A hyperparameter consensus method for agreement under uncertainty

Fraser, Cameron S. R.; Bertuccelli, Luca F.; Choi, Han‐Lim; How, Jonathan P.

doi:10.1016/j.automatica.2011.11.003

Cited by 14 publications

(14 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proof of convergence for each Gaussian element in the joint distribution approximation closely follows in our work, even though our algorithms apply to a larger class of Bayesian filters (e.g., map merging [2]). This generality is shared by the approach of Fraser et al [5] using hyperparameters. However, our work enables the early termination of the consensus-based algorithm without the risk of 'double-counting' any single observation, even when the maximum in/out degree and the number of robots are unknown.…”

Section: Introductionmentioning

confidence: 94%

Distributed Approximation of Joint Measurement Distributions Using Mixtures of Gaussians

Julian¹,

Smith²,

Rus³

2012

Robotics: Science and Systems VIII

View full text Add to dashboard Cite

Abstract-This paper presents algorithms to distributively approximate the continuous probability distribution that describes the fusion of sensor measurements from many networked robots. Each robot forms a weighted mixture of scaled Gaussians to represent the continuous measurement distribution (i.e., likelihood) of its local observation. From this mixture set, each robot then draws samples of Gaussian elements to enable the use of a consensus-based algorithm that evolves the corresponding canonical parameters. We show that these evolved parameters form a distribution that converges weakly to the joint of all the robots' unweighted mixture distributions, which itself converges weakly to the joint measurement distribution as more system resources are allocated. The innovation of this work is the combination of sample-based sensor fusion with the notion of pre-convergence termination without the risk of 'double-counting' any single observation. We also derive bounds and convergence rates for the approximated joint measurement distribution, specifically the elements of its information vectors and the eigenvalues of its information matrices. Most importantly, these performance guarantees do not come at a significant cost of complexity, since computational and communication complexity of the canonical parameters scales quadratically with respect to the Gaussian dimension, linearly with respect to the number of samples, and constant with respect to the number of robots. Results from numerical simulations for object localization are discussed using both Gaussians and mixtures of Gaussians.

show abstract

Section: Introductionmentioning

confidence: 94%

Distributed Approximation of Joint Measurement Distributions Using Mixtures of Gaussians

Julian¹,

Smith²,

Rus³

2012

Robotics: Science and Systems VIII

View full text Add to dashboard Cite

show abstract

“…In particular, [12] generates informationtheoretically-optimal weights for the LogOP scheme. Combining probability distributions within the exponential family (i.e., probability distributions that can be expressed as exponential functions) is discussed in [13,14]. In the distributed estimation algorithm presented in [16] as well as in our prior work [17,18], the agents combine their local posterior probability distributions using the consensus algorithm, where the multiple consensus loops within each time step are executed much faster than the original time steps of the Bayesian filter.…”

Section: Introductionmentioning

confidence: 99%

“…The third category of algorithms estimates the posterior probability distribution of the states of the target [11,12,13,14,15,16,17,18]. This category forms the most general class of distributed estimation algorithms because these algorithms can be used for estimation over continuous domains, and can incorporate nonlinear target dynamics, heterogeneous nonlinear measure-ment models, and non-Gaussian uncertainties.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Distributed Bayesian filtering using logarithmic opinion pool for dynamic sensor networks

Bandyopadhyay

Chung

2018

Automatica

View full text Add to dashboard Cite

The discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented for the problem of tracking a target dynamic model using a time-varying network of heterogeneous sensing agents. In the DBF algorithm, the sensing agents combine their normalized likelihood functions in a distributed manner using the logarithmic opinion pool and the dynamic average consensus algorithm. We show that each agent's estimated likelihood function globally exponentially converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. We rigorously characterize the convergence, stability, and robustness properties of the DBF algorithm. Moreover, we provide an explicit bound on the time step size of the DBF algorithm that depends on the time-scale of the target dynamics, the desired convergence error bound, and the modeling and communication error bounds. Furthermore, the DBF algorithm for linear-Gaussian models is cast into a modified form of the Kalman information filter. The performance and robust properties of the DBF algorithm are validated using numerical simulations.

show abstract

“…Many distributed estimation algorithms use the notion of consensus to estimate the parameters/states of interest (e.g., [9][10][11][12][13][14][15][16]). In a typical consensus algorithm, an agent attempts to reach an agreement with its neighbors by performing a sequential update that brings its estimate closer to the states/parameters of (a subset of) all of its neighbors.…”

Section: Introductionmentioning

confidence: 99%

Efficient distributed sensing using adaptive censoring based inference

Chowdhary

How

2013

2013 American Control Conference

Self Cite

View full text Add to dashboard Cite

In many distributed sensing applications it is likely that only a few agents will have valuable information at any given time. Since wireless communication between agents is resource-intensive, it is important to ensure that the communication effort is focused on communicating valuable information from informative agents. This paper presents communication-efficient distributed sensing algorithms that avoid network cluttering by having only agents with high Value of Information (VoI) broadcast their measurements to the network, while others censor themselves. A novel contribution of the presented distributed estimation algorithm is the use of an adaptively adjusted VoI threshold to determine which agents are informative. This adaptation enables the team to better balance between the communication cost incurred and the long-term accuracy of the estimation. Theoretical results are presented establishing the almost sure convergence of the communication cost and estimation error to zero for distributions in the exponential family. Furthermore, validation through numerical simulations and real datasets show that the new VoI-based algorithms can yield improved parameter estimates than those achieved by previously published hyperparameter consensus algorithms while incurring only a fraction of the communication cost.

show abstract

A hyperparameter consensus method for agreement under uncertainty

Cited by 14 publications

References 17 publications

Distributed Approximation of Joint Measurement Distributions Using Mixtures of Gaussians

Distributed Approximation of Joint Measurement Distributions Using Mixtures of Gaussians

Distributed Bayesian filtering using logarithmic opinion pool for dynamic sensor networks

Efficient distributed sensing using adaptive censoring based inference

Contact Info

Product

Resources

About