Scalable low-complexity GPS and DGPS positioning using approximate QR decomposition

In this paper we discuss the efficient implementation of GPS and DGPS positioning using COordinate Rotation DIgital Computer (CORDIC)-based approximate rotations for solving the required Least Squares (LS) problems. By changing the number of optimal CORDIC angles (approximation accuracy), different accuracies of the positioning results can be obtained. In particular, we show that coarse approximations are sufficient for obtaining the required positioning accuracies. Experimental results are obtained using Rinex files from high-end GPS receivers and raw GPS data from low-end GPS receivers. The accuracy of the positioning results is compared for varying numbers of iterations and varying approximation accuracies. The presented positioning methods with scalable accuracies allow cost- and power-efficient software/hardware implementations for both GPS and DGPS positioning, while the required accuracies of different Location Based Services (LBS) are obtained.

[1]  Jochen Schiller,et al.  Location Based Services , 2004 .

[2]  Guoping Zhang,et al.  Parallel FFT with CORDIC for ultra wide band , 2004, 2004 IEEE 15th International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE Cat. No.04TH8754).

[3]  Jay A. Farrell,et al.  Differential GPS reference station algorithm-design and analysis , 2000, IEEE Trans. Control. Syst. Technol..

[4]  Mamoun F. Abdel-Hafez,et al.  The Autocovariance Least-Squares Technique for GPS Measurement Noise Estimation , 2010, IEEE Transactions on Vehicular Technology.

[5]  Don Torrieri,et al.  Statistical Theory of Passive Location Systems , 1984, IEEE Transactions on Aerospace and Electronic Systems.

[6]  Tomás Lang,et al.  Redundant and On-Line CORDIC: Application to Matrix Triangularization and SVD , 1990, IEEE Trans. Computers.

[7]  B. Friedlander.  A passive localization algorithm and its accuracy analysis , 1987 .

[8]  Werner Gurtner,et al.  RINEX - The Receiver Independent Exchange Format - Version 3.00 , 2007 .

[9]  Rainer Martin,et al.  Approximate iterative Least Squares algorithms for GPS positioning , 2010, The 10th IEEE International Symposium on Signal Processing and Information Technology.

[10]  Goran M. Djuknic,et al.  Geolocation and Assisted GPS , 2001, Computer.

[11]  Ed F. Deprettere,et al.  Floating point Cordic , 1993, Proceedings of IEEE 11th Symposium on Computer Arithmetic.

[12]  Søren Holdt Jensen,et al.  A Software-Defined GPS and Galileo Receiver , 2007 .

[13]  Malcolm David Macnaughtan,et al.  Positioning GSM telephones , 1998, IEEE Commun. Mag..

[14]  P.K. Enge,et al.  Differential operation of the Global Positioning System , 1988, IEEE Communications Magazine.

[15]  Rudolph van der Merwe,et al.  The square-root unscented Kalman filter for state and parameter-estimation , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[16]  Henry Tirri,et al.  A Statistical Modeling Approach to Location Estimation , 2002, IEEE Trans. Mob. Comput..

[17]  Jean-Michel Muller.  The CORDIC Algorithm , 1997 .

[18]  Christopher J. Zarowski,et al.  An Introduction to Numerical Analysis for Electrical and Computer Engineers: Zarowski/Intro to Numerical Analysis , 2004 .

[19]  Jürgen Götze,et al.  Error Analysis of CORDIC-Based Jacobi Algorithms , 1995, IEEE Trans. Computers.

[20]  Jean-Michel Muller,et al.  The CORDIC Algorithm: New Results for Fast VLSI Implementation , 1993, IEEE Trans. Computers.

[21]  Yilin Zhao,et al.  Standardization of mobile phone positioning for 3G systems , 2002, IEEE Commun. Mag..

[22]  Jürgen Götze,et al.  An Efficient Jacobi-like Algorithm for Parallel Eigenvalue Computation , 1993, IEEE Trans. Computers.

[23]  Julius O. Smith,et al.  Closed-form least-squares source location estimation from range-difference measurements , 1987, IEEE Trans. Acoust. Speech Signal Process..

[24]  Jean-Marc Delosme,et al.  CORDIC Algorithms: Theory And Extensions , 1989, Optics & Photonics.

[25]  Yuheng He,et al.  Learning Geographic Regions using Location Based Services in Next Generation Networks , 2009, 2009 International Conference on Machine Learning and Applications.

[26]  Alvin M. Despain,et al.  Fourier Transform Computers Using CORDIC Iterations , 1974, IEEE Transactions on Computers.

[27]  J. Gotze.  Parallel methods for iterative matrix decompositions , 1991, 1991., IEEE International Sympoisum on Circuits and Systems.

[28]  Xiao-Wen Chang,et al.  An Orthogonal Transformation Algorithm for GPS Positioning , 2003, SIAM J. Sci. Comput..

[29]  Graham W. Pulford,et al.  Analysis of a Nonlinear Least Squares Procedure Used in Global Positioning Systems , 2010, IEEE Transactions on Signal Processing.

[30]  Jose A. Apolinario,et al.  QRD-RLS adaptive filtering , 2009 .

[31]  K. Dickson,et al.  QRD and SVD processor design based on an approximate rotations algorithm , 2004, IEEE Workshop onSignal Processing Systems, 2004. SIPS 2004..

[32]  Konstantinos N. Plataniotis,et al.  Kernel-Based Positioning in Wireless Local Area Networks , 2007, IEEE Transactions on Mobile Computing.

[33]  K. C. Ho,et al.  A simple and efficient estimator for hyperbolic location , 1994, IEEE Trans. Signal Process..

[34]  B. Lakshmi,et al.  Parallel CORDIC-like architecture: For fast rotation implementation , 2011, TENCON 2011 - 2011 IEEE Region 10 Conference.

[35]  D. ErcegovacM.,et al.  Redundant and On-Line CORDIC , 1990 .

[36]  A. Fenwick,et al.  Algorithms for position fixing using pulse arrival times , 1999 .

[37]  Daniel N. Aloi,et al.  Comparative Performance Analysis of a Kalman Filter and a Modified Double Exponential Filter for GPS-Only Position Estimation of Automotive Platforms in an Urban-Canyon Environment , 2007, IEEE Transactions on Vehicular Technology.

[38]  Zoran A. Salcic,et al.  A Comparison of Accuracy Using a GPS and a Low-Cost DGPS , 2006, IEEE Transactions on Instrumentation and Measurement.

[39]  Mohinder S. Grewal,et al.  Global Positioning Systems, Inertial Navigation, and Integration , 2000 .

[40]  M. Kovacic,et al.  Bringing location based services to IP multimedia subsystem , 2006, MELECON 2006 - 2006 IEEE Mediterranean Electrotechnical Conference.

[41]  Ian Sharp,et al.  Enhanced Least-Squares Positioning Algorithm for Indoor Positioning , 2013, IEEE Transactions on Mobile Computing.

[42]  Juergen Goetze,et al.  Iterative version of the QRD for adaptive RLS filtering , 1994 .

[43]  Amit Acharyya,et al.  Coordinate Rotation Based Low Complexity N-D FastICA Algorithm and Architecture , 2011, IEEE Transactions on Signal Processing.

[44]  D. Ludwig,et al.  Galileo: Benefits for Location Based Services , 2003 .

[45]  Kamran Etemad,et al.  Location services in WiMax networks , 2009, IEEE Communications Magazine.