Partial Consensus and Conservative Fusion of Gaussian Mixtures for Distributed PHD Fusion

Abstract

We propose a novel consensus notion, called "partial consensus", for distributed GM-PHD (Gaussian mixture probability hypothesis density) fusion based on a peer-to-peer (P2P) sensor network, in which only highly-weighted posterior Gaussian components (GCs) are disseminated in the P2P communication for fusion while the insignificant GCs are not involved. The partial consensus does not only enjoy high efficiency in both network communication and local fusion computation, but also significantly reduces the affect of potential false data (clutter) to the filter, leading to increased signal-to-noise ratio at local sensors. Two "conservative" mixture reduction schemes are advocated for fusing the shared GCs in a fully distributed manner. One is given by pairwise averaging GCs between sensors based on Hungarian assignment and the other is merging close GCs based a new GM merging scheme. The proposed approaches have a close connection to the conservative fusion approaches known as covariance union and arithmetic mean density. In parallel, average consensus is sought on the cardinality distribution (namely the GM weight sum) among sensors. Simulations for tracking either a single target or multiple targets that simultaneously appear are presented based on a sensor network where each sensor operates a GM-PHD filter, in order to compare our approaches with the benchmark generalized covariance intersection approach. The results demonstrate that the partial, arithmetic average, consensus outperforms the complete, geometric average, consensus.

Second-order statistics analysis and comparison between arithmetic and geometric average fusion: Application to multi-sensor target tracking

“…5] such as the PHD [38] factories into a cardinality distribution on the number of objects and a localization density conditioned on the cardinality. In this case, while the AA of a sum can be straightforwardly expressed as a cascaded sum of the fusing sums (after re-weighting them) that remains in the same form [42,43]te, the fractional order exponential power of a sum does not remain as a sum of the same form, and typically approximation must be resorted to; see, e.g., [64,19,31,65,66].…”

“…In the literature, e.g.,[21,23,35,24,25,43], the most common approach to designing the fusing weights is based on minimizing the (trace or determinant of) variance of the fused estimator, which only equals the MSE when the estimator is unbiased. However, the GA does not guarantee unbiasedness as addressed.…”

Multiobject Fusion With Minimum Information Loss

“…Unfortunately, LOP cannot be directly extended to fuse the majority of RFS densities since, in general, the resulting weighted arithmetic average is not of the same type of the averaged densities (e.g., the weighted arithmetic average of MPP/IIDCP densities is not MPP/IIDCP); hence the fused density cannot be utilized as prior information for the next recursion of local MFs. However, it turns out that the PHD of the fused density equals the weighted sum of the PHDs of the local ones, which results into the so-called arithmetic fusion (AF) [36], [37] rule. The AF rule has shown its benefits compared to the GCI rule in dealing with cardinality inconsistency [38], [37] and missed detections [39].…”

“…However, it turns out that the PHD of the fused density equals the weighted sum of the PHDs of the local ones, which results into the so-called arithmetic fusion (AF) [36], [37] rule. The AF rule has shown its benefits compared to the GCI rule in dealing with cardinality inconsistency [38], [37] and missed detections [39]. In [40], it is shown that the PHD fused via AF is the one minimizing the weighted sum of Cauchy-Schwarz divergences (CSDs) [41] to local densities, but this result only holds whenever all involved local RFS densities are MPP, i.e.…”

On Arithmetic Average Fusion and Its Application for Distributed Multi-Bernoulli Multitarget Tracking

“…The combination of the average consensus approach with the RFS filters originates from the log-linear GA fusion, namely generalized covariance intersection [26]- [28] and exponential mixture density [29], [30] approach. However, the GA fusion has been observed suffering from a delay in detecting new targets [31], [32] and cardinality inconsistency [30] (e.g., underestimating the number of targets [33]), prone to missed detections [20], [25], [32], [34], [35] and vulnerable to non-overlapping fields of view [25], [36], [37]. In particular, the GA fusion may degrade [17], [25], [34], [35] with the increase of the number of fusing sensors and then does not suit large number sensor networks (LNSNs).…”