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## C. Direct Minimization Method

### 1. General

The most probable value (MPV) estimation of an observation set is the one which that minimizes the sum of the squares of the residuals, Equations C-1 and C-2.

Equation C-1 | ||

Equation C-2 | ||

v: Residual o: Observation |

Combining Equations C-1 and C-2 gives Equation C-3; its only unknown is the MPV. To minimize a function, its first derivative is set equal to zero, Equation C-4, and solved for the unknown.

Equation C-3 | |

Equation C-4 |

Because the derivative is set to zero, we will refer to this as the * Direct Minimization* method.