmaran says:
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Febei says:
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Vudosar says:
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Shakajora says:
rows · Jennifer Jean Warnes (born March 3, in Seattle, Washington) is an American singer .

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Journal of Mathematical Finance > Vol.6 No.5, November 2016
The Valuation of Corruption ()
Joseph Atta-Mensah
Capacity Development Division United Nations Economic Commission for Africa, Addis Ababa, Ethiopia.
DOI: 10.4236/jmf.2016.65051 PDF HTML XML 1,489 Downloads 2,684 Views Citations
Unlike the current measures in the literature, where corruption is constructed as an index, this paper provides a formula for quantifying corruption. By using option pricing techniques, the paper shows that the monetary value of a corrupt activity is equivalent to a regular bond and an embedded European call option. This formula is very important because it could be used to gauge the level resources lost to corrupt activities, and also to determine the level of "tax" that could be levied at corrupt-government officials. Results in the paper show that a government committed to reducing corruption should institute measures that will reduce the level and the volatility of the price of the goods in the parallel markets. The paper also finds that a government could reduce corruption by cutting interest rates, which would spur growth and render corruption as an unprofitable exercise.
Corruption, Option Pricing
Atta-Mensah, J. (2016) The Valuation of Corruption. Journal of Mathematical Finance, 6, 728-746. doi: 10.4236/jmf.2016.65051.
Despite the long history of corruption, modern research on economics of corruption began about 40 years ago with the work of [1] . Since then there has been a slew of articles written on the subject. One could also argue that origins of the body of work on corruption can be traced to the seminal paper of [2] on rent-seeking and its impact on economic activities. As [3] suggests, this body of work has three main features: cross country comparisons, data on corruption is derived from perception indices, and corruption is explained as a consequence of a country's institutionalized policy environment. Although the literature has provided us with valuable insights on the subject, it has drawbacks. First, the use of the corruption index is inappropriate since it is fraught with perception bias, as perceptions of corruption change from country to country and from culture to culture. Second, the literature fails to provide us with a quantitative measure of corruption. A quantitative measure is not only important for researchers but necessary for planners and policy makers in determining the size of resources lost to corrupt practices of government agents.
The purpose of this paper is to provide a method of measuring the size of corruption. This is done by providing a formula for pricing a corrupt activity. This is a departure from the literature where the focus of research is on the aggregate determinants of corruption. Corruption is an activity that is done in secrecy and hard to detect. However, in most developing countries, there are "secret" markets for most of the government's goods and services that are difficult to obtain through the normal channels. These markets are run by government officials or their proxies. Although the official prices of these goods are known and set by the government, the prices of the goods and services in these markets are determined by the government official based on the maximum rent that could be extracted. The price in the secret market could be higher or lower than the official set price, depending on the demand for the goods or services.
The question asked in the paper is: in a corrupt environment, what is the price a corrupt government official must pay for the right to sell a government goods or services at a future date? This question is very important because in a country where it is very difficult for a government to curb corruption, it could impose a price or a special "tax" on its corrupt officials. The special taxes collected by the government could then be used to provide public goods for the citizens, or under some circumstance returned to those who purchased the goods or services. In the spirit of Coase theorem, the significant contribution of this paper is an attempt to find a market solution to the problem of corruption. The theoretical basis of the paper is to provide a pricing formula to value a corrupt activity. It draws on the option pricing literature by considering a corrupt activity as a European call option.
In this paper, corruption is defined as "the use of public office for private gains, where an official (the agent) entrusted with carrying out a task by the public (the principal) engages in some sort of malfeasance for private enrichment which is difficult to monitor for the principal" ( [4] , p. 1321). Despite this definition, corruption could mean different things in different contexts. For example, there can be political corruption where the ill-gotten gains are in terms of political power. Corruption could also occur in the private sector. Instead of allowing the market forces to operate, a seller could ration the supply of scarce goods and demand bribes from those who are in need of the goods (for example, paying a higher price to a "scalper" for a sold-out basketball game featuring Lebron James). It must be noted that this paper does not seek to answer the distortionary effects of bribery on resource allocation neither does it answer the question of the impact of corruption on economic development.
