Processing Approximate Moving Range Queries in Mobile Sensor Environments

Processing Approximate Moving Range Queries in Mobile Sensor Environments Antoniya Petkova 1 Kien A. Hua 1 Alexander Aved 2 School of EECS University of Central Florida Orlando, USA 1 {apetkova, kienhua}@cs.ucf.edu 2 aaved@mail.ucf.edu Abstract The ubiquity of mobile devices has led to a rising demand for location-based services and applications. A major part of these services is based on the location-detection capabilities of the mobile devices. Utilization of location data reported by the devices is associated with a certain amount of uncertainty due to the device s mobility. In this paper, we examine an environment, which consists of mobile objects with no location-detection capabilities, and location-aware mobile sensors randomly scattered, that can sense the presence of mobile devices. These sensors can detect the identities of mobile objects that come within their sensing ranges but cannot infer their exact locations. The sensor readings are periodically reported to a database server. This system supports processing of mobile location-dependent range queries over mobile objects. The answer set of each query carries a certain degree of uncertainty due to the approximate nature of the reported object location data. We exploit scenarios of sensor range overlap to reduce the uncertainty inherent in the query result. Our work is validated through an extensive simulation study that provides assessment of the query results accuracy. Keywords- moving range queries over mobile objects; location databases; moving objects; sensors; uncertainty I. INTRODUCTION Due to rapid development and commercialization of wireless network technologies, localization technologies such as the GPS [10], smart mobile devices, radio frequency identifiers (RFID), and sensor networks, mobile communication has not only become ubiquitous, but indistinguishable from our everyday life in the modern world. This rapidly growing trend has resulted in an even greater demand for applications that integrate geographic location and services to satisfy various consumer needs. Such location-based services (LBS) range from military systems to everyday commercial systems such as vehicle navigation, taxi tracking, or environment monitoring. They allow users to query their environment and use the spatial data for various purposes [20]. To support such queries, today s solutions typically rely on location information reported by each participating mobile unit. The scalability of this strategy is limited due to the communication and computation bottleneck at the server. To mitigate this effect, Resident Domain [2] and Safe Region [19] techniques, and many variants (e.g., [23], [8], [12]) have been proposed. In this paper, we consider an environment that involves moving objects without localization and communication capabilities and mobile sensors equipped with GPS devices. The sensors have the ability to sense the presence of moving objects within their sensing ranges and can identify them, but cannot pinpoint their exact locations. RFID (Radio Frequency Identification) is an example of such sensing technology. Periodically, the sensors report their detected objects to the server. This proposed mobile sensor environment is more cost effective and more scalable then the conventional approach. The deployment cost of current solutions is typically proportional to the number of participating mobile units since each participating object is equipped with GPS, a computing device, and a communication device. In contrast, the deployment cost of the proposed environment is determined by the area of the application terrain, and is independent of the number of participants (i.e., moving objects). We focus on processing Approximate Moving Range (AMR) queries over moving objects in this environment. The continuous query is issued for one of the location-unaware mobile objects. The result at any point in time consists of the identities of all moving objects currently detected in the query range with a probability greater than some predefined threshold. The proposed query processing technique utilizes information gathered from the sensors and estimates the likelihood that a detected object is in the range of the query. In practice, not all applications demand exactness in the location information of the objects of interest. For instance, parents want to know if their child is still waiting at school; a student wants to know if a particular book has been returned to the library; a passenger wants to know if the next bus is arriving soon; or a military unit wants to know if a convoy is currently contained within a friendly area. None of these queries needs the exact location of the object of interest. We note that a different type of uncertainty has also been studied in LBS. The location information received at the server might not be accurate due to multiple factors, such as the object having moved since its last location update, delay in location data updates, transmission disruption, noise, or other issues associated with the unreliability of the physical transmission medium. Many probabilistic methods have been devised [3, 5, 6, 7, 11, 16, 17, 18, 21, 22] to address this problem. They compensate location deviations in the database to make discrepancies transparent to the user. The distinction between these studies and our work is as follows.

