Best Fit of Mixture For Distributed Poisson Multi-Bernoulli Mixture Filtering

Abstract

<div>The Poisson multi-Bernoulli mixture (PMBM) filter is extended for distributed implementation using a wireless sensor network. At the core of the proposed networking approach, the PMBM posterior is decomposed into two parts corresponding to the undetected and detected targets, respectively. Fusion is motivated to be performed with regard to the latter only which is represented by MBM based on a distributed flooding algorithm for internode communication, which iteratively shares the MBMs between neighbor sensors. Then, a suboptimal “best-fit-ofmixture” principle is followed at each local sensor to find a MBM that best fits the mixture of MBMs aggregated from distinct sensors, leading to an arithmetic average (AA) of these MBMs. We prove the exact closure of the MBM-AA fusion and discuss its sub-optimality and limitations. Simulation demonstrates the effectiveness and limitations of our approach. </div>

Recent advances in multisensor multitarget tracking using random finite set

“…This best-fit property of both averaging-fusion rules has long been recognized (Heskes, 1998;Hurley, 2002;Abbas, 2009;Da et al, 2019;Li TC et al, 2019e), and has been elaborately emphasized using new terminologies (Gostar et al, 2017a;Gao et al, 2020b). It is, however, important to note that this best fit is suboptimal and what is fitted is a mixture of the fusing local posteriors, not the true multisensor posterior (Li TC and Da, 2020). The former can be viewed as a rule-of-the-thumb substitute for the latter.…”

“…The motivation behind these formulations (Eqs. (28)-(31)) is that both averaging-fusion approaches provide a best fit of the mixture of the fusing distributions (Li TC and Da, 2020). This best-fit property of both averaging-fusion rules has long been recognized (Heskes, 1998;Hurley, 2002;Abbas, 2009;Da et al, 2019;Li TC et al, 2019e), and has been elaborately emphasized using new terminologies (Gostar et al, 2017a;Gao et al, 2020b).…”

“…In all of these cases, AA fusion tends to be more robust in spite of having a larger variance, since it makes better use of the correct parts of the information provided by the local densities. This is the benefit of the "best-fit-of-mixture" performed by AA fusion (Li TC and Da, 2020), which preserves all information from all fusing posteriors. Indeed, the common merging operation and AA fusion are closely related (Li TC et al, 2017c, 2019d.…”

“…Various strategies have been employed to seek the best fusion performance while reducing the cost in both communication and fusion computation. (Mahler, 2009a) Measurement clustering (Li TC et al, 2018a PCAM filter (Mahler, 2010;Ouyang and Ji, 2011) Multisensor Bernoulli filter (Hlinka et al, 2012;Papa et al, 2018) Multisensor PHD filter (Mahler, 2009a(Mahler, , 2009bDelande et al, 2010Delande et al, , 2011) Multisensor CPHD filter (Nannuru et al, 2016) Multisensor MeMber filter (Saucan et al, 2017) Multisensor GLMB filter (Fantacci and Papi, 2016;Wei et al, 2016; AA (best fit of mixture) GA (GCI/EMD) Multisensor MPD/moments fusion Track-to-track fusion based PHD filter without feedback to filter (Li TC et al, 2017a) AA-Bernoulli (Da et al, 2019;Li TC et al, 2019b) AA-PHD (Li TC et al, 2017c, 2019c, 2019dLi TC and Hlawatsch, 2017;Gostar et al, 2017a) AA-CPHD (Yu et al, 2016;Da et al 2020b;Gao et al, 2020b) AA-MeMber (Li TC et al, 2020b) AA-GLMB/LMB (Gao et al, 2019a) AA-PMBM (Li TC and Da, 2020) GA-Bernoulli (Clark et al, 2010;Guld-ogan, 2014) GA-PHD (Clark et al, 2010; al., 2013) GA-CPHD (Clark et al, 2010;Battistelli et al, 2013) GA-MeMber (Wang et al 2017) GA-GLMB/LMB…”

“…According to the best fit of mixture principle (Li TC and Da, 2020), the optimal fusion weights w w w = [w 1 , w 2 , . .…”