Covariance Analysis of a vector tracking GPS receiver based on MMSE multiuser Detection

Document Type: Research Paper


1 Department of Electrical Engineering and Information Technology,Iranian Research Organization for Science and Technology,Tehran,Iran.

2 Elaectrical and information technology department,IROST (Iranian Research Organization for Science and Technology), Tehran, Iran

3 Faculty of Electrical and Computer Engineering, Tarbiat Modares University

4 Department of Electrical and Computer Engineering, Iranian Research Organization for Science and Technology (IROST)


In high dynamic conditions, using vector tracking loops instead of scalar tracking loops in GPS receivers is proved as an efficient method to compensate the performance. The Minimum Mean Squared Error detector as a multiuser detector is applied in the vector tracking loop for more reliability and efficiency. The Kalman filter does the two tasks of tracking and extracting the navigation data after applying the multiuser detection on the correlator outputs. The covariance analysis is performed to study the effect of applying a multiuser detector along with a vector tracking loop against the conventional one. The covariance analysis is performed and the variance in the pseudorange-rate estimates produced by the two architectures of conventional vector tracking and the one with multiuser detector are used as the performance criteria. The steady state, state covariance of the Kalman filter of vector tracking loop is calculated. Comparing the psuedorange rate variances obtained from covariance analysis of each method shows improved performance of the new joint receiver of vector and multiuser detector.


[1]     M. Lashley, D. M. Bevly and J. Y. Hung, “Performance Analysis of Vector Tracking Algorithms for Weak GPS Signals in High Dynamics,” IEEE Journal of Selected Topics in Signal Processing, vol. 3, no. 4, pp. 661-673 August 2009.

[2]     W.J. Hurd, J.I. Statman, and V.A. Vilnrotter,  “High dynamic GPS receiver using maximum likelihood estimation and frequency tracking,” IEEE Trans. Aerospace and Electronic Systems, vol. 23, no. 4, pp. 425-437, July 1987.

[3]     W. Li, S. Liu, C. Zhou, S. Zhou, and T. Wang, “High Dynamic Carrier Tracking Using Kalman Filter Aided Phase Lock Loop,” International Conference on Wireless Communications, Networking and Mobile Computing, WiCom 2007.

[4]     K.-H. Kim, G.-I. Jee and J.-H. Song, “Carrier Tracking Loop using the Adaptive Two-Stage,” International Journal of Control, Automation, and Systems, vol. 6, no. 6, pp. 948-953, December 2008.

[5]     P. A. Roncagliolo, J. G. Garc´ıa, and C. H. Muravchik, “Optimized Carrier Tracking Loop Design for Real-Time High-Dynamics GNSS Receivers,” International Journal of Navigation and Observation, vol. 2012, 18 pages, 2012.

[6]     A. Soloviev, S. Gunawardena, and F. Van Graas, “Mitigation of GPS Cross-Correlation Errors using Semi-Codeless Tracking,” IEEE Trans. Aerospace and Electronic Systems, vol. 48, no. 1, pp. 502-513, January 2012.

[7]     A. Sreenivas, M.N.V. Pavan Kumar, “An Adaptive Technique for the Mitigation of GPS Cross-Correlation,” International Journal of Engineering Research and Technology. vol. 2. no. 2 , pp. 1-8, April 2013.

[8]     H. CHEN, W. JIA, and M. YAO, “Cross-Correlation-Function-Based Multipath Mitigation Method for Sine-BOC Signals,” Radioengineering, vol. 21, no. 2, p. 659-665, June 2012.

[9]     T. Shojaeezand, G. R. Mohammad-Khani, and P. Azmi, “Variance Analysis of the New Method of Applying Multiuser Detection in a GPS Receiver in High Dynamic Conditions,” Wireless Personal Communication, vol. 98, no. 2, pp. 2107-2119, Jan 2018.   

[10]  S. Zhao, M. Lu, and Z. Feng, “Implementation and Performance Assessment of a Vector Tracking Method Based on a Software GPS Receiver,”  Journal of Navigation, vol. 64no. S1, pp. S151-S161, November 2011.

[11]  M. Lashley, D. M. Bevly, and J. Y. Hung, “A valid comparison of vector and scalar tracking loops,” IEEE/ION Position, Location and Navigation Symposium, Indian Wells, CA, pp. 464-474, 2010.

[12]  G.L. Stuber, “MMSE Linear Multiuser Detection for a DS-CDMA System,”  ECE6604, Personal and Mobile Communications, Spring 2000.

[13]  M. Lashley, “Modeling and Performance Analysis of GPS Vector Tracking Algorithms,” Ph.D. dissertation, Dept. Elect. Eng., Auburn University, Alabama, December 18, 2009.

[14]  J. B. Bullock, M. Foss, G. J. Geier, and M. King, “Integration of GPS with other sensors and network assistance,” Understanding GPS: Principles and Applications, 2nd edition, E. D. Kaplan and C. J. Hegarty, (eds.), Mobile Communication Series, chapter 9, pages 459–558. Artech House Publishers, 2006.

[15]  T. Lacey, “Tutorial: The Kalman Filter,” Computer Vision,

[16]  N. A. Othman and H. Ahmad, “The Analysis of Covariance Matrix for Kalman Filter based SLAM with Intermittent Measurement,” Proceedings of the 2013 International Conference on Systems, Control and Informatics, Pahang, Malaysia, 2013, pp. 227-231.

[17]  R. N. Crane, “A Simplified Method for Deep Coupling of GPS and Inertial Data,” Proceedings of the 2007 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2007, pp. 311-319.

[18]  V. B. S. Srilatha Indira Dutt, G. Sasi Bhushana Rao, S. Rani, S. Ravindra Babu, R. Goswami and Ch. Usha Kumari, “Investigation of GDOP for Precise user Position Computation with all Satellites in view and Optimum four Satellite Configurations,” Journal of Indian Geophysics Union, vol.13, no.3, pp.139-148,  July 2009.