Title: Second Order Statistics Analysis and Comparison between Arithmetic and Geometric Average Fusion,
Abstract: Two fundamental approaches to information averaging are based on linear and
logarithmic combination, yielding the arithmetic average (AA) and geometric
average (GA) of the fusing initials, respectively. In the context of target
tracking, the two most common formats of data to be fused are random variables
and probability density functions, namely $v$-fusion and $f$-fusion,
respectively. In this work, we analyze and compare the second order statistics
(including variance and mean square error) of AA and GA in terms of both
$v$-fusion and $f$-fusion. The case of weighted Gaussian mixtures representing
multitarget densities in the presence of false alarms and misdetection (whose
weight sums are not necessarily unit) is also considered, the result of which
appears significantly different from that for a single target. In addition to
exact derivation, exemplifying analysis and illustrations are provided.