Method and Apparatus for Modeling of GNSS Pseudorange Measurements for Interpolation, Extrapolation, Reduction of Measurement Errors, and Data Compression

Abstract

Polynomial regression models are used to reduce errors in measurements of pseudorange between a GNSS satellite and a receiving station; for data compression by replacing a large number of measurements with a small number of coefficients of the model polynomial, optionally combined with modeling residuals; for extrapolating usefully accurate estimates of future range between the GNSS satellite and the receiving station; and for providing usefully accurate estimates of future coefficient values of the polynomial regression models themselves.

1 . A method by which a mathematical model is derived from a time history of past and present values of a distance between two objects combined with a time history of estimates of future values of said distance between said two objects, the method comprising:
 a. recording a plurality of measurements of distances between said two objects and times at which said distances occur and storing said measurements and measurement times in a memory device;   b. creating a plurality of estimates of future distances between said two objects and times at which said estimates are expected to occur, and storing said estimates and times in a memory device; and   c. fitting a mathematical model to said plurality of measurements of distances and said plurality of estimates of future distances, together treated as a single composite time history of distance between said two objects without regard for whether individual distances are measured or estimated.   
     
     
         2 . The method of  claim 1 , wherein:
 a. a first one of the two objects is designated as a transmitting device, and   b. a second one of the two objects is designated as a receiving device, and   c. the measurements of distances between said transmitting device and said receiving device, and the times at which the measurements occur, are derived from one or more signals transmitted from said transmitting device to said receiving device.   
     
     
         3 . The method of  claim 2  in which the transmitting device also functions as a receiving device, and in which the receiving device also functions as a transmitting device, and in which at least two signals are mutually exchanged, at least one from each of the transmitting device and the receiving device to the other.