DOA Estimation And Tracking For Wideband Sound Sources Based On Compressive Sensing Joint Sparsity

Compressive sensing(CS) is a key research topic of array signal processing in the field of wideband sound source for the Direction of Arrival(DOA) estimation and tracking. Compared with traditional beamforming algorithms, CS can approximately or exactly reconstruct signal with few snapshots or even single snapshot. What’s more, CS also has good robustness performance and super resolution and can deal with correlate signals. Due to these merits, applying CS to the wideband sound source for DOA estimation and tracking has a great prospect.As the wideband sound source is spatially sparse, the wideband sound source DOA estimation is depicted by the wideband sparsity model. The coherence of measurement matrix with different frequencies is helpful in analyzing the sparse reconstruction property of CS in the frequency. In this paper, two wideband DOA estimation algorithms are proposed. One is the CS for the wideband DOA estimation algorithm based on the kernel density estimator(CS-Kernel). The other is extended the Orthogonal Matching Pursuit(OMP) algrithm to the wideband source DOA estimation based on the joint sparsity model(Joint-Sparsity). In order to verify the performance of two proposed algorithms, we compare the simulation result with that of the Capon wideband DOA algorithm based on arithmetic mean and geometric mean, respectively. The result shows that the Joint-sparsity algorithm and the CS-Kernel algorithm have characteristics of the high precision of DOA estimation with the low sidelobe and good peak value of power spectrum. By comparing the mean square error performance of the DOA reconstruction, the Joint-Sparsity algorithm has agood robustness. However, the robustness of the CS-Kernel algorithm is relatively poor. While, its performance will greatly improve as the signal to noise ratio raises.For the wideband sound source DOA tracking, a tracking algorithm based on the particle filter and CS is proposed. Particle filter is a kind of state filtering algorithm based on the Bayesian theory. The posterior probability distribution of the acoustic source state is estimated by using the weighted particles. Then the DOA estimation method is calculated by means of the sample mean. Based on the DOA estimation by CS, the kernel density estimator is as the likelihood function to estimate the probability of particle position. Simulation results show that, for both of the linear and the random array tracking systems,DOA tracking trajectories are consistent with the real source trajectory with a maximum offset no more than 3 degree and an average error no more than 1 degree. As to the angular resolution, the resolution of the proposed algorithm is close to that of the CS algorithm in the high frequency domain.