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PAPERBACK list:$45.00 Web:$40.50 add to cart PDF BOOK your price: $34.50 add to cart Rights & Permissions Free Resources PDF EXECUTIVE SUMMARY Display this book on your site! Related Titles The Navy's Needs in Space for Providing Future Capabilities The Global Positioning System for the Geosciences: Summary and Proceedings of a Workshop on Improving the GPS Reference Station Infrastructure for Earth, Oceanic, and Atmospheric Science Applications Other Related Titles The Global Positioning System: A Shared National Asset (1995) Commission on Engineering and Technical Systems (CETS) Web Search Builder Use this book's key terms to search within this book, across our collection, or across the Web. Skim This Chapter Skim this chapter and use this chapter's key terms to search within this book. Reference Finder Paste in your own text to find books that relate to your topic. Page 177   E-mail  Facebook  Digg  Stumble  Twitter More The following HTML text is provided to enhance online readability. Many aspects of typography translate only awkwardly to HTML. Please use the page image as the authoritative form to ensure accuracy. Appendix D Accuracy Definitions And Mathematical Relationships Expressions of accuracy stated in this report, unless otherwise noted, are designated as 2 drms.1 When referring to horizontal positioning, 2 drms is defined as where σN2 and σE2, are the variances of the north and east position estimates respectively. The quantity is generally considered to be the uncertainty in the estimation of the two-dimensional (horizontal) position and is called the distance root mean square positional error. Under the simplifying assumption that σN2 = σE2 and that the errors are independent and normally distributed, the probability that the positional errors are less than 2 drms is 98 percent. In other words, 98 percent of the time in repeated determinations of the horizontal position, the errors will be less than the 2 drms value. In actuality, the percentage of horizontal positions contained within the 2 drms value varies between approximately 95.5 percent and 98.2 percent, depending on the degree of ellipticity of the error distribution. Circular Error Probable (CEP) is another common measure of horizontal positioning error. CEP is defined to be CEP = 0.589 (σN + σE). The probability of the actual horizontal position lying inside (or outside) a circle with radius CEP is 50 percent. If it is assumed that positioning errors have a circular normal distribution, then the values of CEP and 2 drms are related as follows: 2 drms = 2.4 CEP. Similarly the Spherical Error Probable (SEP) is defined to be SEP = 0.513 (σN + σE + σh). The probability of the actual position in space lying inside (or outside) a sphere of radius SEP is 50 percent (σh is the square root of the variance in the height). There are other expressions that are commonly used to quantify the uncertainty associated with determination of position. Three such quantities are PDOP, VDOP, and 1   Ronald Braff and Curtis Shively, "GPS Integrity Channel," in vol. III of Global Positioning System - Papers Published in Navigation (Washington, D.C.: The Institute of Navigation, 1986), pp. 258-274. Page 177 Front Matter (R1-R20) Executive Summary (1-12) 1 Introduction (13-18) 2 GPS Applications and Requirements (19-66) 3 Performance Improvements to the Existing GPS Configuration (67-122) 4 Technical Enhancements for Future Consideration (123-134) Appendix A: Study Participants (135-138) Appendix B: Abbreviated Committee Biographies (139-144) Appendix C: Overview of the Global Positioning System . . . (145-176) Appendix D: Accuracy Definitions and Mathematical Relationships (177-178) Appendix E: Report From Mr. Michael Dyment, Booz, Allen & Hamilton (179-200) Appendix F: Report From Dr. Young Lee, The MITRE Corporation (201-212) Appendix G: Increased Bandwidth Performance Analysis (213-214) Appendix H: Signal Structure Options (215-220) Appendix I: Report from Mr. Melvin Barmat, Jansky/Barmat... (221-248) Appendix J: Selective Denial of Civilian GPS Signals by the Military (249-252) Appendix K: Direct Y-Code Acquisition (253-254) Appendix L: Enhanced Signal Structures for the Military (255-262) Appendix M: Accuracy of a 14-Satellite Ensemble Versu a 24-Satellite Ensemble (263-264)

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OCR for page 177
--> Appendix D Accuracy Definitions And Mathematical Relationships Expressions of accuracy stated in this report, unless otherwise noted, are designated as 2 drms.1 When referring to horizontal positioning, 2 drms is defined as where σN2 and σE2, are the variances of the north and east position estimates respectively. The quantity is generally considered to be the uncertainty in the estimation of the two-dimensional (horizontal) position and is called the distance root mean square positional error. Under the simplifying assumption that σN2 = σE2 and that the errors are independent and normally distributed, the probability that the positional errors are less than 2 drms is 98 percent. In other words, 98 percent of the time in repeated determinations of the horizontal position, the errors will be less than the 2 drms value. In actuality, the percentage of horizontal positions contained within the 2 drms value varies between approximately 95.5 percent and 98.2 percent, depending on the degree of ellipticity of the error distribution. Circular Error Probable (CEP) is another common measure of horizontal positioning error. CEP is defined to be CEP = 0.589 (σN + σE). The probability of the actual horizontal position lying inside (or outside) a circle with radius CEP is 50 percent. If it is assumed that positioning errors have a circular normal distribution, then the values of CEP and 2 drms are related as follows: 2 drms = 2.4 CEP. Similarly the Spherical Error Probable (SEP) is defined to be SEP = 0.513 (σN + σE + σh). The probability of the actual position in space lying inside (or outside) a sphere of radius SEP is 50 percent (σh is the square root of the variance in the height). There are other expressions that are commonly used to quantify the uncertainty associated with determination of position. Three such quantities are PDOP, VDOP, and 1   Ronald Braff and Curtis Shively, "GPS Integrity Channel," in vol. III of Global Positioning System - Papers Published in Navigation (Washington, D.C.: The Institute of Navigation, 1986), pp. 258-274.

OCR for page 178
--> HDOP (Position, Vertical, and Horizontal Dilution of Precision, respectively). Mathematically where σr2 is the variance of a single (pseudorange) observation. Here the level of significance associated with the recovery of position is tied to the uncertainty of the measurements used. This is a function of geometry between the receiver and the tracked satellites.

Representative terms from entire chapter:

lying inside