Selection of a subset of global navigation satellite system measurements based on relation between shifts in target parameters and sum of residuals

An apparatus for generating an optimum measurement subset from a set of input global navigation satellite system (GNSS) measurements, wherein the number of input GNSS measurements in the set of input GNSS measurements is a first integer, wherein the number of input GNSS measurements in the optimum measurement subset is a specified second integer, and wherein the specified second integer is less than the first integer, the apparatus comprising:

• means for receiving the set of input GNSS measurements;
• means for generating a design matrix, wherein the design matrix is based at least in part on partial derivatives of the set of input GNSS measurements with respect to at least one target parameter, wherein the at least one target parameter is selected from the group consisting of:
• a one-dimensional position;
• a two-dimensional position;
• a three-dimensional position;
• and
• a time offset from a GNSS time;
• means for generating a weight matrix, wherein the weight matrix is based at least in part on measurement errors associated with the set of input GNSS measurements;
• means for calculating values of a set of coefficients, wherein each specific coefficient in the set of coefficients corresponds to a specific input GNSS measurement in the set of input GNSS measurements, and wherein the means for calculating values of a set of coefficients comprises means for, for each specific input GNSS measurement in the set of input GNSS measurements:
• calculating, based at least in part on the design matrix and based at least in part on the weight matrix, a change in value of the at least one target parameter resulting from a change in value of the specific input GNSS measurement;
• calculating, based at least in part on the design matrix and based at least in part on the weight matrix, a change in value of a sum of squared residuals resulting from a change in value of the specific input GNSS measurement;
• and
• calculating the value of a specific coefficient as the ratio of the change in value of the at least one target parameter resulting from the change in value of the specific input GNSS measurement to the change in value of the sum of squared residuals resulting from the change in value of the specific input GNSS measurement;
• and
• means for selecting the optimum measurement subset based at least in part on the values of the set of coefficients.

A computer readable medium storing computer program instructions for operating a navigation receiver by generating an optimum measurement subset from a set of input global navigation satellite system (GNSS) measurements, wherein the number of input GNSS measurements in the set of input GNSS measurements is a first integer, wherein the number of input GNSS measurements in the optimum measurement subset is a specified second integer, and wherein the specified second integer is less than the first integer, the computer program instructions defining the steps of:

• receiving, by the navigation receiver, the set of input GNSS measurements;
• generating, by the navigation receiver, a design matrix, wherein the design matrix is based at least in part on partial derivatives of the set of input GNSS measurements with respect to at least one target parameter, wherein the at least one target parameter is selected from the group consisting of:
• a one-dimensional position;
• a two-dimensional position;
• a three-dimensional position;
• and
• a time offset from a GNSS time;
• generating, by the navigation receiver, a weight matrix, wherein the weight matrix is based at least in part on measurement errors associated with the set of input GNSS measurements;
• calculating, by the navigation receiver, values of a set of coefficients, wherein each specific coefficient in the set of coefficients corresponds to a specific input GNSS measurement in the set of input GNSS measurements, and wherein the step of calculating values of a set of coefficients comprises the steps of, for each specific input GNSS measurement in the set of input GNSS measurements:
• calculating, based at least in part on the design matrix and based at least in part on the weight matrix, a change in value of the at least one target parameter resulting from a change in value of the specific input GNSS measurement;
• calculating, based at least in part on the design matrix and based at least in part on the weight matrix, a change in value of a sum of squared residuals resulting from a change in value of the specific input GNSS measurement;
• and
• calculating the value of a specific coefficient as the ratio of the change in value of the at least one target parameter resulting from the change in value of the specific input GNSS measurement to the change in value of the sum of squared residuals resulting from the change in value of the specific input GNSS measurement;
• and
• selecting, by the navigation receiver, the optimum measurement subset based at least in part on the values of the set of coefficients.