Earth-Referenced Aircraft Navigation and Surveillance Analysis

This document addresses a basic function of aircraft (and other vehicle) surveillance and navigation systems analyses — quantifying the geometric relationship of two or more locations relative to each other and to the earth. Here, geometry means distances and angles, including their projections in a defined coordinate frame. Applications that fit well with these methods include (a) planning a vehicle’s route; (b) determining the coverage region of a radar or radio installation; and (c) calculating a vehicle’s latitude and longitude from measurements (e.g., of slant- and spherical-ranges or range differences, azimuth and elevation angles, and altitudes). The approach advocated is that the three-dimensional problems inherent in navigation/surveillance analyses should, to the extent possible, be re-cast as a sequence of sub-problems: Vertical-Plane Formulation; Spherical-Surface Formulation; Three-Dimensional Vector Formulation; and Non-Linear Least-Squares (NLLS) Formulation. These techniques are applied, in the context of a spherical earth, to a series of increasingly complex situations, starting with two problem-specific points (e.g., a route’s origin and destination) and extending to three or more points (e.g., an aircraft and multiple surveillance/navigation stations). Closed-form solutions are presented for measurements involving virtually every combination of ranges, pseudo ranges, azimuth/elevation angles and altitude. The Gauss-Newton NLLS methodology is employed to address the most complex situations. These include circumstances where there are more measurements than unknowns and/or the measurement ‘equations’ cannot be inverted analytically (including those for an ellipsoidal-shaped earth) and/or are not analytic expressions (e.g., involve empirical data).

  • Record URL:
  • Corporate Authors:

    Volpe National Transportation Systems Center

    55 Broadway
    Cambridge, MA  United States  02142

    Federal Aviation Administration

    800 Independence Avenue, SW
    Washington, DC  United States  20591
  • Authors:
    • Geyer, Michael
  • Publication Date: 2016-6


  • English

Media Info

  • Media Type: Digital/other
  • Edition: Project Memorandum
  • Features: Appendices; Figures; References; Tables;
  • Pagination: 274p

Subject/Index Terms

Filing Info

  • Accession Number: 01604580
  • Record Type: Publication
  • Report/Paper Numbers: DOT-VNTSC-FAA-16-12
  • Created Date: Jul 1 2016 11:39AM