Geotrekking - Navigation Equations - Trilateration

Trilateration

The receiver can use trilateration and one dimensional numerical root finding. Satellite position and pseudorange determines a sphere centered on the satellite with radius equal to the pseudorange. Trilateration is used to estimate receiver position based on the intersection of three sphere surfaces so determined. In the usual case of two intersections of three sphere surfaces, the point nearest the surface of the sphere corresponding to the fourth satellite is chosen. Let d denote the signed distance from the current estimate of receiver position to the sphere around the fourth satellite. The notation, d(correction) denotes this as a function of the clock correction. The problem is to determine the correction such that d(correction) = 0. This is the familiar problem of finding the zeroes of a one dimensional non-linear function of a scalar variable. Iterative numerical methods, such as those found in the chapter on root finding in Numerical Recipes can solve this type of problem.