This paper also assumes that the punishment for detecting corruption is negligible since there are a lot of corrupt officials. [5] has a model that demonstrates the expected punishment for corruption when detected declines as more officials become corrupt. This is because it is preferable to be discovered by a corrupt superior than a non-corrupt one. Furthermore, our model implies that the potential bribers' demand for corrupt services decreases as the bribe size increases.
This paper is organised as follows. Section 2 presents a brief review of issues related to corruption. Section 3 lays out a model for pricing a corruption activity. Concluding remarks are made in Section 4.
2. A Brief Review of the Issues1
Corruption, or the perception of corruption, has been observed to have a pervasive impact on a nation's economic development. [4] reports that corruption is not a new phenomenon. Bardhan points out that in the fourth century B.C, then prime minister of an Indian King, Kautiliya, writes in his book Arthasastra:
Just as it is impossible not to taste the honey (or the poison) that finds itself at the tip of the tongue, so it is impossible for a government servant not to eat up, at least, a bit of the king's revenue. Just as fish moving under water cannot possibly be found out either as drinking or not drinking water, so government servants employed in the government work cannot be found out (while) taking money (for themselves) ( [4] , p 1320).
Dante and Shakespeare also give prominence to the negative effects of corruption in their works and in the Bible, Jesus Christ condemns tax collectors for their corrupt practices (I Timothy 4:5).
In the literature, corruption is observed to grow out government regulations and controls, as government officials embark on rent-seeking activities which in turn slows down economic growth ( [4] [6] - [13] among others). In most developing countries, government authorization is required for the opening of factories, for exportation and importation of goods and services and others. The procurement of the authorization notes or permits may involve different government agencies and several government officials. As pointed out by [11] , the presence of regulation and authorizations gives monopoly power to government officials. These officials tend to use this power to extract bribes from those who need government authorization or permits.
Trade restrictions could also fester corruption. Some countries impose import restriction on certain goods so as to protect home industry. However, the quantity restriction on the flow of foreign goods makes import licences for the restricted goods very valuable and therefore attracts bribes from importers. On the other hand home producers of the good could also corrupt influential lawmakers to maintain such restriction even if it is through the imposition of tariffs.
Another source of corruption in some countries is the tax system. [11] indicates that corruption tend to be higher in countries where, the tax code is complicated, or the settlement of taxes require frequent meetings between the taxpayer and tax official, or the wages of tax officials are low, or there is a lack of transparency, or lack or mild penalties for corrupt official who are discovered.
Price controls, differential exchange rates, exchange rate controls and lower paid civil servants are part of the contributing factors of corruption.2 Keeping the price of government goods and services below their market value allows government officials to engage in rent-seeking activities. Corruption grows in countries with differential exchange rates―one for importers, one for exporters, one for multinationals, one for tourists, one for investors, etc.―because individuals or firms would pay a bribe to corrupt official to get the "best" rate. In countries where public servants are paid significantly lower than their counterparts in the private sector and sanctions are non-existent for corrupt officials, public servants tend to take bribes in performing their duties.
Corruption has been observed to impact negatively on economic growth ( [4] [6] [8] [9] [17] [18] [19] and others). This is because corruption distorts incentives and market signals leading to productive resources, such as human talent, to be diverted into rent-seeking activities. Financial rewards gained from corruption act as an incentive to lure the more talented and better educated to pursue rent-seeking activities instead of productive engagements, which in turn impact negatively on economic growth. Corruption impacts adversely on investment and growth because the payment of bribes by investors to secure investment licenses increases the cost of doing business and consequently reduces the incentive to invest. [4] points out that the tax code in some countries allow for losses to be deducted from taxable investment income, while losses from the payment of bribes can not be offset, making bribery harmful for risk-taking in the context of innovation. [20] finds corruption to be more distortionary than taxes. Wei argues that because of the secrecy and arbitrariness of corruption, the implicit contract between the briber and bribe cannot be enforced in a proper court of law. [8] shows theoretically that countries with a more disorganised pattern of corruption are not attractive for investors. Holding the level of corruption constant, [20] empirically finds countries with disorganized corruption structure receive far less direct foreign investment.3
Corruption has negative effects on productivity enhancing growth. For example, computers meant for the work place that are diverted for personal use by government officials, in some countries, do affect output growth negatively. Corruption also cut into profit margins of productive investments relative to rent seeking investments. As pointed out by [21] , there are increasing returns to rent-seeking, as a rise in rent-seeking activity reduces the cost of further rent-seeking relative to that of productive investment. It is generally known that a fall in the returns to productive investment have a negative impact on growth. However, corruption could also induce an "accelerator effect" on growth. The fall in the return to productive investment could in turn raise the returns to rent-seeking activities, which in turn would slow down growth. [22] has indicated that corruption acts as a tax on profits and could hinder the entry of new goods or technology to the market. This is because innovators or new producers need permits and licenses which are obtained by paying hefty bribes.
