Acoustic Tomography of the Atmosphere Using Unscented Kalman Filter

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 new statistical-based acoustic travel-time tomography algorithm based on unscented Kalman filter (UKF) which is capable of reconstructing and tracking temperature and wind velocity fields (state variables) within a specified investigation area. The method exploits an iterative ray-tracing algorithm to handle situations when straight-ray assumption no longer holds. The observations used in the UKF process consists of the acoustic travel times computed for every pair of transmitter/reciever nodes deployed in the investigation area. A first-order spatial-temporal autoregressive model is used to account for state evolution in the UKF. To evaluate the performance of the UKF-based acoustic tomography method, 2-D fractal Brownian motion is used to generate synthetic temperature and wind velocity fields with spatial and temporal resolution of 1 m and 12 s, respectively. The UKF-based acoustic tomography algorithm is then compared to the well-known time-dependent stochastic inversion method. The results reveal the effectiveness of the proposed method for accurate and fast reconstruction of temperature and wind velocity fields.