Time-delay estimation for TOA-based localization of multiple sensors

In many applications using multiple sensors, knowledge of the relative positions of the sensors is required. The locations of the sensors can be obtained from measured time-of-arrivals (TOAs) of events generated by sources. Although several TOA-based localization techniques exist, practical TOA measurements are incomplete because they include an unknown internal delay; the time taken from the signal reaching the sensor to that it is registered as received by the capturing device. In order to localize the sensors properly, these internal delays need to be estimated accurately. In this paper we propose a method for estimating the internal delays by using a data fitting technique based on structured total least squares. Under reasonable assumptions we show that the algorithm is guaranteed to converge to the optimal solution and ultimately achieves a quadratic rate of convergence. Experimental results show that the execution time is less than 1% of the execution time of existing methods while attaining an even higher accuracy.

[1]  Alessio Del Bue,et al.  A closed form solution to the microphone position self-calibration problem , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[2]  Rong Peng,et al.  Angle of Arrival Localization for Wireless Sensor Networks , 2006, 2006 3rd Annual IEEE Communications Society on Sensor and Ad Hoc Communications and Networks.

[3]  C. Eckart,et al.  The approximation of one matrix by another of lower rank , 1936 .

[4]  Richard Heusdens,et al.  Auto-localization in ad-hoc microphone arrays , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[5]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[6]  Marc Moonen,et al.  Evaluation of signal enhancement algorithms for hearing instruments , 2008, 2008 16th European Signal Processing Conference.

[7]  Minghua Chen,et al.  Energy-Based Position Estimation of Microphones and Speakers for Ad Hoc Microphone Arrays , 2007, 2007 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics.

[8]  Peter Brida,et al.  A new Complex Angle of Arrival location method for ad hoc networks , 2010, 2010 7th Workshop on Positioning, Navigation and Communication.

[9]  K. J. Ray Liu,et al.  Handbook on Array Processing and Sensor Networks , 2010 .

[10]  Philip E. Gill,et al.  Practical optimization , 1981 .

[11]  Ivan Himawan,et al.  Microphone Array Shape Calibration in Diffuse Noise Fields , 2008, IEEE Transactions on Audio, Speech, and Language Processing.

[12]  Yiu-Tong Chan,et al.  Exact and approximate maximum likelihood localization algorithms , 2006, IEEE Trans. Veh. Technol..

[13]  J. Ben Rosen,et al.  Total Least Norm Formulation and Solution for Structured Problems , 1996, SIAM J. Matrix Anal. Appl..

[14]  Stanley T. Birchfield,et al.  Microphone array position calibration by basis-point classical multidimensional scaling , 2005, IEEE Transactions on Speech and Audio Processing.

[15]  W. Torgerson Multidimensional scaling: I. Theory and method , 1952 .

[16]  J. B. Rosen,et al.  Low Rank Approximation of a Hankel Matrix by Structured Total Least Norm , 1999 .

[17]  Yubin Kuang,et al.  Time delay estimation for TDOA self-calibration using truncated nuclear norm regularization , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[18]  Alessio Del Bue,et al.  A Bilinear Approach to the Position Self-Calibration of Multiple Sensors , 2012, IEEE Transactions on Signal Processing.

[19]  Zicheng Liu,et al.  Energy-Based Sound Source Localization and Gain Normalization for Ad Hoc Microphone Arrays , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[20]  Sabine Van Huffel,et al.  Formulation and solution of structured total least norm problems for parameter estimation , 1996, IEEE Trans. Signal Process..

[21]  Regina Kaune,et al.  Accuracy studies for TDOA and TOA localization , 2012, 2012 15th International Conference on Information Fusion.

[22]  Sebastian Thrun,et al.  Affine Structure From Sound , 2005, NIPS.

[23]  Joshua N. Ash,et al.  Self‐Localization of Sensor Networks , 2010 .

[24]  Michael S. Brandstein,et al.  Microphone Arrays - Signal Processing Techniques and Applications , 2001, Microphone Arrays.

[25]  Gene H. Golub,et al.  An analysis of the total least squares problem , 1980, Milestones in Matrix Computation.