2-D toy: 3 unknowns (px, py, b) so we need at least 3 satellites. In real 3-D GPS the unknowns are (x, y, z, b) and you need at least 4. The receiver runs a Gauss-Newton nonlinear least-squares fit and outputs the position estimate as a black box.
Drag any satellite around the orbit in the constellation panel to change the geometry. The zoom panel shows the same scenario near the receiver — where pseudorange bands cross is where the receiver could be. Tight intersection ⇒ small HDOP. Smeared intersection ⇒ large HDOP.