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Issue No.12 - December (2011 vol.10)
pp: 1769-1784
Yasamin Mostofi , University of New Mexico, Albuquerque
ABSTRACT
In this paper, we consider a mobile cooperative network that is tasked with building a map of the spatial variations of a parameter of interest, such as an obstacle map or an aerial map. We propose a new framework that allows the nodes to build a map of the parameter of interest with a small number of measurements. By using the recent results in the area of compressive sensing, we show how the nodes can exploit the sparse representation of the parameter of interest in the transform domain in order to build a map with minimal sensing. The proposed work allows the nodes to efficiently map the areas that are not sensed directly. We consider three main areas essential to the cooperative operation of a mobile network: building a map of the spatial variations of a field of interest such as aerial mapping, mapping of the obstacles based on only wireless measurements, and mapping of the communication signal strength. For the case of obstacle mapping, we show how our framework enables a novel noninvasive mapping approach (without direct sensing), by using wireless channel measurements. Overall, our results demonstrate the potentials of this framework.
INDEX TERMS
Mobile networks, compressive sensing, cooperative spatial mapping, mapping of obstacles, mapping of communication signal strength.
CITATION
Yasamin Mostofi, "Compressive Cooperative Sensing and Mapping in Mobile Networks", IEEE Transactions on Mobile Computing, vol.10, no. 12, pp. 1769-1784, December 2011, doi:10.1109/TMC.2011.31
REFERENCES
[1] Y. Mostofi and P. Sen, “Compressive Cooperative Mapping in Mobile Networks,” Proc. 28th Am. Control Conf. (ACC '09), pp. 3397-3404, June 2009.
[2] Y. Mostofi and P. Sen, “Compressed Mapping of Communication Signal Strength,” Proc. IEEE Military Comm. Conf. (MILCOM '08), 2008.
[3] H. Gonzalez-Banos and J.C. Latombe, “Navigation Strategies for Exploring Indoor Environments,” The Int'l J. Robotics Research, vol. 21, nos. 10/11, pp. 829-848, 2002.
[4] N.E. Leonard, D.A. Paley, F. Lekien, R. Sepulchre, D.M. Fratantoni, and R.E. Davis, “Collective Motion, Sensor Networks, and Ocean Sampling,” Proc. IEEE, vol. 95, no. 1, pp. 48-74, Jan. 2007.
[5] I.I. Hussein, “Motion Planning for Multi-Spacecraft Interferometric Imaging Systems,” PhD thesis, Univ. of Michigan, 2005.
[6] F. Dellaert, F. Alegre, and E.B. Martinson, “Intrinsic Localization and Mapping with 2 Applications: Diffusion Mapping and Macro Polo Localization,” Proc. IEEE Int'l Conf. Robotics and Automation, vol. 2, pp. 2344-2349, 2003.
[7] R. Sim, G. Dudek, and N. Roy, “A Closed Form Solution to the Single Degree of Freedom Simultaneous Localisation and Map Building (SLAM) Problem,” Proc. IEEE Conf. Decision and Control, vol. 1, pp. 191-196, 2000.
[8] P. Krauthausen, F. Dellaert, and A. Kipp, “Exploiting Locality by Nested Dissection for Square Root Smoothing and Mapping,” Proc. Robotics: Science and Systems (RSS '06), 2006.
[9] R. Sim, G. Dudek, and N. Roy, “Online Control Policy Optimization for Minimizing Map Uncertainty during Exploration,” Proc. IEEE Int'l Conf. Robotics and Automation, vol. 2, pp. 1758-1763, 2004.
[10] R. Gartshore, A. Aguado, and C. Galambos, “Incremental Map Building Using an Occupancy Grid for an Autonomous Monocular Robot,” Proc. Seventh Int'l Conf. Control, Automation, Robotics and Vision, vol. 2, pp. 613-618, Dec. 2002.
[11] R. Pito, “A Solution to the Next Best View Problem for Automated Surface Acquisition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 10, pp. 1016-1030, Oct. 1999.
[12] J.J. Kuffner and S.M. LaValle, “RRT-Connect: An Efficient Approach to Single-Query Path Planning,” Proc. IEEE Int'l Conf. Robotics and Automation, pp. 995-1001, Apr. 2000.
[13] A. Ganguli, J. Cortes, and F. Bullo, “Maximizing Visibility in Nonconvex Polygons: Nonsmooth Analysis and Gradient Algorithm Design,” Proc. Am. Control Conf., pp. 792-797, June 2005.
[14] R. Grabowski, P. Khosla, and H. Choset, “Autonomous Exploration via Regions of Interest,” Proc. IEEE/RSJ Int'l Conf. Intelligent Robots and Systems (IROS '03), pp. 1691-1696, Oct. 2003.
