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Motion Planning for Optimal Information Gathering in Opportunistic Navigation Systems
Motion planning for optimal information gathering in an opportunistic navigation (OpNav)
environment is considered. An OpNav environment can be thought of as a radio
frequency signal landscape within which a receiver locates itself in space and time by extracting
information from ambient signals of opportunity (SOPs). The receiver is assumed
to draw only pseudorange-type observations from the SOPs, and such observations are
fused through an estimator to produce an estimate of the receiver’s own states. Since
not all SOP states in the OpNav environment may be known a priori, the receiver must
estimate the unknown SOP states of interest simultaneously with its own states. In this
work, the following problem is studied. A receiver with no a priori knowledge about its
own states is dropped in an unknown, yet observable, OpNav environment. Assuming that
the receiver can prescribe its own trajectory, what motion planning strategy should the
receiver adopt in order to build a high-fidelity map of the OpNav signal landscape, while
simultaneously localizing itself within this map in space and time? To answer this question,
first, the minimum conditions under which the OpNav environment is fully observable are
established, and the need for receiver maneuvering to achieve full observability is highlighted.
Then, motivated by the fact that not all trajectories a receiver may take in the
environment are equally beneficial from an information gathering point of view, a strategy
for planning the motion of the receiver is proposed. The strategy is formulated in a
coupled estimation and optimal control framework of a gradually identified system, where
optimality is defined through various information-theoretic measures. Simulation results
are presented to illustrate the improvements gained from adopting the proposed strategy
over random and pre-defined receiver trajectories.Aerospace Engineering and Engineering Mechanic
Observability and nonlinear filtering
This paper develops a connection between the asymptotic stability of
nonlinear filters and a notion of observability. We consider a general class of
hidden Markov models in continuous time with compact signal state space, and
call such a model observable if no two initial measures of the signal process
give rise to the same law of the observation process. We demonstrate that
observability implies stability of the filter, i.e., the filtered estimates
become insensitive to the initial measure at large times. For the special case
where the signal is a finite-state Markov process and the observations are of
the white noise type, a complete (necessary and sufficient) characterization of
filter stability is obtained in terms of a slightly weaker detectability
condition. In addition to observability, the role of controllability in filter
stability is explored. Finally, the results are partially extended to
non-compact signal state spaces
Space-Time Sampling for Network Observability
Designing sparse sampling strategies is one of the important components in
having resilient estimation and control in networked systems as they make
network design problems more cost-effective due to their reduced sampling
requirements and less fragile to where and when samples are collected. It is
shown that under what conditions taking coarse samples from a network will
contain the same amount of information as a more finer set of samples. Our goal
is to estimate initial condition of linear time-invariant networks using a set
of noisy measurements. The observability condition is reformulated as the frame
condition, where one can easily trace location and time stamps of each sample.
We compare estimation quality of various sampling strategies using estimation
measures, which depend on spectrum of the corresponding frame operators. Using
properties of the minimal polynomial of the state matrix, deterministic and
randomized methods are suggested to construct observability frames. Intrinsic
tradeoffs assert that collecting samples from fewer subsystems dictates taking
more samples (in average) per subsystem. Three scalable algorithms are
developed to generate sparse space-time sampling strategies with explicit error
bounds.Comment: Submitted to IEEE TAC (Revised Version
Convergence Rate Analysis of Distributed Gossip (Linear Parameter) Estimation: Fundamental Limits and Tradeoffs
The paper considers gossip distributed estimation of a (static) distributed
random field (a.k.a., large scale unknown parameter vector) observed by
sparsely interconnected sensors, each of which only observes a small fraction
of the field. We consider linear distributed estimators whose structure
combines the information \emph{flow} among sensors (the \emph{consensus} term
resulting from the local gossiping exchange among sensors when they are able to
communicate) and the information \emph{gathering} measured by the sensors (the
\emph{sensing} or \emph{innovations} term.) This leads to mixed time scale
algorithms--one time scale associated with the consensus and the other with the
innovations. The paper establishes a distributed observability condition
(global observability plus mean connectedness) under which the distributed
estimates are consistent and asymptotically normal. We introduce the
distributed notion equivalent to the (centralized) Fisher information rate,
which is a bound on the mean square error reduction rate of any distributed
estimator; we show that under the appropriate modeling and structural network
communication conditions (gossip protocol) the distributed gossip estimator
attains this distributed Fisher information rate, asymptotically achieving the
performance of the optimal centralized estimator. Finally, we study the
behavior of the distributed gossip estimator when the measurements fade (noise
variance grows) with time; in particular, we consider the maximum rate at which
the noise variance can grow and still the distributed estimator being
consistent, by showing that, as long as the centralized estimator is
consistent, the distributed estimator remains consistent.Comment: Submitted for publication, 30 page
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