Aggregation in sensor networks: an energy–accuracy trade-off
Introduction
The technological advances in embedded computers, sensors, and radios have led to the emergence of wireless ad hoc sensor networks (WASNs) as a new class of system with uses in diverse and useful applications. Indeed, the early papers in the area [1], [2], [3], [4] talk about the vision of cheap self-organizing ad hoc networks that are able to perform a higher level sensing task through the collaboration of a large number of cheaper and resource constrained wireless sensor nodes. Leveraging numerous sensing devices placed close to the actual physical phenomena, the information that such networks can provide is more accurate and richer than the information provided by a system of few, expensive, state-of-the-art sensing devices. Since WASNs operate largely unattended, often in environments where the access cost of deploying or maintaining nodes is high, a key problem in designing WASNs is how to prolong their useful lifetime by conserving energy. Consequently, a large fraction of research in WASNs has been dedicated to aspects of the energy-efficiency problem.
The original vision and promise of WASNs was that multiple nodes collectively perform the sensing task requested by the users and communicate the results to the users. However, most of the research so far has simply viewed WASNs as just another kind of wireless ad hoc networks, albeit one composed of nodes that are more energy-constrained and whose data sources are sensors. So, for example, much work has focused on issues such as energy-efficient MAC and ad hoc routing protocols to realize the needed point-to-point and point-to-multipoint communication patterns in WASNs. But, little has been done to develop an understanding of a WASN as a collective or an aggregate where sensor nodes collaborate to jointly estimate the desired answer about the sensed environment. In part this is because not many actual applications useful to the end-user have been studied. The only notable exception is the target-tracking problem, which has drawn attention from several research groups. Otherwise, the applications that have been examined are usually “toy” scenarios used to showcase the abilities of protocols and programming frameworks (e.g., [5]), or very specific applications examined for the sake of some energy-saving technique (e.g., [6]).
In this research we have made a first attempt at exploring and understanding the performance of a WASN as a collective that performs a sensing task. We examine a general class of WASN applications that we call aggregation applications where the desired answer depends on the sensed value at multiple nodes. In particular, we explore the energy vs. accuracy subspace, i.e. how much energy savings can one get by relaxing some accuracy requirements and vice versa. We propose an algorithm that exploits this trade-off and jointly considers networking and signal processing issues to create a distributed estimation mechanism.
Many of the examples and simple applications presented in WASN research are based around some kind of aggregation function. The most popular and simple examples of aggregation functions are “maximum” and “average”. That is, a user may be interested in knowing the max (or average) of a value in the WASN or in some restricted area of the WASN. If this function needs to be performed once, we refer to it as “snapshot aggregation”. If the user needs an update in periodic intervals we refer to it as “periodic aggregation”.
The snapshot aggregation problem is trivial for a single static user. The user sends a request to flood the sensor network (or the area of interest). Upon reception of a request message a node sets the sender of the message as its parent, leading towards the user. This way an aggregation tree is formed with the user node at its root. Data are flowing along the aggregation tree towards the user while being aggregated at intermediate nodes. For instance, in the max function a node receiving multiple values (i.e., its own local reading and values sent by other nodes) finds their maximum and sends it to its parent. For more details on snapshot aggregation the reader can refer to [7], [8].
More generally, in aggregation applications, the user seeks a condensed view of the physical environment the WASN is monitoring, or a condensed view of the network’s state. To achieve this, the values from all the nodes (i.e., sensor readings or node state values) are aggregated to a size-bounded vector describing this condensed view. Furthermore, several important properties hold for the aggregation process: (i) multiple local values can be combined to an aggregated description with a single pass, (ii) multiple aggregated descriptions and multiple local values can be combined to an aggregated description with a single pass. These properties permit the aggregation process to be done easily within the network, without the need for multiple passes of the data. A counter-example is the calculation of median, as it requires two passes of the data. The bound on the aggregated description (i.e., vector) is O(1). In order to include more specific cases of applications (like some referenced in related work) the bound can be relaxed to O(N), where N is the number of nodes in the network.
Some examples more advanced than “max” and “average” include: (i) approximate contours of nodes’ residual energy (similar to the specific case studied in [9]), (ii) approximate the boundary line between sensing and no-sensing (e.g. of light) with a straight line or a parabola (similar to the specific case studied in [6]). Whatever the aggregation function is, the basic structure of in-network processing in snapshot aggregation remains the same, combining values and descriptions at intermediate nodes until the final aggregated description reaches the user. This kind of in-network processing is similar to traditional distributed/parallel computing where precise information is handled and the correct execution of the algorithm often depends on the right number and order of messages exchanged. We call such processing type-I.
If periodic aggregation is needed then one could run snapshot aggregations periodically, executing accurate type-I algorithms periodically. This indeed is the conventional approach.
