# Device-Free Crowd Size Estimation Using Wireless Sensing on Subway Platforms
## 1 Introduction  
The demand for crowd-monitoring solutions has increased significantly in the past decade as large-scale events increase in size and frequency [1]. Another important use case for crowd monitoring is in improving the safety and efficiency of large cities. As of 2018, The United Nations reports that 4.2 billion people are living in urban areas, with a projected increase to 6.7 billion people by 2050 [2]. Performing crowd management in cities has its own set of challenges. Large-scale events such as music festivals and soccer games tend to be held in demarcated areas with designated entrances and exits. This allows for the use of gate-counting solutions, such as ticket scans, turnstile gates, and down-facing counting cameras. In cities, people move freely without passing through such bottlenecks at which the aforementioned people-counting techniques can be utilized. We cannot give every individual a tracking device to collect data regarding their movement throughout the city, and it is no longer possible to rely on people carrying personal devices, such as cellphones, that transmit identifiable WiFi or Bluetooth signals due to the fact that efforts are being made to prevent such messages from being used for tracking purposes by randomizing identifiable information [3, 4, 5]. Metro and train stations are similarly challenging environments. While these types of environments have entrances that can be equipped with gate-counting solutions, they can only be installed at certain locations. In practice, counting people who are rapidly embarking and disembarking from railway vehicles is largely infeasible. This limitation effectively makes significant parts of these environments free-flow environments. An important distinction can be made between direct and indirect measurement solutions. Gate counting is a form of indirect counting. In order to obtain a value for the number of people in the environment, one has to take the difference between the 'in' and 'out' counts. This leads to the important requirement that such a system needs to be running for the full period of time when people are able to enter or leave the environment of interest. Even a short downtime of the system will lead to an offset error in the data. In contrast, direct methods, such as counting cameras [6; 7] or Wi-Fi counting [8; 9], are capable of estimating the number of people in the area directly from a single sample or short period of measurement. An emerging technology for directly estimating the crowd density at events and in urban areas consists of using device-free wireless sensing (DFWS) [10]. The DFWS technique makes use of a set of wireless nodes that are placed in and around the environment of interest. These nodes periodically transmit messages to each other, creating a mesh of links for which we are able to collect signal strength values. Prior research has established a strong correlation between the signal strength attenuation and the crowd density in the environment [11]. This estimation technique is an application derived from the field of Radio Tomographic Imaging (RTI), which is a popular technique for device-free localization applications [12]. The ability of RTI to detect the presence and location of dynamic obstacles such as road vehicles is demonstrated in [13]. A regression model describing the relation between signal strength and crowd density can be trained based on collected ground-truth data. A simple regression model, such as linear or polynomial regression, expects a static environment. When big changes in the environment take place, e.g., a metal fence is removed or a car stops in the environment, the resulting changes regarding line-of-sight propagation, as well as multipath propagation, will affect the relationship between the measured signal strength and the number of people present in the environment, rendering the trained model inaccurate. The use of multiple models in time-series analysis is commonly referred to as regime switching.