ENERGY-EFFICIENT ALGORITHMS FOR SENSOR NETWORKS

Transcription

1 ENERGY-EFFICIENT ALGORITHMS FOR SENSOR NETWORKS Prepared for: DARPA Prepared by: Krishnan Eswaran, Engineer Cornell University May 12, 2003 ENGRC 350 RESEARCH GROUP 2003 Krishnan Eswaran

2 Energy-Efficient Algorithms for Sensor Networks Krishnan Eswaran ii TABLE OF CONTENTS ABSTRACT... iii 1 INTRODUCTION METHODS RESULTS IDSQ Definition of Terms Sensor Selection The Algorithm Tracking Implementation DISCUS Asymmetric Approach Symmetric Approach CONCLUSIONS IDSQ Shortcomings DISCUS Shortcomings Addressing Issues LIST OF REFERENCES GLOSSARY.... G.1 LIST OF ILLUSTRATIONS Figure 1. Tracking Example with Sensor Networks Figure 2. Symmetric Coding Figure 3. IDSQ+DISCUS Comparison.... 6

3 Energy-Efficient Algorithms for Sensor Networks Krishnan Eswaran iii ABSTRACT This report presents two algorithms for sensor networks that save the energy used when sensors communicate. The first is Information Driven Sensor Querying (IDSQ). This technique uses a utility measure, such as the Mahalanobis distance or mutual information, to limit the number of sensors that need to communicate. The second technique is Distributed Source Coding Using Syndromes (DISCUS). This approach takes advantage of side information and redundancy among sensor readings to compress data, thereby reducing the number of bits sensors need to transmit. While these approaches save energy, by combining them into a single algorithm that uses IDSQ for tracking, and includes DISCUS as part of the communication system, we can save energy from both techniques.

4 Energy-Efficient Algorithms for Sensor Networks Krishnan Eswaran 1 1. INTRODUCTION Sensor networks inspire a lot of research, particularly in the areas of computer science, signal processing, and communications theory. The military already sees applications in the area of vehicle tracking, as demonstrated in figure 1. One of the major hurdles ad-hoc, wireless sensor networks face before they can be deployed, however, is that they need to use energy efficiently across the sensors. Sensor Tank Figure 1. Sensors can track vehicles by communicating their data from different locations, which interests the military. I will compare two algorithms that reduce energy usage in sensor networks. The first, called Information Driven Sensor Querying (IDSQ), was developed at the Palo Alto Research Center (PARC). This algorithm uses mutual information 1 as a utility measure, so a sensor only communicates with those sensors that will provide it with the most information. Since communication drains energy, by removing unnecessary communication, IDSQ saves energy [1]. The second algorithm, called Distributed Source Coding Using Syndromes (DISCUS), was developed by a professor at Berkeley and explored further at the University of Michigan. DISCUS is a compression technique that eliminates the energy wasted when sensors convey redundant data. Consider two sensors: A and B. When A receives information from B, entropy associated with A s data decreases. DISCUS takes advantage of the Slepian-Wolf coding theorem, which allows A to compress its data to the limit of the lower entropy even if it does not receive information from B [2], [3]. The effect is that sensors remove redundant data without having to communicate beforehand. When we compare IDSQ and DISCUS, certain questions arise. Are they feasible to implement? Do they minimize energy? Can they be combined? I explore these questions in the rest of this report. 2. METHODS My initial research in this area began while I was interning at PARC. I received most of the IDSQ papers there, and the rest of my papers came from engineering databases and the web. IEEE Xplore and Citeseer helped me retrieve papers cited by others and get background information on the topic. Professors who conduct research in sensor networks have web sites that list papers on this topic. This helped me find the DISCUS articles. The articles also cite books that I am using in my classes, so these became my final references. 1 Bold words indicate that the definition is in the glossary.

