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# Introduction to Global Navigation Satellite Systems ASEN 5090

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This 2 page Class Notes was uploaded by Laila Windler on Friday October 30, 2015. The Class Notes belongs to ASEN 5090 at University of Colorado at Boulder taught by Kristine Larson in Fall. Since its upload, it has received 33 views. For similar materials see /class/232166/asen-5090-university-of-colorado-at-boulder in Aerospace Engineering at University of Colorado at Boulder.

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Date Created: 10/30/15

ASEN 5090 Introduction to GNSS ASEN 5090 NOTES on POSITIONING ERRORS Introduction A variety of error measures are used in positioning deriving from different positioning requirements People are generally most familiar with error measures for a scalar random variable In navigation and positioning two dimensional distributions are of interest for horizontal positioning Three dimensional errors are also important although very often the vertical direction has very different performance requirements and is specified separately 1 D For a scalar measurements x we have the following 7 1 n The mean value over n measurements is x i 2 x1 EIxi l 739 il The deviation ofa measurement from the mean is 6x x1 J 2 The standard deviation is defined as 3 The variance is oz The root mean square value is 4 For a scalar random variable or measurement with a Normal Gaussian distribution the probability of being within 10 of the mean is 683 2 D For a two dimensional measurement say x1 and y we have 7 l n 7 l n The mean value over n measurements is x 7 2 x1 y 7 Z yl 5 7 7 171 171 The deviation ofa measurement from the mean is 5x x1 J 11 yl 7 6 I n I 2 5x152 7x 2 n 1 The covariance matrix is P 11 7 n 2 5 51 371 2 n 1 y ASEN 5090 Introduction to GNSS The covariance matrix defines the error ellipse The eigenvalues of P are the squares of the semimajor and semiminor axes of the ellipse 512 and 022 and the eigenvectors show the orientation of the error ellipse DRMS Distance Root Mean Square 2D DRMS 012 022 12 Radial Error Mean Square Position Error or RSS 8 Probability of being inside DRMS circle For 01 02 probability 63 For 01 1002 probability 68 ZDRMS Two definitions 2 X DRMS Probability between 954 and 98 US Federal Radionavigation Plan definition 2D RMS Same as DRMS 6368 NATO39s Standardization Agreement CEP Circular Error Probable is the radius of a circle inside which 50 of the points fall How 0 you compute this From the data find the median radius How does it compare to 01 and 02 For a normal distribution For 01 02 CEP 118 0 Approximate CEP 05901 02 i 3 for 02 3 lt 01 lt 3 02 9 95 circle is CEP X 208 2 X DRMS 99 circle is CEP X 258 3D Error ellipsoid Based on covariance matrix same as 2D Probability of being inside the 10 ellipsoid is 20 MRSE Mean Radial Spherical Error MRSE 012 022 032 12 Probability of being inside MRSE sphere 61 SEP Spherical Error Probable is the radius of sphere inside which 50 of the points fall Approximate SEP 059 01 02 03 References 1 Aerospace Avionics Systems A Modern Synthesis G M Siouris Appendix A 1993 ASEN5190ErrorNotesdoc 090801

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