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Multidimensional Newton-Raphson Calculations

Alternatively, multidimensional root finding methods such as the Newton-Raphson method can be used. The approach is to linearize around an approximate solution, say from iteration k, then solve the linear equations derived from the quadratic equations above to obtain . Although there is no guarantee that the method always converges due to the fact that multidimensional roots cannot be bounded, when a neighborhood containing a solution is known as is usually the case for GPS, it is quite likely that a solution will be found. It has been shown that results are comparable in accuracy to those of Bancroft's method.