Extending the corruption literature to the open economy, [17] find that the correlation between corruption and growth in a closed economy to be positive but negative in an open economy. The authors' analysis is founded on the observation that: richer countries are less corrupt, while corrupt economies are poor. Based on this observation ( [17] , p. 2) pose the following puzzle: "If poorer countries do indeed experience higher levels of corruption, and if indeed as suggested by a number of empirical studies ( [19] and others), corruption hampers growth, then how did rich countries, who were poor once, become rich?" [17] provides an answer to the puzzle by conjecturing that the western economies of the 19th century were relatively closed economies and that the gains of corruption remained in the country as part of the productive capital. However, because of the inter-connectedness of current economies, the rewards of corruption are dispatched to foreign bank accounts, robbing the country of productive capital. The implication of this analysis is that poor developing countries should be slow at becoming global partners.
Corruption also affects economic efficiency. In the literature there are proponents who argue that corruption is the oil needed to grease the economic engine of an over- regulated economy. [23] argues that corruption could improve economic efficiency by correcting for the ills of bad government regulation. [24] buttresses this view by pointing out that, in a rigid and over-centralized environment, it is better to have a dishonest bureaucracy than an honest one. Using Coase's analysis, [4] argues that allocation efficiency is achieved in a competitive bidding by private firms for a government procurement contract and the corrupt government official awards the contract to the highest bidder in bribes. In this example, allocation efficiency is unaffected even though the producer surplus goes to the corrupt official.4
The efficiency-enhancing view of corruption is not shared by all in the literature. As [4] points out, corruption does not always remove distortions created in an economic environment. [4] 's argument is that distortions are not exogenous to the economic environment and are part of built-in corrupt practices. Inefficient allocation outcomes may be attained in the bidding exercise if the bribee is influenced by other factors than the size of the bribe or the briber could get away with supplying low-quality good at high-quality price. With respect to corruption as the oil for a "squeaky" economic engine, anecdotal evidence points to countries where corrupt officials slows down the wheels of bureaucracy in order to attract more bribes. Theoretically, there are no efficiency gains in an environment of asymmetric information as the briber and bribee may not have an agreement on the size of the bribe. Moreover, because of its illegality, corruption agreements are not protected by the courts of law, making it easier for the bribee to renege on the contract. Corruption also fails to achieve economic efficiency when the procurement of the government good or service requires the approval of several government officials. [29] notes that corrupt government officials could, instead of speeding up, reduce the speed of processing files thereby attracting more bribes. [8] also points out that corruption aggravates distortions in the economy because of its secrecy and resources spent by government officials to prevent detection and punishment. [30] contends that existing practices in more corrupt societies tend to encourage rent- seeking activities. Thus, the beneficiaries of corrupt practices are the most successful at rent-seeking, and not necessarily the most economically efficient.
