NEW MATH MODEL FOR INDEPENDENT-MODEL TRIANGULATION

A NEW MATHEMATICAL MODEL FOR INDEPENDENT-MODEL AERIAL TRANGULATION IS BASED ON THE COLLINEARITY PRINCIPLE. THE VALIDITY OF THE MODEL WAS ASSURED USING VARIOUS SETS OF TEST DATA. THE STEREOMODELS ARE FIRST RELATIVELY ORIENTED; THEN THE MODEL COORDINATES ARE OBSERVED, AND TRANSFORMED TO THE IMAGE PLANE. THESE TRANSFORMED COORDINATES ARE USED AS OBSERVATIONS TOGETHER WITH EXPOSURE STATION UNKNOWNS AND THE PASS-POINT COORDINATES AS PARAMETERS IN A SIMULTANEOUS LEAST-SQUARES SOLUTION. THIS MATHEMATICAL MODEL WAS SEARCHED FOR BY USING DIFFERENT GEOMETRICAL APPROACHES AND VARIOUS STATISTICAL MODELS. THE APPROACHES TO THE GEOMETRICAL MODELS ARE BASED ON THE COLLINEARITY EQUATION, CONDITIONS BETWEEN UNKNOWN PARAMETERS FOR THE EXPOSURE STATIONS, AND CONDITIONS BETWEEN THE TRANSFORMED IMAGE COORDINATES. A SUITABLE GEOMETRICAL MODEL WAS CHOSEN FROM A COMPARATIVE TEST OF THESE APPROACHES, USING THE COLLINEARITY EQUATION AS A BASIC EQUATION IN THE ADJUSTMENT. THIS MODEL GIVES THE BEST AGREEMENT BETWEEN THE OBSERVATIONS AND THE PARAMETERS IN THE SOLUTION, USES A HALF-PHOTOGRAPH AS A BASIC UNIT IN A SIMULTANEOUS LEAST-SQUARES SOLUTION, AND ASSIGNS FOR EACH BASIC UNIT THREE ROTATION PARAMETERS. THE CHOICE OF THE STATISTICAL MODEL FOR THIS GEOMETRICAL MODEL IS OBTAINED BY USING DIFFERENT WEIGHT COEFFICIENT MATRICES FOR THE TRANSFORMED IMAGE COORDINATES AS OBSERVATIONS TO OBTAIN THE BEST AGREEMENT BETWEEN THESE OBSERVATIONS AND THE PARAMETERS IN THE SOULUTION. FOR THE SPECIFIC STATISTICAL MODEL THAT SATISFIES THIS CONDITION, IT IS FOUND THAT THE TRANSFORMED IMAGE COORDINATES CAN BE TREATED AS UNCORRELATED OBSERVATIONS WITH EQUAL WEIGHTS. INASMUCH AS THE MATHEMATICAL MODEL WAS USED FOR THE FIRST TIME IN A SIMULTANEOUS ADJUSTMENT, THE RESULTS WERE CHECKED BY STATISTICAL AND GEOMETRICAL ANALYSES. FURTHERMORE, THE MATHEMATICAL MODEL IS USED IN A COMPARISON STUDY WITH THE EXISTING ANALYTICAL SYSTEMS, USING VARIOUS TEST DATA ON DIFFERENT STEREOPLOTTERS AND ON ONE STEREOCOMPARATOR. FROM THE RESULTS OF THESE TESTS, IT IS CONCLUDED THAT: (1) INDEPENDENT-MODEL AERIAL TRIANGULATION MAY BE USED AS A SUBSTITUTE FOR ANALYTICAL AERIAL TRIANGULATION; (2) THE FORMATION OF THE ADJUSTMENT OF AERIAL TRIANGULATION MUST INCLUDE THE COLLINEARITY EQUATION; AND (3) MATHEMATICAL CORRELATION BETWEEN THE IMAGE COORDINATES MAY BE NEGLECTED. /AUTHOR/

  • Supplemental Notes:
    • 1 APP
  • Authors:
    • Maarek, A
  • Publication Date: 1973-10

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  • Accession Number: 00203047
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Apr 11 1974 12:00AM