Alternative positioning techniques, such as those using ambient signals-of-opportunity, have been increasingly developed for global navigation satellite system (GNSS)-challenging urban and indoor environments. For instance, cellular long-term evolution (LTE) network supports a variety of positioning methods based on signal measurements such as received signal strength or time-of-arrival (TOA). Carrier phase measurement extracted from LTE signals has also received substantial attention due to its potential high ranging accuracy. This paper presents a closed-loop (CL) carrier phase tracking architecture for positioning in LTE networks with robustness to the channel fading effects. The pilot cell-specific reference signal (CRS) is exploited for generating the channel estimation results, which are inputs for the carrier phase discriminator to measure the carrier phase error. The undesired bias corrupting the phase discriminator output for multipath channels is analytically derived. Then, the state-space model of LTE carrier signal tracking in light of the specific CRS time-frequency domain pattern is established and the state estimator gain matrix is derived based on the proportional integral filter deign. Simulation assessment of the proposed carrier phase tracking architecture is performed in a single path Rician fading channel under different Rician factors and signal powers. The impact of loop parameters, e.g., loop bandwidth and updating interval, is investigated. Real collected LTE data in a multipath fading channel is also used to comparatively analyze the performances of the existing open-loop and proposed CL carrier tracking methods combined with three LTE signal TOA estimators. The proposed algorithm in conjunction with the multipath estimating delay lock loop is shown to provide accurate and robust carrier phase measurements against multipath fading effects compared to other considered tracking schemes.