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.
In this paper, we present the single frequency PPP algorithms based on our GR models with applying CLAS (Centimeter Level Augmentation Service) data from Japan Quasi-Zenith-Satellite-System (QZSS). Throughout the numerical experiments by using the single frequency (L1-band, only) measurement data for the static position, we have very accurate positioning results; namely the total 3D-RMS errors by applying CLAS is approximately 0.13 [m], which is the superior positioning result achieved as a single frequency GPS measurements.