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

arXiv: https://arxiv.org/abs/1901.08015 · HTML: https://mlsanity.com/paper/1901.08015/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2019.

## Built on by (most cited first, 4 of 4)

- [Bayesian data fusion with shared priors](https://mlsanity.com/paper/2212.07311/) (2022)
- [A Gaussian Process-based Streaming Algorithm for Prediction of Time Series With Regimes and Outliers](https://mlsanity.com/paper/2406.00570/) (2024)
- [Policy Evaluation in Decentralized POMDPs with Belief Sharing](https://mlsanity.com/paper/2302.04151/) (2023)
- [On the Fusion Strategies for Federated Decision Making](https://mlsanity.com/paper/2303.06109/) (2023)

## Abstract (arXiv)

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.