1. A position detection apparatus, comprising: a calculation unit configured to calculate a plurality of values for a parameter defining a two-dimensional or three-dimensional shape using one or more combinations of selection points selected from a plurality of detection points associated with the shape; an extraction unit configured to extract, from the plurality of values calculated by the calculation unit, one or more calculated values whose relevance to a provisional parameter falls within a predetermined range, the provisional parameter being a value or a range of values estimated for the parameter defining the shape with a method different from a calculation method with which the calculation unit calculates the values; and a determination unit configured to determine, from the one or more calculated values extracted by the extraction unit, a value with the highest evaluation performed using the plurality of detection points as an estimated value for the parameter defining the shape.