Empirically, the literature has also investigated the effects of corruption on economic growth. Using data from some developed and developing countries, [19] finds that corruption has a negative and significant impact on economic growth, with decreased investment in physical capital responsible for most of the negative effect. Based on a cross-sectional dataset for a number of countries, [31] finds that corruption decreases private investment and education, and increases political instability, all combining to push down economic growth. [11] and [32] find that higher corruption is associated with lower quality of public infrastructure and decreasing private investment. Using a measure of corruption-induced uncertainty, [33] finds that the uncertainty associated with corruption reduces foreign direct investment. [34] finds that corruption increases income inequality and poverty, distorts the progressivity of the tax system and stifle the formation of human capital and above all reduces growth. [9] examines the impact of corruption in a number of African countries and concludes that corruption decreases economic growth and that increased corruption leads to increased income inequality. [35] find corrupt governments to receive more foreign aid under some circumstances.
Examining the effects of corruption on income and the Gini coefficient of income distribution, [36] find a non linear relationship between corruption and the Gini coefficient; positive relationship between the Gini coefficient and corruption in countries with intermediate level of corruption, and negative relationship for countries with high or low levels of corruption. [37] finds that reductions in the level of corruption results in significant social welfare as proxied by child and infant mortality rates, percentage of low-birth weight babies and primary school dropout rates. [38] also finds corruption to be significantly associated with higher military spending in about 120 countries.
In the empirical studies cited above, the corruption variable is based on a qualitative measure rather than a quantitative one. The qualitative measure or corruption index is constructed from either published reports on corruption, such as newspapers or the internet, or questionnaire-based surveys. A popular index used by researcher and the business community is the Transparency International index.5 This index measures the perception of corruption on a scale of 0 to 10, with 0 indicating that most transactions or relations in the country are tainted by corruption and 10 indicates the country is free of corruption.
Despite the usefulness of the corruption index it has some drawbacks. First, it measures perceptions of corruption and not the size of corruption. This imposes a potential problem as the index may be fraught with perception bias, as perceptions of corruption change from country to country and from culture to culture. Second, the index is not helpful to governments or economic planner who would like to know the resource cost of corruption as the index fails to provide one. In the next section we would attempt to provide a method of measuring the size of corruption. This is done by providing a formula for pricing a corrupt activity.
3. Valuation of Corruption
Corruption is a secret activity that is very difficult to detect in some countries. Even when discovered, the monetary value of the transaction tends to be elusive. In some countries around the world, "secret" or unofficial markets exist for most of the government produced goods and services that are difficult to obtain through the normal process. These markets, which are run by government officials or their proxies, exist because government officials restrict the quantity of the goods or services sold in the "normal" markets. Furthermore, although the official price of the good is set by the government, the price in the unofficial markets fluctuates, depending on the maximum rent that could be extracted by the government official. With this observation as the back drop, we attempt to provide a model for valuing corruption. The focus of this section is to answer the question: in a corrupt environment, what is the maximum rent a corrupt government official could extract from the sale of the good or service at a future date?
In this paper, we consider a homogenous government produced goods. Following [8] the paper assumes that the government's agent has the opportunity to restrict the quantity of the good sold.6 We also assume that corruption can not be detected or punished because of the corrupt environment. This is a reasonable assumption given that in many corrupt nations, corrupt officials incur no penalties when caught because their bosses share in the "spoils" and the law is blind. Furthermore, the total cost of producing the good is assumed to be borne by only the government and is of no concern to the corrupt official.
A corrupt official is faced with two options when he or she decides to sell the government good. The official could decide to sell the good by a multiple of the government price and then pocket proceeds without accounting for it. This first option is what [8] refer to as corruption with theft. The official has a second option, where he/she sells the good at a price (government price plus bribe) prevailing in the secret market and truthfully accounts to the government the quantity of goods or services sold at the government price. Under the second option, the government official keeps the difference between the secret market price and government set price and returns the rest to the government. [8] refers to the second option as corruption without theft.
Let K be the government set price of the good, and P be the price (government price plus bribe) of the good in the secret market. The options facing the government official can then be summarized as:
where a is a positive number. The first part of Equation (1) summarises the first option while the second part capture the second option. What Equation (1) suggests is that a rational corrupt official will choose which ever options give the maximum return. Equation (1) could then be rewritten as:
If we assume that corruption activity will take place T period from now, then we can interpret the present value of the corrupt official's gains from the sale of a unit of government produced good or service as being equivalent to a bond with face value aK and a call option on the good, in the secret market, at an exercise price of (1 + a)K. With this interpretation, we can proceed to use the option pricing literature to provide a formula for quantifying the value of a corruption activity.
