1. An encoder for encoding data defining coded positions representing a trajectory of an object based on spatio-temporal data representing a time series of positions of the object, the encoder comprising: a deriver configured to derive a plurality of components of a motion vector difference between a last coded motion vector pointing from a second last coded position to a last coded position and a current motion vector pointing from the last coded position to a current position of the object; a selector configured to select a component of the plurality of components of the motion vector difference; and a coder configured to code the current motion vector by coding the selected component of the motion vector difference to acquire a current coded motion vector, thereby defining a current coded position, wherein the coder is configured to not code another component or components of the plurality of components of the motion vector difference; wherein the time series of positions of the object are detected by a position sensor, an integrating velocity sensor or a twice-integrating acceleration sensor; the deriver is configured to derive the plurality of components of the motion vector difference such that a first component of the plurality of components corresponds to a first affine component of an affine coordinate system and a second component of the plurality of components corresponds to a second affine component of the affine coordinate system, wherein the affine coordinate system is oriented relative to the last coded motion vector; the affine coordinate system is a three-dimensional coordinate system; the first affine component of the affine coordinate system is a first angle measured relative to the last coded motion vector in a plane spanned by the last coded motion vector and a first vector, and the second affine component of the affine coordinate system is a second angle measured in a plane spanned by the last coded motion vector and a second vector, perpendicular to the first vector; and each of the deriver, the selector, and the coder is implemented using an integrated circuit, a field programmable gate array, or a digital signal processor, or a combination of at least two of the integrated circuit, the field programmable gate array, and the digital signal processor.