System and method for gaussian process enhanced gnss corrections generation

Abstract

A system and method for generating a set of GNSS corrections using a GNSS corrections model comprising a Gaussian process.

We claim: 
     
         1 . A method for determining a mobile receiver position comprising:
 receiving a set of satellite observations; and   generating a set of GNSS corrections using a set of Gaussian processes, wherein inputs to the set of Gaussian processes comprise a set of covariance functions relating combinations of satellite observations from the set of satellite observations, wherein the set of covariance functions comprise:
 a covariance function relating satellite orbit errors between two satellite observations; 
 a covariance function relating hardware bias between two satellite observations; and 
 a covariance function relating clock errors between two satellite observations; 
   
       wherein a mobile receiver receives a second set of satellite observations, corrects the second set of satellite observations using the set of GNSS corrections; and determines a position of the mobile receiver using the set of corrected satellite observations. 
     
     
         2 . The method of  claim 1 , wherein the set of covariance functions further comprises a covariance function relating atmospheric delays comprising:
 a radial covariance function relating a first pierce point associated with a first satellite observation and a second pierce point associated with a second satellite observation; and   an altitude covariance function relating an altitude of the first pierce point and an altitude of the second pierce point.   
     
     
         3 . The method of  claim 2 , wherein the radial covariance function comprises a squared exponential function relating a great circle distance between the first pierce point and the second pierce point. 
     
     
         4 . The method of  claim 1 , wherein at least one of:
 the covariance function relating satellite orbit errors between two satellite observations comprises a sum of a constant function, a squared exponential function, and an Ornstein-Uhlenbeck function;   the covariance function relating hardware bias between two satellite observations comprises a sum of a squared exponential function and an Ornstein-Uhlenbeck function; or   the covariance function relating clock errors between two satellite observations comprises an Ornstein-Uhlenbeck function.   
     
     
         5 . The method of  claim 1 , wherein one or more hyperparameters associated with at least one of the covariance functions is determined using a numerical optimization routine. 
     
     
         6 . The method of  claim 5 , wherein the numerical optimization determines the one or more hyperparameters that minimize an out-of sample error. 
     
     
         7 . The method of  claim 1 , further comprising determining Melbourne-Wubbena combinations from the set of satellite observations, wherein the inputs to the set of Gaussian processes comprise the Melbourne-Wubbena combinations. 
     
     
         8 . The method of  claim 1 , wherein the set of Gaussian processes comprises a sparse Gaussian process using a partially independent training conditional approximation. 
     
     
         9 . A method for generating GNSS corrections comprising:
 receiving, from a set of reference stations, a set of satellite observations corresponding to one or more satellites of one or more satellite constellations; and   generating a set of GNSS corrections using a sparse Gaussian process, wherein inputs to the sparse Gaussian process comprise the set of satellite observations and a set of covariance functions, wherein the sparse Gaussian process approximates a Gaussian process using at least one of a fully independent training conditional approximation, partially independent training conditional approximation, or a hierarchical gaussian process approximation;   determining a position of a receiver based on the set of GNSS corrections.   
     
     
         10 . The method of  claim 9 , wherein the inputs to the sparse Gaussian Process further comprise an atmospheric delay for each reference station of the set of reference stations, wherein the atmospheric delay for each reference stations is determined using a precise point precision (PPP) filter, wherein a covariance function relating two atmospheric delays comprises:
 a reference station covariance function relating the two atmospheric delays at a common reference station;   a satellite covariance function relating the two atmospheric delays for a common satellite; and   a covariance function comprising a convolution between an altitude covariance and a radial covariance.   
     
     
         11 . The method of  claim 10 , wherein the convolution between the altitude covariance and the radial covariance comprises a convolution over a plurality of shells of a multi-shell atmospheric model, wherein the multi-shell atmospheric model comprises at least one of a distinct shell associated with each satellite of the set of satellites or a plurality of shells associated with the set of satellites. 
     
     
         12 . The method of  claim 9 , further comprising rebasing inducing points of the sparse Gaussian process. 
     
     
         13 . The method of  claim 12 , wherein the inducing points are rebased based on a posterior prediction associated with a second set of inducing points. 
     
     
         14 . The method of  claim 13 , wherein the inducing points are scaled based on a prior associated with the inducing points based on the posterior prediction. 
     
     
         15 . The method of  claim 9 , further comprising identifying one or more outliers in the set of satellite observations using a random sample consensus method. 
     
     
         16 . The method of  claim 9 , further comprising determining a hyperparameter of the sparse Gaussian process by:
 predicting a set of GNSS corrections and the sparse Gaussian process using a second set of satellite observations, wherein satellite observations associated with at least one reference station or satellite is withheld from the second set of satellite observations;   determining a quality metric associated with each predicted GNSS corrections from the set of GNSS corrections; and   selecting the hyperparameter based on the quality metric of the predicted GNSS corrections.   
     
     
         17 . The method of  claim 9 , further comprising stitching together a GNSS correction associated with a first time and a GNSS correction associated with a second time. 
     
     
         18 . The method of  claim 17 , wherein stitching together the GNSS corrections at the first and second time comprises constraining a mean quantity of satellite observations detected at a master reference station of the set of reference stations to a common value at the first and second times. 
     
     
         19 . The method of  claim 9 , wherein the set of GNSS corrections are operable to correct for at least one of: satellite clock error, satellite orbit error, satellite hardware bias, satellite antenna phase windup, phase center offset (PCO), phase center variation (PCV), solid earth tides, solid earth pole tides, ocean tidal loading, ionosphere delays, troposphere delays, receiver clock error, receiver hardware bias, receiver antenna phase windup/PCO/PCV, carrier phase ambiguity, or multi-path effects. 
     
     
         20 . The method of  claim 9 , wherein the inputs to the sparse Gaussian process comprise at least one of Melbourne-Wubbena pseudorange or Melbourne-Wubbena carrier phase. 
     
     
         21 . The method of  claim 9 , further comprising determining a carrier phase ambiguity for each satellite of the set of satellite observations, wherein inputs to the sparse Gaussian process further comprise the set of carrier phase ambiguities. 
     
     
         22 . The method of  claim 21 , wherein each carrier phase ambiguity is fixed to an integer value.