In WASNs though, unlike traditional distributed computing systems, there is a strong coupling to the physical world as we are monitoring some parameters of a physical process. The WASN by its nature can only sample this physical process, which in turn implies that we are only getting an approximation of the parameters sought. Once this point is understood, it is realized that the algorithms in WASNs have an inherent extra dimension: accuracy. We can exploit this extra dimension to produce more energy-efficient algorithms. The less accuracy is required, the more energy can be saved using proper algorithmic techniques. For example, in our particular case, the spatial–temporal correlation of sensor node’s values is leveraged to create estimates of the aggregated descriptions of the environment. The less accurate the estimates need to be, the fewer messages need to be exchanged. We argue that approximation and estimation are an inherent part of WASN algorithms and should be taken into account while designing algorithms for WASN. We call such type of in-network processing type-II. Type-II algorithms are essentially distributed estimation algorithms.
Essential to our development of such distributed estimation algorithms is the joint consideration, or co-design, of the signal processing algorithms and networking protocols that have thus far been treated separately in WASNs. In this paper, we propose a distributed estimation algorithm that explores the energy/accuracy subspace for the periodic aggregation domain.
We have validated our approach through simulation using the “max” aggregation function as an example. The “min” aggregation function is completely symmetrical. Note that the “max” aggregation function can be on any property of the actual local measurements. For instance, if we are interested in the maximum rate of change among local measurements, the aggregation function will be done on the derivatives of the local measurements. We are currently working to extend our algorithm to the more general kth max case. In its current form, the algorithm cannot be applied to summary aggregation functions [10] like “average”, “count” etc.
In Section 2 we examine related work. In Section 3 we introduce some initial approaches to the problem. In Section 4 we describe our distributed estimation algorithm. Section 5 presents simulation results. Finally, Section 6 concludes the paper.
Section snippets
Related work
Aggregation applications have been popular among researchers in WASN. This is mainly because the concept of aggregation is simple enough to be executed at each node with minimal effort. The main problem is how to orchestrate the whole procedure to save energy. Efforts such as [11], [12] seek to provide a framework for flexible aggregation in sensor networks. They investigate constructs to program the sensor network to perform arbitrary aggregation functions. However, all the prior work has been
Initial approaches
Since distributed estimation for aggregation applications is not a well-researched area, it is beneficial to start by describing some of the intuitive approaches to the problem. The different approaches are individually useful under certain circumstances but they cannot be applied universally. For each approach we will identify some of its major weak points. Through this process the reader can get a deeper insight into the problem and appreciate its difficulty in the general case. We will be
Distributed estimation algorithm
In this section, we propose a distributed estimation algorithm that can be applied to a large class of aggregation problems. More specifically we classify aggregation functions into two categories: (i) aggregation functions whose result is determined by the values of a few nodes (e.g., the max result is based on one node), and (ii) aggregation functions whose result is determined by the values of all the nodes (e.g., the average function). We have found that different kinds of distributed
Simulation results
In this section we present the simulation platform, a general model to describe diverse physical processes, and finally measurements on several aspects of the energy and accuracy quantities.
Conclusions
In this paper we study a large class of applications in WASNs, namely aggregation applications. We propose a distributed estimation algorithm that can be applied to a subclass of periodic aggregation problems. Our algorithm exploits the energy–accuracy trade-off in WASNs to provide the user with a larger solution space than the conventional approach of periodically running snapshot aggregations. We validate our algorithm through simulation, achieving promising results.
Acknowledgements
This paper is based in part on research funded through Office of Naval Research’s AINS program, and DARPA’s PAC/C program. The views expressed in this paper are those of the author’s, and do not necessarily represent those of the above funding agencies.
Athanassios Boulis is a Ph.D. student in the Electrical Engineering department at UCLA. He received his M.S. degree from the same department in 1999, and his B.S. degree from the Technical University of Crete, Greece, in 1997. His current research interests focus on distributed estimation algorithms for wireless ad hoc sensor networks, as well as the design of platforms to dynamically deploy such algorithms into the sensor network.
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Athanassios Boulis is a Ph.D. student in the Electrical Engineering department at UCLA. He received his M.S. degree from the same department in 1999, and his B.S. degree from the Technical University of Crete, Greece, in 1997. His current research interests focus on distributed estimation algorithms for wireless ad hoc sensor networks, as well as the design of platforms to dynamically deploy such algorithms into the sensor network.
Saurabh Ganeriwal received the degree of B.Tech and M.Tech in Electrical Engineering from Indian Institute of Technology, Bombay in 2001. Since 2001, he has been pursuing M.S. in Electrical Engineering at the University of California, Los Angeles. His research interests are in wireless communications and networking. Currently his research focus is on wireless ad hoc sensor networks. He has received UCLA fellowship in 2001 and 2002.
Mani B. Srivastava (Ph.D. Berkeley 1992) is an Associate Professor of Electrical Engineering department at UCLA. Previously, he was at Bell Laboratories Research at Murray Hill, NJ from 1992 through 1996. At UCLA his research group Networked and Embedded Systems Laboratory (http://nesl.ee.ucla.edu) conducts research on various aspects of power-aware and wireless distributed embedded computing systems. He has published over 80 papers, received five US patents, and was awarded the Okawa Foundation grant (1998), the NSF CAREER award (1997), and the President of India’s Gold Medal (1985).