This paper considers single-sensor estimation of vortex shedding in cylinder wakes at Re = 100 in simulations and at Re = 1036 in experiments. A model based on harmonic decomposition is developed to capture the periodic dynamics of vortex shedding. Two model-based methods are proposed to estimate time-resolved flow fields. First, Linear Estimation (LE) which implements a Kalman Filter to estimate the flow. Second, Linear-Trigonometric Estimation (LTE), which utilizes the same Kalman Filter together with a nonlinear relationship between harmonics of the vortex shedding frequency. LTE shows good performance and outperforms LE regarding the reconstruction of vortex shedding. Physically this suggests that, at the Reynolds numbers considered, the higher harmonic motions in the cylinder wake are slave to the fundamental frequency.