3 research outputs found
A Finite-Time Algorithm for the Distributed Tracking of Maneuvering Target
This paper presents a novel distributed algorithm for tracking a maneuvering
target using bearing or direction of arrival measurements collected by a
networked sensor array. The proposed approach is built on the dynamic
average-consensus algorithm, which allows a networked group of agents (nodes)
to reach consensus on the global average of a set of local time-varying signals
in a distributed fashion. Since the average-consensus error corresponding to
the presented dynamic average-consensus algorithm converges to zero in finite
time, the proposed distributed algorithm guarantees that the tracking error
converges to zero in finite time. Numerical simulations are provided to
illustrate the effectiveness of the proposed algorithm
Distributed Algorithms that Solve Boolean Equations with Local and Differential Privacies
In this paper, we propose distributed algorithms that solve a system of
Boolean equations over a network, where each node in the network possesses only
one Boolean equation from the system. The Boolean equation assigned at any
particular node is a {\em private} equation known to this node only, and the
nodes aim to compute the exact set of solutions to the system without
exchanging their local equations. We show that each private Boolean equation
can be locally lifted to a linear algebraic equation under a basis of Boolean
vectors, leading to a network linear equation that is distributedly solvable
using existing distributed linear equation algorithms as a subroutine. A number
of exact or approximate solutions to the induced linear equation are then
computed at each node from different initial values. The solutions to the
original Boolean equations are eventually computed locally via a Boolean vector
search algorithm. We prove that given solvable Boolean equations, when the
initial values of the nodes for the distributed linear equation solving step
are i.i.d selected according to a uniform distribution in a high-dimensional
cube, our algorithms return the exact solution set of the Boolean equations at
each node with high probability. Furthermore, we present an algorithm for
distributed verification of the satisfiability of Boolean equations, and prove
its correctness. Finally, we show that by utilizing linear equation solvers
with differential privacy to replace the in-network computing routines, the
overall distributed Boolean equation algorithms can be made differentially
private. Under the standard Laplace mechanism, we prove an explicit level of
noises that can be injected in the linear equation steps for ensuring a
prescribed level of differential privacy.Comment: 34 pages, 5 figure
Distributed Linear Equations over Random Networks
Distributed linear algebraic equation over networks, where nodes hold a part
of problem data and cooperatively solve the equation via node-to-node
communications, is a basic distributed computation task receiving an increasing
research attention. Communications over a network have a stochastic nature,
with both temporal and spatial dependence due to link failures, packet dropouts
or node recreation, etc. In this paper, we study the convergence and
convergence rate of distributed linear equation protocols over a -mixing
random network, where the temporal and spatial dependencies between the
node-to-node communications are allowed. When the network linear equation
admits exact solutions, we prove the mean-squared exponential convergence rate
of the distributed projection consensus algorithm, while the lower and upper
bound estimations of the convergence rate are also given for independent and
identically distributed (i.i.d.) random graphs. Motivated by the randomized
Kaczmarz algorithm, we also propose a distributed randomized projection
consensus algorithm, where each node randomly selects one row of local linear
equations for projection per iteration, and establish an exponential
convergence rate for this algorithm. When the network linear equation admits no
exact solution, we prove that a distributed gradient-descent-like algorithm
with diminishing step-sizes can drive all nodes' states to a least-squares
solution at a sublinear rate. These results collectively illustrate that
distributed computations may overcome communication correlations if the
prototype algorithms enjoy certain contractive properties or are designed with
suitable parameters.Comment: 35 page