In addition to the above assumption we shall make the usual assumptions for modelling continuous time asset pricing models: 1) in the secret market, the trading of the government good is traded continuously; and 2) the price of the good follows a continuous time diffusion process of the form:
where ap is the instantaneous average return of holding one unit of the good, σp is the instantaneous standard deviation of rate of change of the price and dzp has a standard normal distribution with mean of zero and variance dt. Note that ap and σp may be functions of P and t. However, for the purpose of this exercise we shall assume they are constants. Given that the government price is fixed, we must also mention that it is the size of the bribe that is responsible for the diffusion process.
3.1. Pricing a Corrupt Activity
Given the secret market price of the government produced good, P, let the value of the corrupt activity at any time be C(P, t). Then applying Ito's lemma the drift and the diffusion of the value of the activity is given as:
which upon simplifying, yields:
Proposition 1: The partial differential equation governing the corruption activity is:
Proof: See Appendix.
Remarks: Intuitively, the differential equation governing the valuation of the corruption activity is explained as follows. The first term on the left hand side of Equation (8) captures the Jensen's inequality effect coming from the variance of the price of the commodity. The second term represents the risk-adjusted expected drift of the price of the good. The third term reflects the shrinking time to maturity. The last term represent the net flows to the corrupt official. It is important to note that the drift term of the price of the good plays no role in the valuation of the corruption activity. However, the variance of the price of the goods plays an important role.
Proposition 2: Under the set of assumptions given earlier, the present value of the gains from corruption activity is:
where E(P, K, τ) is an European call option to purchase the government produced good in the secret market at an exercise price of (1 + a)K. The value of the call option is
and N(.) is the cumulative normal distribution function.
Based on Equation (2), it is shown that the present value of the corrupt official's gains from the sale of a unit of government produced good or service is a equivalent to a bond with face value aK and a call option on the good, in the secret market, at an exercise price of (1 + a)K. The first term of Equation (10) corresponds to the present value of a bond and the second term is the value of the call option. The call value option follows from [39] - [44] . Note that the differentiation of Equation (10) yields the stochastic partial differential (Equation (8)).
Remarks: Propositions (2) in very important on a number of reasons. First, it provides us with a method of placing a monetary value on a corruption activity. Second, for budgetary purposes, a government facing a pervasive level of corruption could use this formula to gauge the level resources lost to corruption activity. Third, the formula could be used to tax government officials for their corrupt activities. Fourth, the recognition of corruption activity as a European call option provides an analytical framework for improved understanding of the corruption literature. In the next section, we will examine how the underlying parameters of the model influence corrupt activities.
3.2. Properties of the Valuation Model
In this section, we attempt to learn more about the factors that influence corruption activity, and the implied policy implications.
Proposition 3: The value of corruption activities rises with the increase in the "secret" market price of the government produced goods.
Differentiating Equation (10) with respect to P and using Equation (A16) in the appendix:
Remarks: The results suggest that a strong demand for the good in the secret market would enhance the value of corrupt activities. The result corroborates the view that government officials could deliberately restrict the supply of goods and services so as to profit substantially from corruption activities.
On the other hand, a government interested in curtailing corruption could embark on policies that could contribute to the fall in the price of the good in the secret market. Such policies could include more government officials supplying the government produced goods. For example, the government could decentralize the issuing of passports by having more passport offices. Because of the difficulty for several government officials to collude, such a measure would reduce the amount of bribe and therefore the price the good in the "secret" market which in turn leads to a fall in monetary value of corruption.
Proposition 4: Corruption activities increases with the rise in the volatility of "secret" market price of the goods.