These techniques operate on location information obtained from individual objects through location updates, whereas our proposed technique deals with the presence of particular objects as detected by mobile sensors. Due to this difference, while existing techniques focus on estimating the true location of an object given its possibly outdated location, our challenge is to estimate the relative locations of objects given sensor readings. To simplify our study, we are not concerned with uncertainty due to the periodic nature of location data updates, transmission delays, signal disruptions, or limited server capacity. The remainder of this paper is organized as follows. We formally define the problem and introduce the framework in Section 2. The solution is presented in Section 3. The findings of our simulation study are presented and analyzed in Section 4. Finally, we conclude the paper in Section 5. II. PROBLEM DEFINITION In this section, we first present the uncertainty model for moving objects on which we base our study. Its purpose is to describe the imprecision of the data collected from the environment and to quantify the uncertainty that the query answers carry. A. Uncertainty Model In this subsection, we introduce a location uncertainty model to capture the uncertainty in a moving objects environment. The model distinguishes between two types of mobile objects, targets and sensors, deployed in a twodimensional area. We use a moving point with 2D Euclidean coordinates as an abstraction of a target object T i, T i {T 1,,T n } in the environment. The physical extent of the target in the 2D plane is irrelevant [9]. Each sensor, S j, S j {S 1,,S m }, is represented as a square centered at c j, such that c j {c 1,, c m }, and having a range r (i.e., the size of its sensing area). This representation accounts for the physical sensing device and its square detection range. Throughout the paper, S j is also used to represent the set of targets detected by the sensor. For simplicity, we assume all sensors have equal sensing ranges. Unlike existing works [4, 6, 8, 21], the targets in our model are not location-aware and they cannot communicate location information to the server. On the other hand, all sensor entities are equipped with locationdetection devices. They can sense the presence of moving objects within their sensing ranges but cannot identify their exact locations. Periodically, they send an update to the server that comprises their identity and location, together with the identities of all targets detected within their sensing ranges. Thus, a sensor S j can be modeled by the following tuple: < sid, loc t, r>, where sid stands for the sensor s id, loc t represents the location of the sensing object at time t, and r is the size of its sensing range. Even though the server does not have precise information regarding the targets locations, it can fuse the data reported by all sensors and approximate the targets locations. The extrapolation yields the whereabouts of the targets. Note that a target has to be detected by at least one sensor in order for the server to have any information about its current whereabouts. The extrapolated approximate target location has a rectangular shape with size bounded by the size of the sensor s range. A target T i detected by a sensor S j can be found, with certain probability, at any one location within S j. Thus, the scope of uncertainty for every object detected by a reader is determined by the recorded location of the sensor and its range size. In addition, each sensor is associated with a 2D probability density function, which describes at which positions within its sensing range the detected objects are more likely to be found. Hence, a target T i can be modeled with the tuple < tid, U tid >, where tid = i and represents the id of the target. U i denotes the uncertainty region of T i. When data from the sensors is received at the server, initially U i = S j. That is, the initial uncertainty region of a target object T i is the sensing region of the sensor that detected it. If T i has been detected by more than one sensor, the target s uncertainty region is updated to U i = S i S z, where z is the number of sensors that sensed T i in their sensing ranges. Thus, the location uncertainty of an object can be greatly reduced as multiple sensors detect that object. Similarly to [3, 6], we define an uncertainty region and an uncertainty probability density function to help quantify the location uncertainty of the moving objects in the proposed environment: Definition 1: An uncertainty region of an object T i at time t is defined as follows: f x S j, S j S z, if T i if T i S j T i Sk, j k. (1) S i T i S z Definition 2: The uncertainty probability density function (pdf) of an object T i, denoted by f i (x,y) is defined as follows: 0; 1, x, y if T U f i i. (2) i 0, otherwise Definition 1 implies that the uncertainty region of a target is either the sensing area of one sensor, in the case when the object was detected only by that sensor, or in the overlap area of multiple sensors, in the case when all of these sensors have detected the object in their sensing regions. Definition 2 is a general description of an uncertainty pdf. The pdf has the property that S j fi x, y dxdy 1. (3) The precise pdf formula may vary according to the specifications of different applications. Popular distributions like Gaussian and uniform have been studied in the context of uncertainty regions in [3, 6, 17, 21]. In this paper, we present a general uncertainty framework that can be adopted for different probability distributions. B. Approximate Moving Range Queries Based on the presented framework, in this paper we consider a new kind of probabilistic range query, Approximate Moving Range (AMR) query. Each query is pinned to one of the uncertain objects in the environment. However, due to the lack of precise location information about the moving objects in the environment, an AMR query is affixed to the

