Cooperative Parameter Estimation on the Unit Sphere Using a Network of Diffusion Particle Filters

Cooperative Parameter Tracking on the Unit Sphere Using Distributed Adapt-Then-Combine Particle Filters and Parallel Transport

“…Those situations arise naturally due to geometric constraints on the states or parameters in different fields such as e.g. attitude or pose estimation in navigation or robotics [1][2][3], computer vision [4], communication channel identification [5,6], and tracking problems using microphone arrays [7]. Moreover, modern engineering systems often involve cooperation between multiple agents to execute a common global task [8][9][10].…”

“…In [6], we introduced two new distributed network particle filters (PFs) [11] to perform cooperative tracking of a timevarying state vector that evolved on the unit sphere 1 S L−1 This work was supported by grant #18/26191-0, São Paulo Research Foundation (FAPESP). 1 For simplicity, we use the terms sphere and plane respectively to refer to hyperspheres and hyperplanes in R L when L > 3.…”

“…The two proposed algorithms were based on the techniques of Random Exchange (RndEx) [12,13] and Adapt-then-Combine (ATC) [14,15] diffusion, respectively. Differently, however, from [12] and [14], that operate on a linear, Gaussian framework, the algorithms in [6] were formulated in a more general Bayesian framework, see e.g. [16] and [17].…”

“…[16] and [17]. Furthermore, to account for the fact that, unlike in [9,[12][13][14][15], the state vector in [6] (as in [18]) was constrained to S L−1 , we used a Von Mises-Fisher (vMF) distribution [19] to model the dynamic evolution of the state on the manifold.…”

“…That is followed by a combine step, where those local updated beliefs are merged within local neighborhoods using an optimal information-theoretic criterion [16,17]. In [6], the adapt step is implemented at each mode using a marginal particle filter [20,21]. The combine step, in turn, is implemented using methods of directional statistics [22] to build vMF parametric approximations of the local updated posterior probability density functions (p.d.f.…”