Joint-Sparse Heterogeneous Data Fusion for Target State Estimation with Weak Signals

Recently, we developed a joint-sparse data-level fusion (JSDLF) approach to fuse heterogeneous sensor data for target detection and estimation. In this approach, the target state space is discretized and the data fusion problem is formulated as a joint sparse signal reconstruction problem, and solved by simultaneous orthogonal matching pursuit. In this paper, we continue our work on JSDLF, and our new work is different from our previous work in two aspects. First, the performance of the JSDLF is investigated for cases with very low signal to noise ratio (SNR). Further, to compare the JSDLF approach with decision/feature level fusion approaches, we develop a new maximum likelihood (ML) decision-level fusion approach. In this approach, first each sensor makes its local detections, by comparing the signal's discrete Fourier transform amplitude at each frequency bin (or the image intensity at each pixel) with a threshold. The sensor detection results provide target Doppler shift estimates from radio frequency sensors and target location estimates from the video camera. Then a likelihood function is derived to statistically characterize the detected frequency bins or image pixels, by considering missed detections and false alarms. With the likelihood function, the sensor detections are fused using an ML estimator for target state estimation. We name this fusion approach, which considers both missed detections and false alarms, MLE-MDFA. The MLE-MDFA has assumed the perfect knowledge of the signals' distributions under both hypotheses, which in practice is very difficult to obtain. In contrast, the JSDLF approach requires minimum prior knowledge of the signal model. Hence, the MLE-MDFA only serves as a benchmark for the JSDLF approach. Our numerical results show that at high SNR, the MLE-MDFA provides similar performance as the JSDLF approach. At low SNR values, the JSDLF approach significantly outperforms the MLE-MDFA algorithm. This clearly demonstrates the benefits of data-level fusion over decision-level fusion.