Method and apparatus for calibrating base station locations and perceived time bias offsets in an assisted GPS transceiver

A method for calibrating a base station location in a mobile station having a satellite positioning receiver, comprising the steps of:

• collecting at least three TOA measurements TOA1, TOA2, TOA3 arriving at the mobile station from a base station at different times t, wherein a TOA measurement is capable of being expressed as TOAt=b′+[(x−xt)2+(y−yt)2], with variable b′ being a perceived time bias offset of the base station and (x, y) being base station coordinates;
• simultaneously collecting at least three satellite position measurements of a position of the satellite positioning receiver, wherein a position measurement is denoted as xt and yt as a function of time;
• determining through a geometry matrix that the at least three TOA measurements and the at least three satellite position measurements are sufficient for determining the base station location;
• subtracting a first TOA measurement TOA1 from at least two subsequent TOA measurements TOA2, TOA3 to create at least two TOA differences TOA31, TOA21;
• substituting a distance variable d1 for the base station coordinates x, y in the at least two TOA differences TOA31, TOA21 to produce a quadratic equation for the distance variable d1, where the distance variable d1=[(x−xt)2+(y−yt)2];
• solving the quadratic equation for the distance variable d1 to obtain an estimated range de;
• solving for the base station coordinates x, y using the estimated range de;
• and
• obtaining the perceived time bias offset b′ by subtracting the estimated range de from a TOA measurement.

An apparatus for calibrating a base station location in a mobile station, comprising:

• a satellite positioning receiver;
• a radio transceiver;
• a time-of-arrival (TOA) measurement storage for storing a plurality of TOA measurements;
• a satellite positioning receiver position fix storage for storing a plurality of position fixes;
• a base station coordinates storage;
• a time bias offset storage;
• and
• a processor, for communicating with the radio transceiver and satellite positioning receiver to receive signals from satellite positioning satellites and from a base station, and further communicating with the TOA measurement storage, the satellite positioning receiver position fix storage, the base station coordinates storage, and the time bias offset storage, with the processor capable of collecting and storing TOA measurements, collecting and storing a corresponding number of satellite position measurements, subtracting a first TOA measurement from subsequent TOA measurements to create TOA differences, substituting a distance variable d1 for base station coordinates x, y in the TOA differences to produce a quadratic equation, solving the quadratic equation for the distance variable d1 to obtain an estimated range de, solving for the base station coordinates x, y, obtaining a perceived time bias offset b′ by subtracting an estimated range de from the TOA measurements, linearizing the TOA measurements to produce linearized TOA equations, generating a vector of measurement residuals TOAres, computing a weighted least squares solution xsol of the linearized TOA equations, using the weighted least squares solution xsol to assess an accuracy of the linearized TOA equations, and repeating the generating, computing, and using until a solution error variance of the weighted least squares solution xsol becomes less than a solution error variance threshold.