[15] S. Martínez, “Distributed Interpolation Schemes for Field Estimation by Mobile Sensor Networks,” IEEE Trans. Control Systems Technology, vol. 18, no. 2, pp. 491-500, Mar. 2009.
[16] J. Choi, J. Lee, and S. Oh, “Swarm Intelligence for Achieving the Global Maximum Using Spatio-Temporal Gaussian Processes,” Proc. Am. Control Conf., pp. 135-140, June 2008.
[17] E. Fiorelli, N.E. Leonard, P. Bhatta, D. Paley, R. Bachmayer, and D.M. Fratantoni, “Multi-AUV Control and Adaptive Sampling in Monterey Bay,” Proc. IEEE/OES Autonomous Underwater Vehicles (AUV '04), pp. 134-147, June 2004.
[18] E. Candès, J. Romberg, and T. Tao, “Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information,” IEEE Trans. Information Theory, vol. 52, no. 2, pp. 489-509, Feb. 2006.
[19] D.L. Donoho, “Compressed Sensing,” IEEE Trans. Information Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
[20] C.E. Shannon, “Communication in the Presence of Noise,” Proc. Inst. of Radio Engineers, vol. 37, no. 1, pp. 10-21, Jan. 1949.
[21] M.C. Wicks, “RF Tomography with Application to Ground Penetrating Radar,” Proc. Asilomar Conf. Signals, Systems and Computers, pp. 2017-2022, Nov. 2007.
[22] A.M. Haimovich, R.S. Blum, and L.J. Cimini, “Mimo Radar with Widely Separated Antennas,” IEEE Signal Processing Magazine, vol. 25, no. 1, pp. 116-129, Jan. 2008.
[23] J. Wilson and N. Patwari, “Radio Tomographic Imaging with Wireless Networks,” IEEE Trans. Mobile Computing, vol. 9, no. 5, pp. 621-632, May 2010.
[24] M. Kanso and M. Rabbat, “Compressed RF Tomography for Wireless Sensor Networks: Centralized and Decentralized Approaches,” Proc. IEEE Int'l Conf. Distributed Computing in Sensor Systems, June 2009.
[25] J. Tropp and A. Gilbert, “Signal Recovery from Random Measurements via Orthogonal Matching Pursuit,” IEEE Trans. Information Theory, vol. 53, no. 12, pp. 4655-4666, Dec. 2007.
[26] US Geological Survey, http:/www.usgs.gov, 2011.
[27] F. Santosa and W.W. Symes, “Linear Inversion of Band-Limited Reflection Seismograms,” SIAM J. Scientific and Statistical Computing, vol. 7, no. 4, pp. 1307-1330, 1986.
[28] R. Gribonval and M. Nielsen, “Sparse Representations in Unions of Bases,” IEEE Trans. Information Theory, vol. 49, no. 12, pp. 3320-3325, Dec. 2003.
[29] E.J. Candès, “The Restricted Isometry Property and Its Implications for Compressed Sensing,” Compte Rendus de l'Academie des Sciences, vol. 346, pp. 589-592, 2008.
[30] E.J. Candès and T. Tao, “Decoding by Linear Programming,” IEEE Trans. Information Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005.
[31] E.J. Candès, M. Rudelson, T. Tao, and R. Vershynin, “Error Correction via Linear Programming,” Proc. IEEE 46th Ann. Symp. Foundations of Computer Science (FOCS '05), pp. 668-681, Oct. 2005.
[32] D. Needell and R. Vershynin, “Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit,” Foundations of Computational Math., vol. 9, no. 3, pp. 317-334, 2007.
[33] E.J. Candès, J. Romberg, and T. Tao, “Stable Signal Recovery from Incomplete and Inaccurate Measurements,” Comm. Pure and Applied Math, vol. 59, no. 8, pp. 1207-1223, 2005.
[34] “Compressive Sensing Resources,” http://www.dsp.ece.rice. educs, 2011.
[35] M. Rudelson and R. Vershynin, “Sparse Reconstruction by Convex Relaxation: Fourier and Gaussian Measurements,” Proc. 40th Ann. Conf. Information Sciences and Systems, pp. 207-212, Mar. 2006.
[36] Handbook of the Geometry of Banach Spaces, W.B. Johnson and J. Lindenstrauss, eds., vols. 1/2. Elsevier Science Ltd., 2001.
[37] S.J. Szarek, “Condition Numbers of Random Matrices,” J. Complexity, vol. 7, no. 2, pp. 131-149, 1991.
