Kalman-filter-based time-domain plane wave superposition method for reconstructing an instantaneous sound field

A Kalman-filter-based time-domain plane wave superposition method (KF-TDPWSM) is proposed for reconstructing the instantaneous sound field generated by a source. In the KF-TDPWSM, a discrete state formulation is first acquired using the superposition formula of time-varying pressure on a hologram plane, which forms a multiple-input and multiple-output acoustical system. Then, an eigensystem realization algorithm is implemented to obtain the minimum realization of this system. The process and measurement equations of the KF-TDPWSM are established by combining the equation of the first-order smoothness condition with the minimum realization. Finally, the forward iteration calculation of the Kalman filter is used to estimate the state vector, including the pressure time–wavenumber spectra on a virtual source plane. The spectra estimated at all times are employed to calculate the time-varying pressure on a reconstruction plane. The KF-TDPWSM utilizes a forward iteration calculation and does not use the inverse calculation with the time-marching characteristic to improve the reconstruction stability of the instantaneous sound field. A numerical simulation is designed to investigate the reconstruction performance of the KF-TDPWSM. Simulation results confirm that the KF-TDPWSM effectively reconstructs the instantaneous sound field of a source in the time and space domains. The effects of certain parameters of the KF-TDPWSM are examined through simulations, and it is shown that its reconstruction accuracy is superior to that of the time-domain plane wave superposition method. An experiment is conducted to further validate the KF-TDPWSM.