Stochastic Characterization of a MEMs based Inertial Navigation Sensor using Interval Methods

摘要

The aim here remains to introduce effectiveness of interval methods in analyzing dynamic uncertainties for marine navigational sensors. The present work has been carried out with an integrated sensor suite consisting of a low cost MEMs inertial sensor, GPS receiver of moderate accuracy, Doppler velocity profiler and a magnetic fluxgate compass. Error bounds for all the sensors have been translated into guaranteed intervals. GPS based position intervals are fed into a forward-backward propagation method in order to estimate interval valued inertial data. Dynamic noise margins are finally computed from comparisons between the estimated and measured inertial quantities It has been found that the intervals as estimated by proposed approach are supersets of 95% confidence levels of dynamic errors of accelerations. This indicates a significant drift of dynamic error in accelerations which may not be clearly defined using stationary error bounds. On the other side bounds of non-stationary error for rate gyroscope are found to be in consistence with the intervals as predicted using stationary noise coefficients. The guaranteed intervals estimated by the proposed forward backward contractor, are close to 95% confidence levels of stationary errors computed over the sampling period. Reference [1]Priyanka Aggarwal, Zainab Syed, Aboelmagd Noureldin, Naser El-Sheimy, "MEMS-Based Integrated Navigation", Artech House, 2010, MA, pp. 35-61. [2]Sameh Nassar, PhD Thesis, "Improving the Inertial Navigation System (INS) Error Model for INS and INS/DGPS Applications", University of Calgari, Canada, 2003, URL: http://www.geomatics.ucalgary.ca/links/GradTheses.html. [3]Aboelmagd Noureldin, Tashfeen B. Karamat, Mark D. Eberts, and Ahmed El-Shafie, Performance Enhancement of MEMS-Based INS/GPS Integration for Low-Cost Navigation Applications, IEEE Transactions On Vehicular Technology, Vol. 58, No. 3, March 2009. [4]M. Hayes, "Statistical Digital Signal Processing and Modeling", Hoboken, NJ: Wiley, 1996. [5]L. Jackson, "Digital Filters and Signal Processing", Norwell, MA: Kluwer, 1975. [6]J. Burg, "Maximum entropy spectral analysis," Ph.D. dissertation, Dept. Geophys., Stanford Univ., Stanford, CA, 1975. [7]D. W. Allan, "Statistics of atomic frequency standards," In Procs. Of IEEE, vol. 54, no. 2, pp. 221–230, Feb. 1966 [8]Haiying Hou, MS Thesis, "Modeling Inertial Sensors Errors Using Allan Variance", University of Calgary, 2004. [9]Minha Park, MS Thesis, "Error Analysis and Stochastic Modeling of MEMS based Inertial Sensors for Land Vehicle Navigation Applications", University of Calgary, 2004. [10]Naser El-Sheimy, Haiying Hou, and Xiaoji Niu, "Analysis and Modeling of Inertial Sensors Using Allan Variance", IEEE Transactions on Instrumentation And Measurement, Vol. 57, No. 1, January 2008. [11]M. M. Tehrani, "Ring laser gyro data analysis with cluster sampling technique," In Procs. Of SPIE, Vol. 412, 1983, pp. 207–220. [12]Denne, W., "Magnetic Compass Deviation and Correction", 3rd Ed. Brown, Son, and Ferguson, 1998, 165 pp. [13]P.L.N. Raju, "Fundamentals of GPS, Satellite Remote Sensing and GIS Applications in Agricultural Meteorology", pp. 121-150. [14]Richard B. Langley, "Dilution of Precision", GPS World, May 1999. [15]Novatel, Technical Report, "GPS Position Accuracy Measures", APN-029 Rev 1, December, 2003. [16]Luc Jaulin, Michel Kieffer, Olivier Didrit and Eric Walter, "Applied Interval Analysis", Springer-Verlag, London, 2001, pp. 77-81. [17]D. Waltz, "Generating semantic descriptions from drawings of scenes with shadows," in The Psychol. Comput. Vision, New York, 1975, pp. 19–91. [18]Andrew Lammas, Karl Sammut and Fangpo He, "6-DoF Navigation Systems for Autonomous Underwater Vehicles", DOI: 10.5772/8978, Chapter 23 of Book, "Mobile Robots Navigation", Ed. By Alejandra Barrera, 2010.