Speckle tracking is widely used for the detection and estimation of minute tissue motion and deformation with applications in elastography, shear-wave imaging, thermography, etc. The center frequency of the echo data within the tracking window is an important parameter in the estimation of the tissue displacement. Local variations in this quantity due to echo mixtures (specular and speckle components) may produce a bias in the estimation of tissue displacement using correlation-based speckle tracking methods. We present a new algorithm for estimation and tacking of the center frequency variation in pulse-echo ultrasound as a quantitative tissue property and for robust speckle tracking applications. The algorithm employs multiband analysis in the determination of echo mixtures as a preprocessing step before the estimation of the center frequency map. This estimate, in turn, is used to improve the robustness of the displacement map produced by the correlation-based speckle tracking. The performance of the algorithm is demonstrated in two speckle tracking applications of interest in medical ultrasound: (1) ultrasound thermography and (2) vascular wall imaging.