Distributed Sensor Fusion Performance Analysis Under an Uncertain Environment

Distributed multi-sensor fusion has been widely used in military and civilian applications. In the statistical sensor fusion domain, the design of an optimal fusion processor usually requires the joint statistics of the local sensor outputs. When accurate joint statistical knowledge is not readily available, popular solutions are either to estimate the joint statistics from training data or to simply assume independence of the data. Although it is well known that a fusion solution constructed using empirical data or simplified assumptions often cannot reach the optimal performance, little research has been focused on analyzing the performance difference. This paper presents a systematic analysis of distributed sensor fusion performance in an uncertain operating environment using a Bayesian likelihood ratio fusion model. For the problem where joint statistics of the local sensor outputs cannot be obtained accurately, the sub-optimal fusion processor is assumed to have an estimated correlation coefficient and its performance difference from the optimal scenario is derived analytically using a Gaussian model. We use the detectability index, which fully characterizes the receiver operating characteristic (ROC) curve for the Gaussian model, as the performance metric to compare the optimal and suboptimal cases. The ratio of detectability indices for the sub-optimal and optimal cases is derived as a function of the true correlation coefficient, the estimated value, and the performance difference between individual local sensors. We prove that the closer the individual local sensor performances, the less vulnerable the fusion performance is to a mismatched estimation of the correlation coefficient. Furthermore, we show that for the special case where all local sensors have the same performance, the optimal fusion performance is always achieved regardless of the estimation deviation from the true correlation coefficient. We provide discussions on the deeper physical meaning of such phenomena. For non-Gaussian sensor noise models, we extend our analysis via computer simulation and provide experimental validations using application specific sensor data of military relevance (e.g., multispectral, hyperspectral). Our results show that similar conclusions hold for a family of heavy-tailed non-Gaussian distribution models.