Andrew Holme explains a some of these things succinctly on his home made GPS receiver project page[0]. Search for "Solving for user position", where he even mentions ionospheric propagation. He also has an appendix showing his math[1]

[0] http://www.aholme.co.uk/GPS/Main.htm [1] http://www.aholme.co.uk/GPS/user_position_solution.pdf