Differential Forms for Target Tracking and Aggregate Queries in Distributed Networks

Abstract

Consider mobile targets in a plane and their movements being monitored by a network such as a field of sensors. We develop distributed algorithms for in-network tracking and range queries for aggregated data (for example returning the number of targets within any user given region). Our scheme stores the target detection information locally in the network, and answers a query by examining the perimeter of the given range. The cost of updating data about mobile targets is proportional to the target displacement. The key insight is to maintain in the sensor network a function with respect to the target detection data on the graph edges that is a differential form such that the integral of this form along any closed curve C gives the integral within the region bounded by C. The differential form has great flexibility making it appropriate for tracking mobile targets. The basic range query can be used to find a nearby target or any given identifiable target with cost O(d) where d is the distance to the target in question. Dynamic insertion, deletion, coverage holes and mobility of sensor nodes can be handled with only local operations, making the scheme suitable for a highly dynamic network. It is extremely robust and capable of tolerating errors in sensing and target localization. Targets do not need to be identified for the tracking, thus user privacy can be preserved. In this article, we only elaborate the advantages of differential forms in tracking of mobile targets. Similar routines can be applied for organizing many other types of informations, for example streaming scalar sensor data (such as temperature data field), to support efficient range queries. We demonstrate through analysis and simulations that this scheme compares favorably with existing schemes that use location services for answering aggregate range queries of target detection data.

A Distributed Energy-Efficient Algorithm for Cellular Target Tracking in Wireless Sensor Networks

“…To assess the efficiency of the proposed algorithm, it has been compared with three well-known algorithms, VigilNet [17], Forms [18], and iTOA (improved Time Of Arrival measurement model) [19]. VigilNet algorithm has been chosen for the similar concepts used in this paper, its high speed in tracking operations, and specifications of the sensors.…”

Optimal nearest neighbor queries in sensor networks

“…1b). However, in contrast to [30], we do not need to know the directionality of the object movement. A delete event goes upward in HS following in reverse the object path pointing to the original location of the object.…”

“…Recently, Sarkar and Gao [30] studied differential forms for target tracking and range queries for aggregate data. Their technique allows to find a nearby target in question at distance d with cost at most O(d).…”

“…Set spcl_parent(p k (v i )).spcl_pointer = ⊥ to its special child p k (v i ); 30 Change delete message type from erase to relay; 31 If delete message is of type relay then Forward the delete message to p k+1 (v i ); 32 k ← k + 1; 33 delete_downward_fragment(x, y): 34 Set y.pointer = ⊥ for x; 35 If y.degree = 0 then delete_downward_fragment( y, y ) for y which has y .pointer = y;…”

Efficient Sleep Scheduling Algorithm for Target Tracking in Double-Storage Energy Harvesting Sensor Networks

“…As mentioned previously, sleep scheduling is an efficient way to save energy. In the tracking procedure, sleep scheduling means that only the sensors which are near to the target keep awake [31], while other sensors which are far away from the target stay in the sleep mode. In [32], a sleep strategy was proposed that each node autonomously determines the sleeping time.…”