Differentiating Equation (10) with respect to the variance of P, , and using Equation (A22) in the appendix:
Remarks: The result demonstrates that corrupt government officials profit a great deal from increased volatility of the price of the good in the secret market. The increased volatility of the price increases the value of the call option implied in the value of the corrupt activity. An explanation for this is that a call option has no downside risk as the value of the call is zero irrespective of how far it finishes out of the money. Hence, an increase in the volatility of the price of the good goes to increase the chances that the call option will expire in the money. The rise in the volatility of the price of the good also increases the general uncertainty in the secret market which in turn enhances the gains from corruption.
To curb corruption, the government could embark on measures that will reduce the volatility of the price of the good in the secret market. One measure would be for the government allowing competition in the supply of the good. Such an action would not only reduce the level of bribe but also the volatility of the price in the secret market, and eventually decrease the incentive to engage in corrupt activities.
Proposition 5: A rise in the government set price, K, may or may not reduce the gains from corruption activity.
Differentiating Equation (10) with respect to K and using Equation (A28) of the appendix:
which is clearly indeterminate.
Remarks: As mentioned earlier a corrupt official has two options: corruption with theft and corruption without theft. Corruption with theft gives the implied "bond" feature to the gains from corruption and corruption without theft gives the embedded call value in the gains. Proposition (5) is explained by the fact that an increase in government set price leads to an increase in the value of the "bond" implied in the gains from corruption and a decrease in the value of the embedded call option. The value of the call falls because the rise in the government set price increases the probability that the call finishes out of the money. The net impact of the rise in the government set price on corruption activity depends on which effects dominate. In other words, if official's accountability of the goods and services is weak then we may see corruption with theft rising. In which case the first term in Equation (13) will dominate the second term and therefore corruption activity will rise with the increase in K.
Corollary: A rise in the government set price, K, would reduce the monetary value of corruption if it is backed by tough accountability for all government-produced goods sold by officials.
Remarks: If the government mechanism of ensuring that all goods supplied to government officials are properly accounted for then officials would find it very difficult to carry out corruption with theft activities. Thus in Equation (13) a would be close to 0, and the impact of the rise in K on corruption activity will be negative. The policy implication of this result is that, in an environment of unstoppable levels of corruption, a government could reduce corruption by raising its price of goods while maintaining strong accounting standards.
Proposition 6: The rise in the factor (a) by which the government official, engaged in corruption with theft, sells the good or service for leads to an increase in the gains form corruption.
Differentiating Equation (10) with respect to a and using Equation (A34):
since .
Remarks: Following the explanation given for the remarks made for Proposition 5, an intuitive explanation for this result is that a rise in the parameter a, enhances the value of the implied bond and decreases the embedded call value. However, in this case, the net impact is positive because the bond dominates the call. Although corruption without theft falls, the implication of the results is that the rise in the parameter a raises the rewards to corruption because of the increase in corruption with theft.
Proposition 7: Interest rates have indeterminate effects on the gains from corrupt activities.
Differentiating Equation (10) with respect to the interest rate, r, and making use of Equation (A40) yields:
Remarks: The result shows that rising interest rates have an ambiguous impact on corruption. Again, following the remarks for Proposition 5, the rise in interest rates reduces the value of the implied bond in the gains of corruption activity, discouraging corruption with theft. At the same time the rewards from corruption without theft rises since the exercise price on the embedded option reduces. The impact on corruption activity depends on which effect dominates. Intuitively, interest rate increases tends to slowdown the economy and consequently raise the level of unemployment. Using the efficiency wage argument, increased unemployment pool would serve as a deterrent to officials who would want to keep their jobs from engaging in corruption with theft for fear of being fired. If that is the case then a would be close to zero and therefore the impact of the rise in interest rate on corruption activity would be positive.
Corollary: In a country with strict accounting standards for all government-produced goods sold by officials, a rise in the interest rate would result in higher corruption.
Remarks: A country with strict accounting standards suggests that a would be close to zero and therefore the sign for Equation (15) would be clearly positive. The monetary value of corruption activity rises because the embedded option rises in value as the rise in interest rate reduces the exercise price of the option. The implication of this result is that a government committed to a higher accounting standard could reduce corruption by cutting interest rates, which in turn spurs economic growth. The rise in economic growth would in turn curtail acts of corruption, since the acts would be less lucrative.
