Checking GNSS-determined positions with EDM-observed distances. Issue 331 (July 2013)

• Record Type: Journal Article
• Authors: Meyer, T H; Pozdnyakov, V
• Is Part Of: Survey review. Volume 45:Issue 331(2013:Jul.)
• Page Start: 275
• Page End: 280
• Publication Date: 2013-07
• Subjects: Check shot -- GNSS positioning -- EDM -- Likelihood ratio test; Surveying -- Periodicals; Great Britain -- Surveys -- Periodicals; 526.9
• DOI: 10.1179/1752270612Y.0000000033
• Languages: English
• ISSNs: 0039-6265

Abstract

Abstract : Standard surveying practice in Connecticut requires that positions determined using global navigation satellite system methods be checked by comparing their inversed distance against an electronic distance measuring device distance, but no guidance was provided how to do this. A statistical test is called for, which requires means, variance and a probability density function for the test statistic. The electronic distance measuring device distance can be assumed to follow a normal distribution, but inversed distances belong to an unnamed distribution (it would be akin to a chi distribution). This paper first formulates a standard statistical test to perform the check using a maximum likelihood ratio that turns out to be not very practical. Several simplifying assumptions are shown to be warranted that allow a much simpler, but practically equivalent, z -test. Formulas for three-dimensional, geocentric Cartesian and two-dimensional, topocentric Cartesian positions are developed with allowable limits placed on horizontal and vertical separations for topocentric coordinate system positions.