5 Energy-Efficient Algorithms for Sensor Networks Krishnan Eswaran 2 Although I found over twenty sources, only ten deal with the solutions I described in the introduction. Two of them are books that provide a theoretical framework for solving these problems [3], [4]. The papers base their arguments on the theories developed in these books. Of the eight papers, five explain the elements of IDSQ. Two of these papers describe approaches that the other three combine to develop the algorithm [5], [6], [1], [7], [8]. The final three papers outline the development of DISCUS. Two of these papers describe the general technique [2], [9], and the third puts the solution in the context of sensor networks [10]. The details in these papers form the bulk of my report. The main researchers that wrote these papers come from various institutions. While Feng Zhao, a researcher at PARC, led the development of IDSQ, Leonadis Guibas, a professor at Stanford, developed the theory for energy-efficient sensing used in its development [6]. DISCUS was principally developed at Berkeley by Professor Kannan Ramchandran and Sandeep Pradhan, his graduate student. Pradhan is now an assistant professor at the University of Michigan, where he is continuing research in this area. 3. RESULTS Through my research, I have discovered two algorithmic solutions that would save energy in places where sensor networks are vulnerable to wasting it. The first is IDSQ, which has already been used to track vehicles [7]. The second is DISCUS. While DISCUS has only been tested in simulation, it shows promise to reducing energy use in tracking applications. 3.1 Information Driven Sensor Querying (IDSQ) A trivial way to save energy in a sensor network would be to turn off all the sensors. Such an approach ignores our implicit goal: to use as little energy as possible when estimating the position of the vehicle we are tracking. If we keep only one sensor active, then we save as much energy as possible while still tracking our vehicle. This is the approach IDSQ takes, and we explain how it does so in the remainder of section Definition of Terms In IDSQ, we only have one sensor active. We call this sensor the leader node. The remaining sensors are follower nodes. The leader can use its measurement and measurements from follower nodes to determine the probability the vehicle is in a certain area. We express this probability formally as a conditional density in the following equation: p(x {z i } i U ) (1) where x = position of vehicle z i = measurement of sensor i U = set of sensors with measurements the leader knows.

6 Energy-Efficient Algorithms for Sensor Networks Krishnan Eswaran 3 We call equation (1) the belief state of the vehicle [8]. We can update the belief state to incorporate new measurements using a Kalman filter [4] Sensor Selection Our goal is to prioritize sensors that will provide us with the most useful measurements. To get these priorities, we use a utility function, and then update the belief state by going down a list of sensors ordered by this priority [6]. The leader stops requesting data from these sensors when it is satisfied with the quality of its belief state. The effect is that the leader calculates the belief state using only the sensors that provide the most utility. The right kind of utility measure would allow us to compute a belief state using the least number of sensor measurements possible. We call this utility measure the information utility, which includes information-theoretic measures, the Mahalanobis distance, and conditional expectation on posterior distributions. For more information, refer to [1]. The leader in an IDSQ system uses an information utility measure to determine which sensors to select to update its belief state. We now describe the algorithm used in such a system The Algorithm The algorithm, as described in [8], is as follows: 1. Initialization: The sensor network decides on a leader, and this leader receives sensor characteristics of the remaining sensors in the network, such as their positions. 2. Follower Nodes: If a node is not a leader, it remains idle until it receives a request from the leader to send it information. 3. Initial Sensor Reading: The leader calculates an initial belief state based on equation (1). For this calculation, the leader l knows only its own measurement, so we initialize the set U={l}. 4. Belief Quality Test: If the belief state passes some test of goodness, the leader finishes processing. 5. Sensor Selection: Based upon the belief state in equation (1) and the characteristics of other sensors, the leader selects a sensor j among the remaining sensors not in U that satisfies the criterion of an information utility measure. The leader then: requests sensor j s measurement. updates its belief state to include this measurement. adds sensor j to U, so that U = U {j} The algorithm goes back to step 3 and continues through the remaining steps. After we execute this algorithm, only the leader needs to be active since it contains all the relevant information about the vehicle s position Tracking Implementation Although our IDSQ algorithm outlines an approach to saving energy in sensor networks, a lot of the details in the algorithm are purposely left unspecified. In order to verify that we can track