S 3 Q k U k uncertainty region of the query point. Each query has a rectangular area that denotes its range. For simplicity, all query regions have the same range. Each query is concerned with finding which moving objects are located within its range. More formally, given a rectangular object, Q k, where Q k {Q 1,,Q l } with a query point O k, such that O k U k, and having a range R, we can define the following type of query: Definition 3: An Approximate Moving Range query over uncertain mobile objects can be modeled as a tuplet <qid, R, U k, τ>, where qid is the id of the query point O k (a moving point in the database), R represent the size of the range of the query, U k denotes the uncertainty region associated with the query point, and τ stands for the qualifying threshold. An AMR returns a set of objects {T i, i[1,n] p i τ, i [1,n]}, (4) where p i is the qualifying probability of T i for satisfying the corresponding AMR. Let us consider the example illustrated in Fig. 1. The query object Q k is pinned to a moving point O k, O k {T 1,,T n }, which is bound by an uncertainty region U k. Due to the uncertainty of the query point O k reflected by the uncertainty region U k, the range of the query object Q k has to be expanded to compensate for the variation in the location of O k. The query region is extended by a value equal to half of the sizes of the sides of the rectangular uncertainty region, accordingly (see Fig. 1), which yields the query s new range, called uncertainty query range, R_new k. Note that this is different from the uncertainty region of the query point. Thus, the qualification probability of a target object T i of being in the answer set of query Q k has to be evaluated with respect to the new query range. III. S 1 O k AMR QUERY PROCESSING Uncertainty region of query point O k Uncertainty query range R_new k Figure 1. Determining the uncertainty region U k of query point O k; expanding the range of query Q k to compensate for the variance in the location of the query point O k. This section presents the AMR query evaluation technique in the context of the uncertainty model described in Section 2. The user poses an AMR query Q k to the server S 2 by specifying the id of the target object that is to be tracked. We refer to this object as the query point O k associated with Q k. Since the server has no records of the exact coordinates of O k, the query has to be pinned to the uncertainty region U k associated with O k. Thus, U k is used in the process of query evaluation. Similarly, since the server is aware only of the whereabouts of each target object in the monitored environment that has been detected by a sensor, it uses the objects uncertainty regions to decide their membership in the result set of a particular AMR query. This section consists of three subsections presenting different aspects of the query processing method. Section 3A describes the data structures stored on the central server. Section 3B presents the algorithm for object detection and finally, Section 3C describes the AMR query evaluation algorithm. A. Data Structures To support AMR queries, the database server maintains the following information: TargetObjects: This table contains the identities of all target objects in the monitored environment. It has the following schema: TargetObjects (tid, x 1, y 1, x 2, y 2 ), where tid represents the id of the target object, and (x 1, y 1 ) and (x 2, y 2 ) specify the coordinates of the upper left point and the lower right point of the uncertainty region of the target, respectively. SensorObjects: This table maintains the current locations of the sensors. That is, for each sid, we record its latest location. The table has the following schema: SensorObjects (sid, x, y, r), where sid denotes the sensor s identity in the database, the ordered pair (x, y) contains the coordinates of the sensor center point in the monitored terrain, and r denotes the side of the square range of the sensor. QueryObjects: This table maintains the identities of the target points, which act as query points. In addition, the table also contains the uncertainty ranges of each query. B. Object Detetection Due to the lack of location-detection capabilities in the target objects scattered throughout the monitored terrain, the server extrapolates their approximate locations by fusing location data received from the mobile sensors. If a target object T i is detected by only one sensor, the sensor region becomes the uncertainty region of the object, that is, U i = S j. However, if T i is detected by multiple objects, U i can shrink significantly and thus decrease the uncertainty associated with the target s location. When a user submits a query by specifying the identity of a target object in the monitored environment, this object becomes the query point O k. In addition to the query id, the user also specifies the query range and a threshold value, which is used for evaluating an objects membership in the result set of the query. When the server receives this request, it tries to locate the query point O k using object location

