People spend significant parts of lives in indoor spaces like office buildings and transportation facilities. When many people are inside an indoor space, it is useful and important to measure the densities and find the dense regions in scenarios like flow management and security control. Considering a large airport, it is helpful for the authority to effectively determine which regions are currently most crowded so that actions, e.g., to open more fast tracks, can be taken timely at the right place to help passengers in need. Assuming GPS-like data, density query techniques in free space [2] or road network [5] are unsuitable for indoor density due to the unique challenges in indoor settings. First, indoor spaces feature distinct entities like rooms, walls, and doors, which altogether form the indoor topology that enables and constrains object movements. Second, indoor positioning systems offer lower sampling frequency and report discrete locations, thus leaving considerable uncertainty at a particular time. The issue becomes even more challenging to deal with in the context of complex indoor topology. Specialized in indoor settings, a naive approach is to install counting sensors at the doors of each indoor partition, a basic topological unit (e.g., a room) connected to other units via doors. However, this method requires extra hardware investment and rigorous sensor deployment that falls short in a dynamic indoor environment where indoor topology may change from time to time. Motivated by the limitations of existing approaches, we propose a low-cost, data-driven approach that harvests needed values from online indoor positioning data [4] . Our approach demands no specific hardware, it is not bothered by indoor topology variations, and it works well for user-defined indoor regions. The key contributions of our study are as follows. • We design an indoor density definition amenable to indoor object location uncertainty, and formulate the problem of finding top-k indoor dense regions. • We analyze the indoor location uncertainty, derive bounds of indoor densities, and introduce distance decaying effect into indoor density computing. • By making use of the uncertainty analysis outcomes, we design efficient algorithms to search for the current top-k indoor dense regions. • We conduct extensive experimental studies to evaluate our proposals on synthetic and real datasets. In our setting, only the latest object positioning information (o, loc, t) is maintained in an online indoor positioning table (OIPT), meaning that the object o was last seen at location loc at time t. Given an indoor location loc reported at a past time t l , its indoor uncertainty region UR I (loc, t c , t l ) describes the indoor portions where the object can reach at the current time t c under the maximum speed constraint V max . Introducing the distance decaying effect [4] that reflects the locality of object movement, we define object presence that stipulates how an object should be counted for an indoor region r at time t c . Definition 1 (Distance Decaying Object Presence): Given an indoor region r, an object o's indoor uncertainty region UR I (loc) with the distance decaying function Accordingly, we define density for an indoor region and formulate the top-k indoor dense region search problem. Definition 2 (Density): Given a set O of indoor moving objects, an indoor region r's density is Area(r) . Problem 1 (Top-k Indoor Dense Region Search): Given a set O of indoor objects, whose latest positioning records are captured in the OIPT, and a query set Q of indoor regions, the top-k indoor dense region search returns k densest indoor Our problem setting allows users to customize semanticdependent query regions according to their practical needs. When the top-k search is triggered at t c , the object location in OIPT is already out-of-date due to the discrete nature of indoor positioning, making it complex to compute the precise object presences and indoor densities. To this end, we propose the indoor buffer and core regions to derive bounds of indoor densities, in order to make the density computation concentrate on the relevant objects only. Subsequently, we design the top-k search algorithms based on the derived density bounds. Due to the object location uncertainty, a region r where there was no object at a past time t p can contain objects at time t c . However, such objects cannot come from locations too far away due to the speed constraint V max . Instead, they can only
Considering the uncertain object movements bewteen observed time and query time, Li et al. REF study the problem of searching the current top-k indoor dense regions.
In Search of Indoor Dense Regions: An Approach Using Indoor Positioning Data
2019 IEEE 35th International Conference on Data Engineering (ICDE)
2019 IEEE 35th International Conference on Data Engineering (ICDE)
Computer Science