Second Order Statistics Analysis and Comparison between Arithmetic and Geometric Average Fusion

For example, in the context of target tracking using a decentralized sensor network, the sensor cooperation can compensate for the effect of the misdetection, false-alarms and even the failure of the local sensor and extends their fields of view, eventually resulting in improved estimation accuracy and improved robustness [1, 2, 3, 4, 5, 6]. Particular interest in distributed data fusion has been paid to calculating the "average" over the information owned by locally netted sensors/agents via peer-to-peer communication in an efficient, flexible and scalable way [7, 8, 9, 6, 10]. Fundamentally, the average can be defined in two manners including, the arithmetic average (AA) and the geometric average (GA). Simply put, the former is a type of linear/convex fusion, akin to the linear opinion pool approach, while the latter is nonlinear/logarithmic fusion akin to the logarithmic opinion pool approach [11, 12], or to say, linear versus log-linear pools [13]. In the context of multi-sensor/multi-agent target tracking, the two most important types of information for fusion among local sensors/agents are random variables (representing parameters such as the number of targets, clutter rate, target existing probability, etc.) and probability density functions (PDFs), for which the fusion is referred to as v-fusion and f -fusion, respectively. While it seems that the AA fusion is more common in the former [7, 8, 4, 9], the GA fusion is vibrant in the latter [3, 14, 15], which coincides with the Chernoff fusion [16, 17, 18, 19] and is also known as covariance intersection (CI) when Gaussian functions that are uniquely characterized by the first and second order statistics are particularly considered [20, 21, 22, 23, 24, 25]. The CI approach was originally proposed for fusing unknown-correlated estimates produced at distinct but not necessarily independent sensors to avoid information double accounting in the fusion. Likewise, the AA fusion can also avoid information double accounting [22]. Further approaches to combining probability distributions of unknown cross-correlation can be found in the literature [26, 27, 28, 29, 30].