This study investigates the challenge of time-varying channel estimation under censored data conditions, a prevalent issue in communication systems caused by sensor saturation or detection constraints. Such censoring effects, typically manifested as signal clipping or discontinuous measurements, can introduce significant estimation errors that adversely affect subsequent signal demodulation and channel equalization processes. To address this problem, we propose a Tobit Extended Kalman Filter (TEKF) algorithm that integrates the Tobit censored measurement model with Extended Kalman Filtering. The TEKF enables unbiased and computationally efficient estimation for channels with censored data outputs, making it particularly suitable for complex propagation environments. Numerical simulations demonstrate that the TEKF consistently outperforms Extended Kalman Filter methods in estimation accuracy, providing a reliable approach for recovering channel characteristics from censored communication signals.