Detection Algorithms on GNSS Millimeter Displacement using Orthogonal Functions

This paper presents mathematical algorithms to measure a noise-buried destructive displacement using GNSS (Global Navigation Satellite System) precise positioning and the orthogonal function expansion of its positioning result. In reality, there are 5.25 hundred thousand places in danger of landslide in Japan. The algorithms must retrieve a millimeter-scale displacement in the observation noise, therefore they apply the orthogonal functions from the class of Gegenbauger polynomials and the orthogonal even functions. This method informs the foreboding of a destruction, and will save many lives and infinite property of assets in catastrophic disasters from the present time.