Corruption is a costly activity to a nation as it leads to the diversion of public resources for private use. It has the potential of shifting resources away from the productive sector of an economy. This paper has attempted to address the issue by providing a market based solution by using a financial model to quantify the value of corrupt activities. The approach taken in the paper is very innovative as it provides a solution for a country where it is very difficult for a government to curb corruption. The paper proposes that the government could impose a price or a special "tax" on its corrupt officials. The special taxes collected by the government could then be used to provide public goods for the citizens, or under some circumstance returned to those who purchased the goods or services.
Using option pricing techniques, the paper shows that the monetary value of a corrupt activity is equivalent to a regular bond and an embedded European call option. Unlike the current measures in the literature, where corruption is constructed as an index, this paper provides a formula for quantifying corruption. This formula is very important because it could be used by governments, private sectors and interested parties to gauge the level resources lost to corrupt activities. The formula could also be used to determine the level of tax that corrupt-government officials could be levied. Furthermore, the recognition of corruption as a European call option provides an analytical framework for improved understanding of the corruption literature.
Results in the paper show that a government committed to reducing corruption should institute measures that will reduce the level and the volatility of the price of the goods or services it provides in the parallel markets. The measures could include the government allowing for competition in the supply of the goods or services. Such an action would not only reduce the level of bribe but also the volatility of the price in the secret market and eventually a decrease in the incentive to engage in corrupt activities. The paper also finds that a government committed to a higher accounting standard could reduce corruption by cutting interest rates, which would spur economic growth and render corruption as an unprofitable exercise.
The author would like to acknowledge the useful comments of colleagues at the Economic Commission for Africa. However, any errors or omissions must be attributed to the author. Of course, the views expressed in this paper are those of the author and should not be attributed to the United Nations.
A.1. Proof of Proposition 1
To prove Proposition 1, we use standard arbitrage arguments common in the options pricing literature. Construct a hypothetical portfolio by investing ω in the government produced goods and (1 − ω) in corruption activity. If L is the value of the portfolio then the instantaneous return on portfolio, dL, is:
The portfolio, L, could be made riskless if ω is chosen to satisfy:
implying:
Holding units of the government produced goods and in the corruption activity ensures that portfolio L is riskless. In the absence of arbitrage profits, the instantaneous return on the portfolio must be equal to that of a risk-free asset r. Or:
Equating Equation (A5) to the drift term of Equation (A2) with the substitution of ω we have:
Substituting Equations (6) and (7) into Equation (A6) and re-arranging yields the differential equation governing the loan contract (Equation (8)).
A.2. Properties of the Call Option
1) The value of the call option
In the main text, an expression is derived for valuing a European call option as:
The paper now turns to the sensitivity of the value of the call to the parameters.
2) The effect of the change of the "secret" market price on the call value
Differentiate the call with respect to the secret market price, P:
(A10)
Substitute Equations (A2) and (A3) in the last part of Equation (A7):
which simplifies into:
3) The change of the variance of the "secret" market price on the call value
Differentiate the call price with respect to :
Using Equation (A11),
substituting Equations (A8) and A(9),
which simplifies to:
hence,
4) The change of the government set price, K, on the call value
Differentiate the call value with respect to K:
which could be expressed as:
manipulating further:
which reduces to:
hence
5) The change of the parameter a on the call option value
Differentiate with respect to a:
simplifying,
6) The change of interest rate on the call option value
Differentiate with respect to r:
rearranging:
1Our review of the literature is heavily influenced by [4] [14] [15] [16] .
2For an elaborate discussion of factors affecting corruption see [11] .
3 [20] measure of corruption structure is based on the dispersion of corruption ratings by survey respondents.
4In a repeated game with incomplete information, [26] [27] have also shown a similar outcome where bribery produces efficiency in competitive bidding procedures.
5The website for the Transparency Index is: www.transparency.com.
6The restriction could take the form of the government official refusing to issue a passport, or deny access to a road or place a lot of impediments or requirements in the way of a purchaser of the goods.
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