A method for generating position data of an instrument, wherein the method encompasses the following steps: - capturing position measurement data of at least two position sensors (7, 9) which are arranged at or on the instrument, - determining a plausibility value on the basis of the position measurement data which were captured using the at least two position sensors which are arranged at or on the instrument, - classifying a movement state of the instrument on the basis of currently captured position measurement data and such which were detected in the past, wherein a plausibility threshold value is allocated to each classified movement state of the instrument, - allocating a plausibility threshold value to the classified movement state, so that the plausibility threshold value is continuously adapted to the classified movement state, - filtering the captured position measurement data on the basis of a comparison between the determined plausibility value and the allocated plausibility threshold value, - providing an image data set for displaying or presenting the instrument on a display apparatus at least on the basis of the filtered position measurement data, which is configured to display the instrument on the display apparatus, wherein the image data set is an image data set from at least one of the methods out of the group comprising: computer tomography, digital volume tomography, magnetic resonance tomography, sonography, duplex examination, angiography, nuclear medical imaging, medical imaging using administration of a contrast agent, radiography and radiological addition or subtraction methods, and - providing the image data set for an amended display or presentation of the instrument at least on the basis of the filtered position measurement data, which is configured to display the instrument. - capturing position measurement data of at least two position sensors (7, 9) which are arranged at or on the instrument, - determining a plausibility value on the basis of the position measurement data which were captured using the at least two position sensors which are arranged at or on the instrument, - classifying a movement state of the instrument on the basis of currently captured position measurement data and such which were detected in the past, wherein a plausibility threshold value is allocated to each classified movement state of the instrument, - allocating a plausibility threshold value to the classified movement state, so that the plausibility threshold value is continuously adapted to the classified movement state, - filtering the captured position measurement data on the basis of a comparison between the determined plausibility value and the allocated plausibility threshold value, - providing an image data set for displaying or presenting the instrument on a display apparatus at least on the basis of the filtered position measurement data, which is configured to display the instrument on the display apparatus, wherein the image data set is an image data set from at least one of the methods out of the group comprising: computer tomography, digital volume tomography, magnetic resonance tomography, sonography, duplex examination, angiography, nuclear medical imaging, medical imaging using administration of a contrast agent, radiography and radiological addition or subtraction methods, and - providing the image data set for an amended display or presentation of the instrument at least on the basis of the filtered position measurement data, which is configured to display the instrument.