Editing Global Positioning System (section)

==== Least squares ====
When more than four satellites are available, the calculation can use the four best, or more than four simultaneously (up to all visible satellites), depending on the number of receiver channels, processing capability, and [[Dilution of precision (GPS)|geometric dilution of precision]] (GDOP).

Using more than four involves an over-determined system of equations with no unique solution; such a system can be solved by a [[least-squares]] or weighted least squares method.<ref name=GPS_BASICS_Blewitt />

:<math>\left( \hat{x},\hat{y},\hat{z},\hat{b} \right) = \underset{\left( x,y,z,b \right)}{\arg \min} \sum_i \left( \sqrt{(x-x_i)^2 + (y-y_i)^2 + (z-z_i)^2} + bc - p_i \right)^2</math>