7 Energy-Efficient Algorithms for Sensor Networks Krishnan Eswaran 4 vehicles using this model, we must implement the IDSQ algorithm into a tracking application. One such implementation already exists, and we describe its results in this section [7]. The IDSQ algorithm glosses over how to update the belief state, what utility measure to use, and how to test for goodness of a belief state. To update the belief state, we use a technique known as sequential Bayesian filtering [8]. The Kalman filter is a special case of sequential Bayesian filtering. To prioritize the measurements, we use mutual information as the utility measure. To track a moving vehicle, the leader should be close to sensors that contain useful data on the vehicle s position. The leader achieves this by making the sensor it selects in step 5 of the algorithm (outlined in section 3.1.3) the new leader [7]. This change, combined with our desire to track the vehicle indefinitely, eliminates the need for a belief quality test. Since the vehicle we track will undoubtedly move, changing the leader prevents the vehicle from moving out of the range of our tracking system. DARPA tested this implementation on an armored assault amphibious vehicle in Twenty-nine Palms, California. The system used acoustic amplitude sensors as well as direction of arrival (DOA) sensors to track the vehicle as it moved at a speed of about 15 miles per hour. Details about these results are in [7]. 3.2 Distributed Source Coding Using Syndromes (DISCUS) The more bits a sensor has to transmit, the more energy it uses. The best way to avoid this problem is to compress the data. We can compress these data with traditional source coding techniques, but the Slepian-Wolf Theorem tells us that sensors can compress their data as if they knew the data of other sensors [3]. Since sensor data is inherently distributed, we consider a distributed source coding approach that uses syndrome decoding to compress correlated data across different sensors [2]. We look at two approaches to DISCUS. The first is the asymmetric approach, which is conceptually straightforward. The second is the symmetric approach, which, while more complicated, is relevant to the type of communication that takes place in sensor networks Asymmetric Approach In channel coding, we use syndromes to locate and correct errors in data. Another way to look at syndromes is that they partition data into cosets, so that each coset contains symbols with the maximum number of differences from one another. We use this fact in the seemingly different case in which two sensors have correlated data such that there is exactly one bit that is different between the two. We call these sensors A and B. If sensor A wants to send its data to sensor B, it wastes data by sending all the bits. Instead, sensor A just sends the syndrome, which requires fewer bits. Sensor B then looks at all the vectors in the coset corresponding to this syndrome. Since the symbols in this coset are as different from one another as possible, only one of them will have a difference in exactly one bit from sensor B, and this is the value of the data in A. In the case of a Hamming-(7,4) code, we only transmit 3 bits instead of 7. This is the asymmetric DISCUS algorithm [2].

8 Energy-Efficient Algorithms for Sensor Networks Krishnan Eswaran 5 Since we might want to consider sending continuous valued data and use codes other than Hamming or repetition codes, we must also be able to construct cosets in these cases. Trellis codes provide a more sophisticated solution to this problem than Hamming-(7,4) codes. For further information, see [2] Symmetric Approach Although the asymmetric approach is conceptually simple, sensors in sensor networks communicate differently. The asymmetric framework assumes that one of the two sensors with correlated data will act as the decoder. This assumption does not hold in most tracking applications. Such applications typically have sensors with correlated data send data to a third sensor, as illustrated in figure 2. This is true of the IDSQ algorithm, in particular. We look at a solution to this problem, which extends the fundamental ideas of DISCUS to the symmetric case. In Figure 2 [10]. When two correlated sources are trying to send date to a third source, we consider a symmetric extension to the DISCUS approach. addition to source coding, we need to design channel subcodes for each encoder. The idea here is to partition a code that considers observations from both sensors into linearly independent subcodes. We then assign each subcode to an encoding sensor. Each encoder then sends the syndrome corresponding to its codeword to the decoding sensor. The decoder then looks at the most-likely codeword pair based on these syndromes [9]. Consider the trellis code based upon the Ungerboeck trellis. In this case, the rows of its generator matrix are linearly independent, and it contains exactly two rows. Using this fact, we can construct the following three-step algorithm [9]: 1. Determining Subcodes: We make each row a subcode, and assign each to one of our encoders. 2. Encoding: The encoders send the syndromes associated with their codewords to the decoder. 3. Decoding: The decoder takes the tensor product of the two syndromes, and uses the Viterbi algorithm to determine the most probable pair. This algorithm allows us to apply DISCUS in the symmetric case.

9 Energy-Efficient Algorithms for Sensor Networks Krishnan Eswaran 6 1 m 16 bits 16 bits (a) (b) 4 bits (c) (d) 4 bits Figure 3. Tracking system with distance between nodes all one meter: (a) This uses no energy-efficient algorithm, so we send a total of 192 bits. (b) In this IDSQ toy implementation, we send only 48 bits. (c) In this DISCUS implementation, we send only 48 bits. (d) In this combination IDSQ+DISCUS implementation, we send just 12 bits. 4. CONCLUSIONS Neither IDSQ nor DISCUS is optimal by itself. By examining their shortcomings, however, we determine ways to combine them to compensate for each other. To illustrate the effect of combining them, we rely on the toy example in figure 3. In the example, all sensors are in a grid format, and adjacent sensors are one meter apart. This setup causes the number of bits sent to correspond directly to the amount of energy required. With these restrictions, we see that a combined algorithm saves more energy than either IDSQ or DISCUS individually. These savings motivate the discussion in the remainder of section 4, in which we describe how to combine these algorithms. 4.1 IDSQ Shortcomings The IDSQ implementation outlined in [7] is a greedy algorithm, which limits its performance. The main problem occurs when IDSQ initially determines its belief state. Since we track moving

