A large number of initialised false tracks in clutter environments will cause a heavy burden on the detection and track-processing system. The quantity of initialised false tracks in clutter used to be estimated by experience or simulation, which lacks a fundamental explanation in theory. In order to estimate the amount of linear initialised false tracks with analytical expressions, statistical estimators are proposed based on prior knowledge of the clutter in a two-dimensional scenario. Meanwhile, the differential Hough transform is presented to verify the estimators. To be specific, firstly, a one-dimensional scenario is illustrated to present the statistical estimators of the number of initialised linear and equallength false tracks, which is based on statistical estimation theory. Secondly, regarding the clutter map as a uniform distributed binary image, the estimators described at first are extended to a two-dimensional situation. Finally, to verify the validity of the proposed estimators, a differential Hough transform algorithm is utilised to obtain the number of linear and equal-length tracks in the simulation. The results show that the estimators proposed herein are reasonable in a certain clutter environment.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.