2,531 research outputs found
Gossip and Distributed Kalman Filtering: Weak Consensus under Weak Detectability
The paper presents the gossip interactive Kalman filter (GIKF) for
distributed Kalman filtering for networked systems and sensor networks, where
inter-sensor communication and observations occur at the same time-scale. The
communication among sensors is random; each sensor occasionally exchanges its
filtering state information with a neighbor depending on the availability of
the appropriate network link. We show that under a weak distributed
detectability condition:
1. the GIKF error process remains stochastically bounded, irrespective of the
instability properties of the random process dynamics; and
2. the network achieves \emph{weak consensus}, i.e., the conditional
estimation error covariance at a (uniformly) randomly selected sensor converges
in distribution to a unique invariant measure on the space of positive
semi-definite matrices (independent of the initial state.)
To prove these results, we interpret the filtered states (estimates and error
covariances) at each node in the GIKF as stochastic particles with local
interactions. We analyze the asymptotic properties of the error process by
studying as a random dynamical system the associated switched (random) Riccati
equation, the switching being dictated by a non-stationary Markov chain on the
network graph.Comment: Submitted to the IEEE Transactions, 30 pages
Efficient Constellation-Based Map-Merging for Semantic SLAM
Data association in SLAM is fundamentally challenging, and handling ambiguity
well is crucial to achieve robust operation in real-world environments. When
ambiguous measurements arise, conservatism often mandates that the measurement
is discarded or a new landmark is initialized rather than risking an incorrect
association. To address the inevitable `duplicate' landmarks that arise, we
present an efficient map-merging framework to detect duplicate constellations
of landmarks, providing a high-confidence loop-closure mechanism well-suited
for object-level SLAM. This approach uses an incrementally-computable
approximation of landmark uncertainty that only depends on local information in
the SLAM graph, avoiding expensive recovery of the full system covariance
matrix. This enables a search based on geometric consistency (GC) (rather than
full joint compatibility (JC)) that inexpensively reduces the search space to a
handful of `best' hypotheses. Furthermore, we reformulate the commonly-used
interpretation tree to allow for more efficient integration of clique-based
pairwise compatibility, accelerating the branch-and-bound max-cardinality
search. Our method is demonstrated to match the performance of full JC methods
at significantly-reduced computational cost, facilitating robust object-based
loop-closure over large SLAM problems.Comment: Accepted to IEEE International Conference on Robotics and Automation
(ICRA) 201
Trusted Noise in Continuous-Variable Quantum Key Distribution: a Threat and a Defense
We address the role of the phase-insensitive trusted preparation and
detection noise in the security of a continuous-variable quantum key
distribution, considering the Gaussian protocols on the basis of coherent and
squeezed states and studying them in the conditions of Gaussian lossy and noisy
channels. The influence of such a noise on the security of Gaussian quantum
cryptography can be crucial, even despite the fact that a noise is trusted, due
to a strongly nonlinear behavior of the quantum entropies involved in the
security analysis. We recapitulate the known effect of the preparation noise in
both direct and reverse-reconciliation protocols, as well as the detection
noise in the reverse-reconciliation scenario. As a new result, we show the
negative role of the trusted detection noise in the direct-reconciliation
scheme. We also describe the role of the trusted preparation or detection noise
added at the reference side of the protocols in improving the robustness of the
protocols to the channel noise, confirming the positive effect for the
coherent-state reverse-reconciliation protocol. Finally, we address the
combined effect of trusted noise added both in the source and the detector.Comment: 25 pages, 9 figure
Starling flock networks manage uncertainty in consensus at low cost
Flocks of starlings exhibit a remarkable ability to maintain cohesion as a
group in highly uncertain environments and with limited, noisy information.