information reported by the sensors. If the object has been detected by at least one sensor, its uncertainty region U k is calculated. If the server finds that the object has not been detected by any sensor, it repeats this procedure in the next iteration of the process until either it finds at least one sensor which detected the object or the query expires. C. Query Evaluation The query evaluation technique is presented in Fig. 2. For each iteration, the server computes the new result for each of the currently active queries in QueryObjects as follows: 1) Step 1: The server performs a spatial join between TargetObjects and SensorObjects to determine the set of mobile sensors that detect each mobile object. That is, DetecSet contains all the moving objects, and for each object the list of sensor detecting it. 2) Step 2: The server processes each moving object T i (in DetectSet) with uncertainty area U i as follows: a) Step 3: If the object T i is in the overlap area of multiple sensors, its uncertainty area U i is the intersection of the corresponding sensing areas; otherwise, its uncertainty area is the entire sensing range of the sole sensor that detects T i. We note that every target object in DetectSet must have at least one detecting sensor. b) Step 4: If T i is a query object (i.e., it appears in QueryObjects), the server adds its uncertainty area U i to the UQueries set; otherwise, U i is added to the UTarget set. c) Step 5: The server scans UQueries and computes the uncertainty query range for each of the active queries, as illustrated in Fig. 1, to compensate for the uncertainty in the location of the query object. d) Step 6: The spatial join between UQueries and UTargets is performed to find targets whose uncertainty area overlaps with some uncertainty query range. If this overlap area is more than τ, the target is added to the result of the corresponding query. e) Step 7: The result of the above spatial join is the new results of the currently active AMR queries. These new results are transmitted to the user in Step 8. We note in Step 6 that if the uncertainty area U i of a moving object T i fully overlaps with the uncertainty query region R_new k, then T i is assumed to be in the result set of Q k with a qualification probability p i = 1. In case, U i overlaps with Q k only partially, then T i is in Q k only if p i U R _ new i k f i x, ydxdy. (5) Due to the dynamic nature of the mobile environment, maintaining spatial indexes is very expensive. Non-indexbased spatial join algorithms, such as Partition-based Spatial Merge [15] and Spatial Hash-Joins [13], can be used to find the intersections between targets and sensors or between the uncertainty regions of objects and an uncertainty query range. They are phased algorithms involving a partition phase followed by a merge phase; and each phase involves Algorithm AMRproc input: TargetObjects, SensorObjects, QueryObjects output: AMRresult set for each iteration of query processing 1: spatial join between TargetObjects and SensorObjects DetectSet = SPJ obj.loc( TargetObjects, SensorObjects) 2: iterate through DetectSet 3: if (T i S j,,t i S z) do U i = S i S z only sequential access to the data sets. We note that the complexity of this approach is proportional to the number of objects, instead of having logarithmic computational complexity as in index-based techniques. IV. SIMULATION STUDY In this section, we present simulation results that show the effectiveness of the proposed Approximate Moving Range query processing technique. A. Experimental Setup // determine uncertainty area else U i = S i 4: if ( T i.id is in QueryObjects) // if object is a query point UQueries(qid, U, R, R_new, τ) U i else UTargets (tid, U) U i 5: UQueries(qid, U, R, R_new, τ) calculate R_new 6: spatial join between UQueries and UTargets if ( x, ydxdy U R _ new i k 7: AMRresult Result of spatial join 8: return AMRresult f ) i Figure 2. AMR query processing technique To evaluate the Approximate Moving Range query model we propose in this work, we designed a simulator of a moving object environment, such that the objects (both the targets and the sensors) move in accordance with the Random Waypoint Model (RWP)[1]. Thus, each mobile object chooses a destination, proceeds to move to the destination, and finally pauses for a random amount of time. As mobile objects move into (and out of) the detection range of sensors, the sensors report the identities of sensed objects to the database server. Since the location and sensing ranges of all sensors are known to the database server, it calculates the uncertainty area for each mobile object every step of the simulation. We also assume the detected targets have an equal probability of being at any one spatial point within a sensor s range, or in other words, are uniformly distribution. We use the precision and recall metrics to demonstrate the performance of our model, measured against the ground truth, for various simulation scenarios. The precision provides an indication of the accuracy, or quality, of our result and recall indicates the portion of mobile objects that were correctly identified by the query. TP TP Precision Recall. (6) TP FP TP FN

