46,803 research outputs found
Likelihood Consensus and Its Application to Distributed Particle Filtering
We consider distributed state estimation in a wireless sensor network without
a fusion center. Each sensor performs a global estimation task---based on the
past and current measurements of all sensors---using only local processing and
local communications with its neighbors. In this estimation task, the joint
(all-sensors) likelihood function (JLF) plays a central role as it epitomizes
the measurements of all sensors. We propose a distributed method for computing,
at each sensor, an approximation of the JLF by means of consensus algorithms.
This "likelihood consensus" method is applicable if the local likelihood
functions of the various sensors (viewed as conditional probability density
functions of the local measurements) belong to the exponential family of
distributions. We then use the likelihood consensus method to implement a
distributed particle filter and a distributed Gaussian particle filter. Each
sensor runs a local particle filter, or a local Gaussian particle filter, that
computes a global state estimate. The weight update in each local (Gaussian)
particle filter employs the JLF, which is obtained through the likelihood
consensus scheme. For the distributed Gaussian particle filter, the number of
particles can be significantly reduced by means of an additional consensus
scheme. Simulation results are presented to assess the performance of the
proposed distributed particle filters for a multiple target tracking problem
Distributed Multi-Agent Optimization with State-Dependent Communication
We study distributed algorithms for solving global optimization problems in
which the objective function is the sum of local objective functions of agents
and the constraint set is given by the intersection of local constraint sets of
agents. We assume that each agent knows only his own local objective function
and constraint set, and exchanges information with the other agents over a
randomly varying network topology to update his information state. We assume a
state-dependent communication model over this topology: communication is
Markovian with respect to the states of the agents and the probability with
which the links are available depends on the states of the agents. In this
paper, we study a projected multi-agent subgradient algorithm under
state-dependent communication. The algorithm involves each agent performing a
local averaging to combine his estimate with the other agents' estimates,
taking a subgradient step along his local objective function, and projecting
the estimates on his local constraint set. The state-dependence of the
communication introduces significant challenges and couples the study of
information exchange with the analysis of subgradient steps and projection
errors. We first show that the multi-agent subgradient algorithm when used with
a constant stepsize may result in the agent estimates to diverge with
probability one. Under some assumptions on the stepsize sequence, we provide
convergence rate bounds on a "disagreement metric" between the agent estimates.
Our bounds are time-nonhomogeneous in the sense that they depend on the initial
starting time. Despite this, we show that agent estimates reach an almost sure
consensus and converge to the same optimal solution of the global optimization
problem with probability one under different assumptions on the local
constraint sets and the stepsize sequence
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