Recent work demonstrated that individual starlings within large flocks respond
to a fixed number of nearest neighbors, but until now it was not understood why
this number is seven. We analyze robustness to uncertainty of consensus in
empirical data from multiple starling flocks and show that the flock
interaction networks with six or seven neighbors optimize the trade-off between
group cohesion and individual effort. We can distinguish these numbers of
neighbors from fewer or greater numbers using our systems-theoretic approach to
measuring robustness of interaction networks as a function of the network
structure, i.e., who is sensing whom. The metric quantifies the disagreement
within the network due to disturbances and noise during consensus behavior and
can be evaluated over a parameterized family of hypothesized sensing strategies
(here the parameter is number of neighbors). We use this approach to further
show that for the range of flocks studied the optimal number of neighbors does
not depend on the number of birds within a flock; rather, it depends on the
shape, notably the thickness, of the flock. The results suggest that robustness
to uncertainty may have been a factor in the evolution of flocking for
starlings. More generally, our results elucidate the role of the interaction
network on uncertainty management in collective behavior, and motivate the
application of our approach to other biological networks.Comment: 19 pages, 3 figures, 9 supporting figure
Distributed Detection over Random Networks: Large Deviations Performance Analysis
We study the large deviations performance, i.e., the exponential decay rate
of the error probability, of distributed detection algorithms over random
networks. At each time step each sensor: 1) averages its decision variable
with the neighbors' decision variables; and 2) accounts on-the-fly for its new
observation. We show that distributed detection exhibits a "phase change"
behavior. When the rate of network information flow (the speed of averaging) is
above a threshold, then distributed detection is asymptotically equivalent to
the optimal centralized detection, i.e., the exponential decay rate of the
error probability for distributed detection equals the Chernoff information.
When the rate of information flow is below a threshold, distributed detection
achieves only a fraction of the Chernoff information rate; we quantify this
achievable rate as a function of the network rate of information flow.
Simulation examples demonstrate our theoretical findings on the behavior of
distributed detection over random networks.Comment: 30 pages, journal, submitted on December 3rd, 201
Online Convex Optimization Using Predictions
Making use of predictions is a crucial, but under-explored, area of online algorithms. This paper studies a class of online optimization problems where we have external noisy predictions available. We propose a stochastic prediction error model that generalizes prior models in the learning and stochastic control communities, incorporates correlation among prediction errors, and captures the fact that predictions improve as time passes. We prove that achieving sublinear regret and constant competitive ratio for online algorithms requires the use of an unbounded prediction window in adversarial settings, but that under more realistic stochastic prediction error models it is possible to use Averaging Fixed Horizon Control (AFHC) to simultaneously achieve sublinear regret and constant competitive ratio in expectation using only a constant-sized prediction window. Furthermore, we show that the performance of AFHC is tightly concentrated around its mean
A path planning and path-following control framework for a general 2-trailer with a car-like tractor
Maneuvering a general 2-trailer with a car-like tractor in backward motion is
a task that requires significant skill to master and is unarguably one of the
most complicated tasks a truck driver has to perform. This paper presents a
path planning and path-following control solution that can be used to
automatically plan and execute difficult parking and obstacle avoidance
maneuvers by combining backward and forward motion. A lattice-based path
planning framework is developed in order to generate kinematically feasible and
collision-free paths and a path-following controller is designed to stabilize
the lateral and angular path-following error states during path execution. To
estimate the vehicle state needed for control, a nonlinear observer is
developed which only utilizes information from sensors that are mounted on the
car-like tractor, making the system independent of additional trailer sensors.
The proposed path planning and path-following control framework is implemented
on a full-scale test vehicle and results from simulations and real-world
experiments are presented.Comment: Preprin
Gaussian Post-selection for Continuous Variable Quantum Cryptography
We extend the security proof for continuous variable quantum key distribution
protocols using post selection to account for arbitrary eavesdropping attacks
by employing the concept of an equivalent protocol where the post-selection is
implemented as a series of quantum operations including a virtual distillation.
We introduce a particular `Gaussian' post selection and demonstrate that the
security can be calculated using only experimentally accessible quantities.
Finally we explicitly evaluate the performance for the case of a noisy Gaussian
channel in the limit of unbounded key length and find improvements over all
pre-existing continuous variable protocols in realistic regimes.Comment: 4+4 pages. arXiv admin note: substantial text overlap with
arXiv:1106.082
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