Linear Induction Motor (LIM) possess unique advantages and application prospects in rail transit due to their ability to generate linear motion directly without intermediate transmission mechanisms. However, constrained by their distinctive topological structure, LIM cannot adopt the speed measurement methods used in rotary induction motor. Sensorless control strategies effectively address the high installation and maintenance costs associated with speed sensors. To this end, this paper proposes a sensorless vector control method for LIM based on a Unscented Kalman Filter (UKF). First, a mathematical model of the LIM considering dynamic edge effects is established in a rotating coordinate system. Next, real-time current and voltage signals are selected as inputs, with current, flux linkage and speed as state variables. A discrete state-space model of the motor based on a UKF observer is derived, enabling online observation and closed-loop speed control. Finally, the proposed method is validated through simulation experiments. Results demonstrate that this approach effectively enhances the dynamic response speed and steady-state observation performance of the LIM sensorless vector control system.