10 Energy-Efficient Algorithms for Sensor Networks Krishnan Eswaran 7 vehicles, if IDSQ relies on only one of its sensors at each iteration, it takes longer for it to get an accurate belief state. If IDSQ does not have an accurate belief state, it can select a new leader that is farther away from the vehicle. This selection could then cause IDSQ to lose track of the vehicle. A solution to this problem would be to develop routing applications on top of IDSQ, but such techniques would remove the energy savings that IDSQ introduces. 4.2 DISCUS Shortcomings The main shortcoming of DISCUS is that it is not designed to be a tracking application. All it does is provide a mechanism to conserve energy when such an application exists. 4.3 Addressing Issues To address the problems outlined in sections 4.2 and 4.3, we can combine the two algorithms. While this is not possible with the implementation described in [7], if we modify it to allow DISCUS to be part of the communication protocol, we can still develop an IDSQ tracker consistent with the algorithm in section When developing this hybrid tracker, we assume that all the sensors are of the same type, which would make the compression possible. In those cases in which different types of sensors exist, DISCUS will be difficult to implement. The main change we make to the implementation in [7] is to reintroduce the belief quality test. The test can simply be a time limit, which ensures the tracker selects a new leader before the vehicle moves out of range. This change will allow the leader to receive data from multiple sensors. These data can then be compressed using DISCUS. With more data, the leader will have a more accurate belief state when its selects a new leader, and because the data is compressed, the energy cost will be minimal. The effect is a more robust algorithm for the same energy cost. REFERENCES [1] F. Zhao, J. Shin, and J. Reich, Information-Driven Dynamic Sensor Collaboration for Tracking Applications, IEEE Signal Processing Magazine, vol. 19, no. 2, pp , March, [2] S. Pradhan and K. Ramchandran, Distributed Source Coding Using Syndromes (DISCUS): Design and Construction, Proceedings of IEEE Data Compression Conference (Snowbird, Utah, March 29-31, 1999, pp ). [3] T.M. Cover and J.A. Thomas, Elements of Information Theory. New York: Wiley, [4] H.V. Poor, Introduction to Signal Detection and Estimation. New York: Springer, [5] L. Guibas, Sensing, Tracking, and Reasoning with Relations, IEEE Signal Processing Magazine, vol. 19, no. 2, pp , March, 2002.

11 Energy-Efficient Algorithms for Sensor Networks Krishnan Eswaran 8 [6] J. Byers and G. Nasser, Utility-Based Decision Making in Wireless Sensor Networks, Proceedings of IEEE MobiHOC 2000 (Boston, MA, August 11, 2000, pp ). [7] J. Liu, J. Reich and F. Zhao, Collaborative In-Network Processing for Target Tracking, Journal on Applied Signal Processing, to appear, [8] M. Chu, H. Haussecker, and F. Zhao, Scalable Information-Driven Sensor Querying and Routing for ad hoc Heterogeneous Sensor Networks, International Journal of High- Performance Computing Applications, vol. 16, no. 3, pp , [9] S. Pradhan and K. Ramchandran, Distributed source coding: Symmetric rates and applications to sensor networks, Proceedings of IEEE Data Compression Conference (Snowbird, Utah, March 28-30, 2000, pp ). [10] S. Pradhan, J. Kusuma, and K. Ramchandran. Distributed Compression in a Dense Microsensor Network, IEEE Signal Processing Magazine, vol. 19, no. 2, pp , March, 2002.

12 Energy-Efficient Algorithms for Sensor Networks Krishnan Eswaran G.1 GLOSSARY Channel Coding Adding redundancy to data in a consistent manner in order to find and correct errors if the data is altered. Coset A set of data with the same syndrome. For instance, the coset corresponding to a syndrome of zero is the set of codewords. Greedy Algorithm This class of algorithms select items that are optimal in the short term. Unfortunately, they do not always lead to the optimal answer in the long term. Mutual information For any two random variables U and V, we define mutual information with the following equation: I(U;V) = p(u,v)log[p(u,v)/(p(u)p(v))]dudv (G.1) where p(u,v) = joint probability density function of U and V p(u) = marginal probability density of U p(v) = marginal probability density of V Source Coding Eliminating redundancy from data in a consistent manner (i.e. compression). Syndrome The syndrome tells us the bits that need to be flipped to turn our received data back into a codeword. For linear codes, we get the syndrome by multiplying our received vector by a parity check matrix. The following equation summarizes the approach: s = Hx (G.2) where H = parity check matrix x = received codeword, represented as a column vector s = syndrome of the parity check matrix If the received vector is one of our codewords, the syndrome will be a vector of zeros. Otherwise, the syndrome will indicate the location of errors from the closest codeword.