The estimation of fast-fading LTE downlink channels in high-speed applications of LTE advanced is investigated in this article. In order to adequately track the fast time-varying channel response, an adaptive channel estimation and interpolation algorithm is essential. In this article, the multi-path fast-fading channel is modelled as a tapped-delay, discrete, finite impulse response filter, and the time-correlation of the channel taps is modelled as an autoregressive (AR) process. Using this AR time-correlation, we develop an extended Kalman filter to jointly estimate the complex-valued channel frequency response and the AR parameters from the transmission of known pilot symbols. Furthermore, the channel estimates at the known pilot symbols are interpolated to the unknown data symbols by using the estimated time-correlation. This article integrates both channel estimation at pilot symbols and interpolation at data symbol into the proposed Kalman interpolation filter. The bit error rate performance of our new channel estimation scheme is demonstrated via simulation examples for LTE and fast-fading channels in high-speed applications.