TP: The number of objects correctly determined as belonging to the result set; FN: The number of objects, which were not included in the result set but should have been; FP: The number of objects, which are incorrectly determined as belonging to the result set. B. Simulation Results To validate the query model we present three sets of simulation results such that the focus falls on a single parameter or a combination of parameters used to configure our experimental setup: 1) Effect of Qualification Threshold: We vary the uncertainty threshold with the following percentage values: 65, 75, 85 and 95. That is, for a mobile object to be included in the query result with an uncertainty level of 65%, 65% of the uncertainty region of this object must overlap with the query uncertainty range. The graphs depicted in Fig. 3 show that the variance in the threshold parameter affects both precision and recall. More specifically, it affects the performance of the technique when the size of the sensor range is relatively large. This can be explained with the fact that as the size of the sensor range and the value of the qualification query grow in parallel, the probability that a sensor will overlap with a query region only partially, grows. When the size of a sensor range is larger, there is a higher probability that the overlap between an object s uncertainty area and a query region is not big enough to pass the threshold. 2) Effect of Query Range: The range, of the continuous query is varied in increments of 10 units: 10, 20, 30 and 40 meters. Based on the experimental results presented in Fig. 4 we can conclude that when the range of the query grows in parallel with the range of the sensors, the values of recall and precision improve. It is worth noting that the best performance of the technique is observed when the sensor range remains small while the size of the query range grows. This trend can be justified with the observation that whenever the sensors have smaller ranges, the target objects detected by them have smaller uncertainty regions. The smaller the sensor range, the smaller the location uncertainty of the target objects detected by the sensor. When several sensors with small ranges overlap, the uncertainty region of an object found in this overlap area is significantly smaller than in the case of sensors with larger ranges. However, this observation is valid only down to some lower bound on the sensor region size, after which the range of the sensor is too small to detect a significant number of target objects. Thus, many targets remain undetected and therefore the server has no knowledge of their whereabouts. 3) Effect of Coverage The simulation results for recall and precision under various values of percentage of area coverage are presented in Fig. 5, graphs a) and b), respectively. This coverage parameter indicates how well the mobile sensors cover the 1,000 1,000 simulated space. For example, if we have 50,000 mobile sensors, each with a sensing range of 2 2 spatial units, the coverage is computed as follows: 2 50, 000 2 20% 10001000 Our simulator was run with coverage parameter values of 25%, 50%, 75% and 100%. Based on the graphs in Fig. 5, we can deduce that the best results are again the ones based on a configuration that involves sensors with a smaller sensing range. The reason for this occurrence is that when the ranges of the sensors are small, the system would need more sensors to get a good coverage. The greater the number of sensors scattered throughout the monitored environment, the greater the chance for overlap of the ranges of multiple sensors. V. CONCLUSION In this paper, we introduced a new class of locationbased query called Approximate Moving Range (AMR) query, and presented a probabilistic technique for processing such queries. We consider a mobile sensors environment, in which each sensor is modeled as a moving rectangle representing its sensing range. Each sensor can detect the identities of location-unaware objects within its sensing range. The AMR query is pinned to a moving object with no location-detection capabilities. By fusing location information on moving objects detected by the individual mobile sensors, the database server can evaluate the AMR queries. To assess the effectiveness of the proposed query processing technique, we performed an extensive simulation study. The results show that the query processing technique is very effective and can generate reliable results. This technique is also highly cost effective and scalable. Since only the mobile sensors need to be equipped with location positioning and communication devices, the overall application cost is not dependent on the number of moving objects. 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