== Correcting a GPS receiver's clock == 

 The method of calculating position for the case of no errors has been explained. 
 One of the most significant error sources is the GPS receiver's clock. Because of the very large value of the speed of light, c, the estimated distances from the GPS receiver to the satellites, the pseudoranges, are very sensitive to errors in the GPS receiver clock. This suggests that an extremely accurate and expensive clock is required for the GPS receiver to work. On the other hand, manufacturers prefer to build inexpensive GPS receivers for mass markets. The solution for this dilemma is based on the way sphere surfaces intersect in the GPS problem. 

  
 It is likely that the surfaces of the three spheres intersect, since the circle of intersection of the first two spheres is normally quite large, and thus the third sphere surface is likely to intersect this large circle. It is very unlikely that the surface of the sphere corresponding to the fourth satellite will intersect either of the two points of intersection of the first three, since any clock error could cause it to miss intersecting a point. However, the distance from the valid estimate of GPS receiver position to the surface of the sphere corresponding to the fourth satellite can be used to compute a clock correction. Let  denote the distance from the valid estimate of GPS receiver position to the fourth satellite and let  denote the pseudorange of the fourth satellite. Let . Note that  is the distance from the computed GPS receiver position to the surface of the sphere corresponding to the fourth satellite. Thus the quotient, , provides an estimate of 

 :(correct time) − (time indicated by the receiver's on-board clock), 

 and the GPS receiver clock can be advanced if  is positive or delayed if  is negative. 

 Regrettabilly this does not work, if for example the constellation of <<<>>> is taken, and one calculates the da, one can get the following values for da (), depending which satellite is used as the fourth satellite. It is not possible that each of these value's does correct the clock into the right direction or with the right amount. In fact only two of the values actually converge to a smaller clock-error.