1. A method of detecting a position of an alignment mark on an object including a mark element, said method comprising steps of: obtaining a signal waveform of the mark element with a position detector; extracting at least two kinds of waveform feature values from the signal waveform of the mark element with a controller of the position detector, by using extracting methods different from each other, each of the at least two kinds of waveform feature values being a parameter that characterizes the signal waveform of the mark element; and correcting a shift amount between a true value indicating an ideal position of the mark element and a real position of the mark element with the controller based on a function that correlates the at least two kinds of waveform feature values and the shift amount, wherein one of the at least two kinds of waveform feature values is a difference between two detection results of the mark element that are respectively detected by two signal processings different from each other, and wherein the function is a high-dimensional function which is at least a quadratic function including the at least two kinds of waveform feature values as variables.