[38] A.E. Litvak, A. Pajor, M. Rudelson, and N. Tomczak-Jaegermann, “Smallest Singular Value of Random Matrices and Geometry of Random Polytopes,” Advances in Math., vol. 195, no. 2, pp. 491-523, 2005.
[39] M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, “Single-Pixel Imaging via Compressive Sampling,” IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 83-91, Mar. 2008.
[40] M. Lustig, D. Donoho, and J.M. Pauly, “Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging,” Magnetic Resonance in Medicine, vol. 58, no. 6, pp. 1182-1195, Dec. 2007.
[41] M. Sheikh, O. Milenkovic, and R. Baraniuk, “Designing Compressive Sensing DNA Microarrays,” Proc. IEEE Second Int'l Workshop Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP '07), Dec. 2007.
[42] P. Sen and S. Darabi, “Compressive Dual Photography,” Eurographics, vol. 28, pp. 609-618, 2009.
[43] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge Univ., 2004.
[44] S.J. Wright, R.D. Nowak, and M.A.T. Figueiredo, “Sparse Reconstruction by Separable Approximation,” Proc. IEEE Int'l Conf. Acoustics, Speech and Signal Processing, pp. 3373-3376, Apr. 2008.
[45] M.A.T. Figueiredo, R.D. Nowak, and S.J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Selected Topics in Signal Processing, vol. 1, no. 4, pp. 586-597, Dec. 2007.
[46] Y. Nesterov, “Gradient Methods for Minimizing Composite Objective Function,” discussion paper, Center for Operations Research and Econometrics (CORE), 2007.
[47] P. Patel and J. Holtzman, “Analysis of a Simple Successive Interference Cancellation Scheme in a DS/CDMA System,” IEEE J. Selected Areas in Comm., vol. 12, no. 5, pp. 796-807, June 1994.
[48] Y. Mostofi and S.A. Mujtaba, “Asynchronous Code Acquisition and Channel Estimation for Uplink DS-CDMA Systems,” technical report, Lucent Tech nologies, Sept. 1999.
[49] R. Berinde, A.C. Gilbert, P. Indyk, H. Karloff, and M.J. Strauss, “Combining Geometry and Combinatorics: A Unified Approach to Sparse Signal Recovery,” Proc. 46th Ann. Allerton Conf. Comm., Control, and Computing, pp. 798-805, Sept. 2008.
[50] P. Sen and S. Darabi, “Compressive Rendering: A Rendering Application of Compressed Sensing,” IEEE Trans. Visualization and Computer Graphics, vol. 17 no. 4, pp. 487-499, April 2011.
[51] A.C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging. IEEE, 1988.
[52] R. Ketcham, Computed Tomography for Paleontology and Geology. Cambridge Univ., 2004.
[53] R. Ng, “Fourier Slice Photography,” Proc. ACM SIGGRAPH, pp. 735-744, 2005.
[54] A. Goldsmith, Wireless Communications. Cambridge Univ., 2005.
[55] W.C. Jakes, Microwave Mobile Communications. Wiley-IEEE, 1994.
[56] Y. Mostofi, A. Gonzales-Ruiz, A. Ghaffarkhah, and D. Li, “Characterization and Modeling of Wireless Channels for Networked Robotic and Control Systems—A Comprehensive Overview,” Proc. IEEE/RSJ Int'l Conf. Intelligent Robots and Systems (IROS '09), pp. 4849-4854, Oct. 2009.
[57] “$\ell_1$ Magic Toolbox,” http://www.acm.caltech.edul1magic, 2011.
[58] Y. Mostofi, “Compressive Cooperative Obstacle/Object Mapping and See-Through Capabilities in Robotic Networks,” in preparation for submission, 2011.
[59] Y. Mostofi and A. Gonzalez-Ruiz, “Compressive Cooperative Obstacle Mapping in Mobile Networks,” Proc. IEEE MILCOM, pp. 524-530, Nov. 2010.
[60] W.M. Smith, “Urban Propagation Modeling for Wireless Systems,” PhD thesis, Stanford Univ., 2004.
[61] Y. Mostofi, M. Malmirchegini, and A. Ghaffarkhah, “Estimation of Communication Signal Strength in Robotic Networks,” Proc. IEEE Int'l Conf. Robotics and Automation (ICRA '10), pp. 1946-1951, May 2010.
[62] M. Malmirchegini and Y. Mostofi, ”On the Spatial Predictability of Communication Channels,“ IEEE Trans. Wireless Comm., to appear, 2011.
[63] M. Malmirchegini and Y. Mostofi, “An Integrated Sparsity and Model-Based Probabilistic Framework for Estimating the Spatial Variations of Communication Channels,” Physical Comm., Special Issue on Compressive Sensing in Communications, to appear, 2011.
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