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Optoelectronics & Communications
Taskdriven data compression improves efficiency of sensor networks
Mark Fowler
Small amounts of initial data can determine tradeoffs between the accuracies of estimates made by sensor networks, enabling the remaining data to be optimally compressed.
14 February 2007, SPIE Newsroom. DOI: 10.1117/2.1200610.0441
Recent advances in communication technology have sparked increased interest in the use of sensor networks. Devices in such networks use shared data to make estimations. However, this must be accomplished under constraints on energy, accuracy, and latency. Data compression is a natural tool for achieving tradeoffs between these constraints. As such, developing compression algorithms tailored for the tasks that sensor networks must perform is an important issue in this field of research.
Since the late 1980s there has been extensive development of compression methods for estimation using remote sensors.^{1} Nearly all of these techniques focus on optimizing scalar quantizers against a measure of data quality for a single estimation task (this measure is called Fisher information). But these past methods are limited in two significant ways. First, scalar quantizers cannot exploit the sampletosample signal structure in estimation problems. Additionally, these approaches do not consider tradeoffs between multiple estimation tasks.
We have developed a method that quantizes transform coefficients—for example, wavelet packet coefficients—to maximize the trace of the Fisher information matrix, which is used to characterize multiple estimation tasks.^{2–4} The trace is a viable scalarvalued distortion function for this matrix.^{2}
We compress a block of data x collected at a sensor so that it can be transmitted using no more than a budgeted R bits, while making an estimate with the lowest possible estimation error. Our approach (see Figure 1 for a diagram of the process and the related Fisher information) is to transform the original data into coefficients, only some of which are selected and quantized. The resulting coefficients have Fisher information that is less than that of the original data, while maintaining the lowest estimation error. A subscript on the Fisher information distinguishes between two estimation tasks to be performed.
Figure 1. A block of data x collected at a sensor is compressed into a size of no more than R bits. The data is transformed into coefficients {χ = χ _{n}n = 1,2, …,N}, some of which are selected—Ω is the selected set of indices—and quantized, resulting in = { _{n}nεΩ}. These coefficients have Fisher information that is less than the original data J( ).
We have applied this approach to the problem of locating a radio frequency emitter using aircraftmounted sensors.^{2–4} Each sensor pair makes two estimates from their intercepted signals: the time difference of arrival (TDOA) and the frequency difference of arrival (FDOA). The impact of compression results in fundamental tradeoffs between TDOA accuracy and FDOA accuracy. Scalar quantizer approaches cannot handle this issue, but our method can achieve such tradeoffs.^{3}Figure 2 compares our technique's performance to that achieved without compression, as well as to a scheme that optimizes our transform with respect to the classical meansquared error distortion measure.
Figure 2. Our method achieves a tradeoff between timedifferenceofarrival and frequencydifferenceofarrival accuracies. The tradeoff for compression ratio 3:1, and SNR _{1} = 15dB and SNR _{2} = 15dB, is shown compared with that achieved without compression and with a version of our transform optimized with respect to the meansquared distortion measure. Symbol denotes the operational point closest to that without compression.
Unfortunately, the proper tradeoff point depends on the sensoremitter geometry, which is unknown: as we have discussed, the task at hand is to locate the emitter. To address this issue, we have developed a method called geometryadaptive data compression^{3} that sends a small amount of initial data used to estimate the proper tradeoff, then sends the remaining data compressed accordingly. The resulting improvement in emitter location accuracy is shown in Figure 3, where the accuracy is measured in circular error probable.
Figure 3. Simulation results show a 5× improvement in location accuracy using geometryadaptive data compression relative to the use of the meansquared error distortion metric. Accuracy is measured in circular error probable (CEP).
Data compression plays an important role in enabling efficient cooperation among sensors. We have developed methods that are tailored specifically to the problem of performing compression to support multiple estimation tasks. By formulating the problem as a transform coding compression scheme, we are able to outperform classical compression methods. We also achieve multiestimation tradeoffs that are not possible using the scalar quantization schemes widely studied for application in sensor networks. We are currently exploring better computational methods for evaluating the Fisher information matrix elements,^{5} as well as ways to exploit these ideas for other sensor network functions, such as selecting subsets of sensors that should participate in a given estimation task.^{6}
This work was supported in part by the Air Force Office of Scientific Research through grant number FA95500610249 and through the Air Force Summer Faculty Fellowship Program.
Authors
Mark Fowler
Electrical and Computer Engineering, Binghamton University
Binghamton, NY
Mark Fowler is an associate professor at Binghamton University (State University of New York) in the Department of Electrical and Computer Engineering, and the director of the Emitter Location Research Group. His research interests are in data compression, estimation theory, and emitter location. Since 2000, he has been a member of the program committee for SPIE's conference on Mathematics and Applications of Data/Image Coding, Compression, and Encryption.


