original = {{55.3346, 694.253}, {55.3373, 691.275}, {55.34,
688.323}, {55.3426, 685.396}, {55.3453, 682.494}, {55.348,
679.617}, {55.3506, 676.765}, {55.3533, 673.936}, {55.356,
671.131}, {55.3565, 668.277}, {55.3565, 665.428}, {55.3565,
662.604}, {55.3565, 659.803}};
originalUnion = Union[original, SameTest -> (#1[[1]] == #2[[1]] &)];
fUnion = Interpolation[originalUnion, InterpolationOrder -> 1];
originalMap = MapIndexed[{#2, #} &, original];
fMap = Interpolation[originalMap]