Acoustic travel-time tomography of the atmosphere is a nonlinear inverse problem which attempts to reconstruct temperature and wind velocity fields in the atmospheric surface layer using the dependence of sound speed on temperature and wind velocity fields along the propagation path. This paper presents a statistical-based acoustic travel-time tomography algorithm based on dual state-parameter unscented Kalman filter (UKF) which is capable of reconstructing and tracking, in time, temperature, and wind velocity fields (state variables) as well as the dynamic model parameters within a specified investigation area. An adaptive 3-D spatial-temporal autoregressive model is used to capture the state evolution in the UKF. The observations used in the dual state-parameter UKF process consist of the acoustic time of arrivals measured for every pair of transmitter/receiver nodes deployed in the investigation area. The proposed method is then applied to the data set collected at the Meteorological Observatory Lindenberg, Germany, as part of the STINHO experiment, and the reconstruction results are presented.