WSN06-2: Sensor Localization from WLS Optimization with Closed-form Gradient and Hessian

A non-parametric, low-complexity algorithm for accurate and simultaneous localization of multiple sensors from scarce and imperfect ranging information is proposed. The technique is based on a weighted least-squares (WLS) optimization, where the gradient and Hessian of the quadratic objective are given in closed-form. The performance of the proposed technique is studied through extensive computer simulations, with the intra-node distances randomly generated in accordance to a statistical model constructed from the results of a measurement campaign conducted with a pair of impulsive ultra-wideband (UWB) radios in an indoor scenario. The simulation results reveal that the proposed algorithm, despite its low complexity, is nearly as accurate as the known alternative of best performance, which is based on semi-definite programming and demands significantly more computational power.

[1]  Antoine Souloumiac,et al.  Jacobi Angles for Simultaneous Diagonalization , 1996, SIAM J. Matrix Anal. Appl..

[2]  Thore Graepel,et al.  Kernel Matrix Completion by Semidefinite Programming , 2002, ICANN.

[3]  Charles R. Johnson,et al.  The Euclidian Distance Matrix Completion Problem , 1995, SIAM J. Matrix Anal. Appl..

[4]  Koen Langendoen,et al.  Distributed localization in wireless sensor networks: a quantitative compariso , 2003, Comput. Networks.

[5]  G. Golub,et al.  Inverse Eigenvalue Problems: Theory, Algorithms, and Applications , 2005 .

[6]  Giuseppe Thadeu Freitas de Abreu,et al.  Localization from Imperfect and Incomplete Ranging , 2006, 2006 IEEE 17th International Symposium on Personal, Indoor and Mobile Radio Communications.

[7]  Henry Wolkowicz,et al.  Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming , 1999, Comput. Optim. Appl..

[8]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[9]  Marcos Raydan,et al.  Molecular conformations from distance matrices , 1993, J. Comput. Chem..

[10]  Alfred O. Hero,et al.  Achieving high-accuracy distributed localization in sensor networks , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[11]  Trevor F. Cox,et al.  Multidimensional Scaling, Second Edition , 2000 .

[12]  Petros Drineas,et al.  Distance Matrix Reconstruction from Incomplete Distance Information for Sensor Network Localization , 2006, 2006 3rd Annual IEEE Communications Society on Sensor and Ad Hoc Communications and Networks.

[13]  Kenneth H. Rosen.  Handbook of Discrete and Combinatorial Mathematics , 1999 .

[14]  Wheeler Ruml,et al.  Improved MDS-based localization , 2004, IEEE INFOCOM 2004.