1,341 research outputs found
Kalman Filtering With Relays Over Wireless Fading Channels
This note studies the use of relays to improve the performance of Kalman
filtering over packet dropping links. Packet reception probabilities are
governed by time-varying fading channel gains, and the sensor and relay
transmit powers. We consider situations with multiple sensors and relays, where
each relay can either forward one of the sensors' measurements to the
gateway/fusion center, or perform a simple linear network coding operation on
some of the sensor measurements. Using an expected error covariance performance
measure, we consider optimal and suboptimal methods for finding the best relay
configuration, and power control problems for optimizing the Kalman filter
performance. Our methods show that significant performance gains can be
obtained through the use of relays, network coding and power control, with at
least 30-40 less power consumption for a given expected error covariance
specification.Comment: 7 page
Kalman Filtering Over a Packet-Dropping Network: A Probabilistic Perspective
We consider the problem of state estimation of a discrete time process over a packet-dropping network. Previous work on Kalman filtering with intermittent observations is concerned with the asymptotic behavior of E[P_k], i.e., the expected value of the error covariance, for a given packet arrival rate. We consider a different performance metric, Pr[P_k ≤ M], i.e., the probability that P_k is bounded by a given M. We consider two scenarios in the paper. In the first scenario, when the sensor sends its measurement data to the remote estimator via a packet-dropping network, we derive lower and upper bounds on Pr[P_k ≤ M]. In the second scenario, when the sensor preprocesses the measurement data and sends its local state estimate to the estimator, we show that the previously derived lower and upper bounds are equal to each other, hence we are able to provide a closed form expression for Pr[P_k ≤ M]. We also recover the results in the literature when using Pr[P_k ≤ M] as a metric for scalar systems. Examples are provided to illustrate the theory developed in the paper
Kalman Filtering Over A Packet Dropping Network: A Probabilistic Approach
We consider the problem of state estimation of a discrete time process over a packet dropping network. Previous pioneering work on Kalman filtering with intermittent observations is concerned with the asymptotic behavior of E[P_k], i.e., the expected value of the error covariance, for a given packet arrival rate. We consider a different performance metric, Pr[P_k ≤ M], i.e., the probability that P_k is bounded by a given M, and we derive lower and upper bounds on Pr[P_k ≤ M]. We are also able to recover the results in the literature when using Pr[P_k ≤ M] as a metric for scalar systems. Examples are provided to illustrate the theory developed in the paper
An Optimal Transmission Strategy for Kalman Filtering over Packet Dropping Links with Imperfect Acknowledgements
This paper presents a novel design methodology for optimal transmission
policies at a smart sensor to remotely estimate the state of a stable linear
stochastic dynamical system. The sensor makes measurements of the process and
forms estimates of the state using a local Kalman filter. The sensor transmits
quantized information over a packet dropping link to the remote receiver. The
receiver sends packet receipt acknowledgments back to the sensor via an
erroneous feedback communication channel which is itself packet dropping. The
key novelty of this formulation is that the smart sensor decides, at each
discrete time instant, whether to transmit a quantized version of either its
local state estimate or its local innovation. The objective is to design
optimal transmission policies in order to minimize a long term average cost
function as a convex combination of the receiver's expected estimation error
covariance and the energy needed to transmit the packets. The optimal
transmission policy is obtained by the use of dynamic programming techniques.
Using the concept of submodularity, the optimality of a threshold policy in the
case of scalar systems with perfect packet receipt acknowledgments is proved.
Suboptimal solutions and their structural results are also discussed. Numerical
results are presented illustrating the performance of the optimal and
suboptimal transmission policies.Comment: Conditionally accepted in IEEE Transactions on Control of Network
System
An objective based classification of aggregation techniques for wireless sensor networks
Wireless Sensor Networks have gained immense popularity in recent years due to their ever increasing capabilities and wide range of critical applications. A huge body of research efforts has been dedicated to find ways to utilize limited resources of these sensor nodes in an efficient manner. One of the common ways to minimize energy consumption has been aggregation of input data. We note that every aggregation technique has an improvement objective to achieve with respect to the output it produces. Each technique is designed to achieve some target e.g. reduce data size, minimize transmission energy, enhance accuracy etc. This paper presents a comprehensive survey of aggregation techniques that can be used in distributed manner to improve lifetime and energy conservation of wireless sensor networks. Main contribution of this work is proposal of a novel classification of such techniques based on the type of improvement they offer when applied to WSNs. Due to the existence of a myriad of definitions of aggregation, we first review the meaning of term aggregation that can be applied to WSN. The concept is then associated with the proposed classes. Each class of techniques is divided into a number of subclasses and a brief literature review of related work in WSN for each of these is also presented
Gossip Algorithms for Distributed Signal Processing
Gossip algorithms are attractive for in-network processing in sensor networks
because they do not require any specialized routing, there is no bottleneck or
single point of failure, and they are robust to unreliable wireless network
conditions. Recently, there has been a surge of activity in the computer
science, control, signal processing, and information theory communities,
developing faster and more robust gossip algorithms and deriving theoretical
performance guarantees. This article presents an overview of recent work in the
area. We describe convergence rate results, which are related to the number of
transmitted messages and thus the amount of energy consumed in the network for
gossiping. We discuss issues related to gossiping over wireless links,
including the effects of quantization and noise, and we illustrate the use of
gossip algorithms for canonical signal processing tasks including distributed
estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page
Compressive Privacy for a Linear Dynamical System
We consider a linear dynamical system in which the state vector consists of
both public and private states. One or more sensors make measurements of the
state vector and sends information to a fusion center, which performs the final
state estimation. To achieve an optimal tradeoff between the utility of
estimating the public states and protection of the private states, the
measurements at each time step are linearly compressed into a lower dimensional
space. Under the centralized setting where all measurements are collected by a
single sensor, we propose an optimization problem and an algorithm to find the
best compression matrix. Under the decentralized setting where measurements are
made separately at multiple sensors, each sensor optimizes its own local
compression matrix. We propose methods to separate the overall optimization
problem into multiple sub-problems that can be solved locally at each sensor.
We consider the cases where there is no message exchange between the sensors;
and where each sensor takes turns to transmit messages to the other sensors.
Simulations and empirical experiments demonstrate the efficiency of our
proposed approach in allowing the fusion center to estimate the public states
with good accuracy while preventing it from estimating the private states
accurately
On the steady-state performance of Kalman filtering with intermittent observations for stable systems
Many recent problems in distributed estimation and control reduce to estimating the state of a dynamical system using sensor measurements that are transmitted across a lossy network. A framework for analyzing such systems was proposed in and called Kalman filtering with intermittent observations. The performance of such a system, i.e., the error covariance matrix, is governed by the solution of a matrix-valued random Riccati recursion. Unfortunately, to date, the tools for analyzing such recursions are woefully lacking, ostensibly because the recursions are both nonlinear and random, and hence intractable if one wants to analyze them exactly. In this paper, we extend some of the large random matrix techniques first introduced in to Kalman filtering with intermittent observations. For systems with a stable system matrix and i.i.d. time-varying measurement matrices, we obtain explicit equations that allow one to compute the asymptotic eigendistribution of the error covariance matrix. Simulations show excellent agreement between the theoretical and empirical results for systems with as low as n = 10, 20 states. Extending the results to unstable system matrices and time-invariant measurement matrices is currently under investigation
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