4 research outputs found
Submodularity and Optimality of Fusion Rules in Balanced Binary Relay Trees
We study the distributed detection problem in a balanced binary relay tree,
where the leaves of the tree are sensors generating binary messages. The root
of the tree is a fusion center that makes the overall decision. Every other
node in the tree is a fusion node that fuses two binary messages from its child
nodes into a new binary message and sends it to the parent node at the next
level. We assume that the fusion nodes at the same level use the same fusion
rule. We call a string of fusion rules used at different levels a fusion
strategy. We consider the problem of finding a fusion strategy that maximizes
the reduction in the total error probability between the sensors and the fusion
center. We formulate this problem as a deterministic dynamic program and
express the solution in terms of Bellman's equations. We introduce the notion
of stringsubmodularity and show that the reduction in the total error
probability is a stringsubmodular function. Consequentially, we show that the
greedy strategy, which only maximizes the level-wise reduction in the total
error probability, is within a factor of the optimal strategy in terms of
reduction in the total error probability
Stochastic Sensor Scheduling via Distributed Convex Optimization
In this paper, we propose a stochastic scheduling strategy for estimating the
states of N discrete-time linear time invariant (DTLTI) dynamic systems, where
only one system can be observed by the sensor at each time instant due to
practical resource constraints. The idea of our stochastic strategy is that a
system is randomly selected for observation at each time instant according to a
pre-assigned probability distribution. We aim to find the optimal pre-assigned
probability in order to minimize the maximal estimate error covariance among
dynamic systems. We first show that under mild conditions, the stochastic
scheduling problem gives an upper bound on the performance of the optimal
sensor selection problem, notoriously difficult to solve. We next relax the
stochastic scheduling problem into a tractable suboptimal quasi-convex form. We
then show that the new problem can be decomposed into coupled small convex
optimization problems, and it can be solved in a distributed fashion. Finally,
for scheduling implementation, we propose centralized and distributed
deterministic scheduling strategies based on the optimal stochastic solution
and provide simulation examples.Comment: Proof errors and typos are fixed. One section is removed from last
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