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.

17 pages, 8 figures

References in corpus (4)

• Likelihood Consensus and Its Application to Distributed Particle Filtering
• Distributed Fusion with Multi-Bernoulli Filter based on Generalized Covariance Intersection
• Partial Consensus and Conservative Fusion of Gaussian Mixtures for Distributed PHD Fusion
• A Distributed Particle-PHD Filter with Arithmetic-Average PHD Fusion

Cited by in corpus (11)

• Fusion of Probability Density Functions
• A Distributed Particle-PHD Filter with Arithmetic-Average PHD Fusion
• Arithmetic Average Density Fusion -- Part II: Unified Derivation for Unlabeled and Labeled RFS Fusion
• Heterogeneous Multi-sensor Fusion with Random Finite Set Multi-object Densities
• Arithmetic Average Density Fusion -- Part I: Some Statistic and Information-theoretic Results
• Multi-sensor Suboptimal Fusion Student's $t$ Filter
• Formal Definitions of Conservative Probability Distribution Functions (PDFs)
• Arithmetic Average Density Fusion -- Part IV: Distributed Heterogeneous Fusion of RFS and LRFS Filters via Variational Approximation
• Distributed multi-view multi-target tracking based on CPHD filtering
• Distributed Gaussian Mixture PHD Filtering under Communication Constraints
• Efficient approximations of the multi-sensor labelled multi-Bernoulli filter