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Two fundamental approaches to information averaging are based on linear andlogarithmic combination, yielding the arithmetic average (AA) and geometricaverage (GA) of the fusing initials, respectively. In the context of targettracking, the two most common formats of data to be fused are random variablesand 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 representingmultitarget densities in the presence of false alarms and misdetection (whoseweight sums are not necessarily unit) is also considered, the result of whichappears significantly different from that for a single target. In addition toexact derivation, exemplifying analysis and illustrations are provided.

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