Optimizing weighted least square (WLS) inputs to improve global navigation satellite systems (GNSS) localization

A device comprising:

• a memory;
• and
• one or more processors communicatively coupled with the memory, wherein the one or more processors are configured to:
• obtain an initial position of the device without using Global Navigation Satellite System (GNSS) positioning;
• take GNSS measurements of radio frequency (RF) signals transmitted by GNSS satellites;
• determine initial residuals based, at least in part, on GNSS measured distances determined from the at least a portion of the GNSS measurements and expected distances determined from the initial position;
• estimate errors of the GNSS measurements, based at least in part, on the initial residuals and RF signals;
• perform an optimization using the initial residuals and at least a portion of the errors to produce a modified set of residuals, wherein;
• the optimization is further based on values, separate from the initial residuals and the errors, representing a geometry of the GNSS satellites;
• and
• the modified set of residuals comprises:
• (i) the initial residuals, with a value of one or more of the initial residuals modified,
• (ii) the initial residuals, with one or more of the initial residuals multiplied by a respective weight, or
• (iii) both (i) and (ii);
• and
• use a cost minimization method on the modified set of residuals and the geometry of the GNSS satellites to determine an improved position of the device.

An apparatus for determining a position of a device comprising:

• the apparatus comprising:
• means for obtaining an initial position of the device without using Global Navigation Satellite System (GNSS) positioning;
• means for taking GNSS measurements of radio frequency (RF) signals transmitted by GNSS satellites;
• means for determining initial residuals based, at least in part, on GNSS measured distances determined from the at least a portion of the GNSS measurements and expected distances determined from the initial position;
• means for estimating errors of the GNSS measurements, based at least in part, on the initial residuals and RF signals;
• means for performing an optimization using the initial residuals and at least a portion of the errors to produce a modified set of residuals, wherein:
• the optimization is further based on values, separate from the initial residuals and the errors, representing a geometry of the GNSS satellites;
• and
• the modified set of residuals comprises:
• (i) the initial residuals, with a value of one or more of the initial residuals modified,
• (ii) the initial residuals, with one or more of the initial residuals multiplied by a respective weight, or
• (iii) both (i) and (ii);
• and
• means for using a cost minimization method on the modified set of residuals and the geometry of the GNSS satellites to determine an improved position of the device.

A non-transitory computer-readable medium storing instructions for determining a position of a device comprising:

• the instructions comprising code for:
• obtaining an initial position of the device without using Global Navigation Satellite System (GNSS) positioning;
• taking GNSS measurements of radio frequency (RF) signals transmitted by GNSS satellites;
• determining initial residuals based, at least in part, on GNSS measured distances determined from the at least a portion of the GNSS measurements and expected distances determined from the initial position;
• estimating errors of the GNSS measurements, based at least in part, on the initial residuals and RF signals;
• performing an optimization using the initial residuals and at least a portion of the errors to produce a modified set of residuals, wherein:
• the optimization is further based on values, separate from the initial residuals and the errors, representing a geometry of the GNSS satellites;
• and
• the modified set of residuals comprises:
• (i) the initial residuals, with a value of one or more of the initial residuals modified,
• (ii) the initial residuals, with one or more of the initial residuals multiplied by a respective weight, or
• (iii) both (i) and (ii);
• and
• using a cost minimization method on the modified set of residuals and the geometry of the GNSS satellites to determine an improved position of the device.