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The correct method that does not contribute to establishing horizontal control is vertical leveling. Horizontal control is essential for determining the precise location of points in a two-dimensional plane, which is fundamentally different from vertical leveling that focuses on establishing height differences between points. Vertical leveling methods measure the vertical distance from a reference point, typically a benchmark, which helps in creating a vertical control network rather than a horizontal one.

Triangulation, trilateration, and GPS are all methods that play a key role in defining horizontal positions. Triangulation utilizes angles between different points to calculate a location based on a known baseline. Trilateration, on the other hand, relies on measuring distances from known points to pinpoint a location in a planar coordinate system. GPS involves satellite signals to determine precise horizontal coordinates by calculating distances to multiple satellites. Therefore, vertical leveling stands out as unrelated to horizontal control methods, as it explicitly addresses vertical relationships rather than horizontal positioning.