21 research outputs found
Near-Optimal Sensor Scheduling for Batch State Estimation: Complexity, Algorithms, and Limits
In this paper, we focus on batch state estimation for linear systems. This
problem is important in applications such as environmental field estimation,
robotic navigation, and target tracking. Its difficulty lies on that limited
operational resources among the sensors, e.g., shared communication bandwidth
or battery power, constrain the number of sensors that can be active at each
measurement step. As a result, sensor scheduling algorithms must be employed.
Notwithstanding, current sensor scheduling algorithms for batch state
estimation scale poorly with the system size and the time horizon. In addition,
current sensor scheduling algorithms for Kalman filtering, although they scale
better, provide no performance guarantees or approximation bounds for the
minimization of the batch state estimation error. In this paper, one of our
main contributions is to provide an algorithm that enjoys both the estimation
accuracy of the batch state scheduling algorithms and the low time complexity
of the Kalman filtering scheduling algorithms. In particular: 1) our algorithm
is near-optimal: it achieves a solution up to a multiplicative factor 1/2 from
the optimal solution, and this factor is close to the best approximation factor
1/e one can achieve in polynomial time for this problem; 2) our algorithm has
(polynomial) time complexity that is not only lower than that of the current
algorithms for batch state estimation; it is also lower than, or similar to,
that of the current algorithms for Kalman filtering. We achieve these results
by proving two properties for our batch state estimation error metric, which
quantifies the square error of the minimum variance linear estimator of the
batch state vector: a) it is supermodular in the choice of the sensors; b) it
has a sparsity pattern (it involves matrices that are block tri-diagonal) that
facilitates its evaluation at each sensor set.Comment: Correction of typos in proof
Estimation Diversity and Energy Efficiency in Distributed Sensing
Distributed estimation based on measurements from multiple wireless sensors
is investigated. It is assumed that a group of sensors observe the same
quantity in independent additive observation noises with possibly different
variances. The observations are transmitted using amplify-and-forward (analog)
transmissions over non-ideal fading wireless channels from the sensors to a
fusion center, where they are combined to generate an estimate of the observed
quantity. Assuming that the Best Linear Unbiased Estimator (BLUE) is used by
the fusion center, the equal-power transmission strategy is first discussed,
where the system performance is analyzed by introducing the concept of
estimation outage and estimation diversity, and it is shown that there is an
achievable diversity gain on the order of the number of sensors. The optimal
power allocation strategies are then considered for two cases: minimum
distortion under power constraints; and minimum power under distortion
constraints. In the first case, it is shown that by turning off bad sensors,
i.e., sensors with bad channels and bad observation quality, adaptive power
gain can be achieved without sacrificing diversity gain. Here, the adaptive
power gain is similar to the array gain achieved in Multiple-Input
Single-Output (MISO) multi-antenna systems when channel conditions are known to
the transmitter. In the second case, the sum power is minimized under
zero-outage estimation distortion constraint, and some related energy
efficiency issues in sensor networks are discussed.Comment: To appear at IEEE Transactions on Signal Processin
The Sensing Capacity of Sensor Networks
This paper demonstrates fundamental limits of sensor networks for detection
problems where the number of hypotheses is exponentially large. Such problems
characterize many important applications including detection and classification
of targets in a geographical area using a network of sensors, and detecting
complex substances with a chemical sensor array. We refer to such applications
as largescale detection problems. Using the insight that these problems share
fundamental similarities with the problem of communicating over a noisy
channel, we define a quantity called the sensing capacity and lower bound it
for a number of sensor network models. The sensing capacity expression differs
significantly from the channel capacity due to the fact that a fixed sensor
configuration encodes all states of the environment. As a result, codewords are
dependent and non-identically distributed. The sensing capacity provides a
bound on the minimal number of sensors required to detect the state of an
environment to within a desired accuracy. The results differ significantly from
classical detection theory, and provide an ntriguing connection between sensor
networks and communications. In addition, we discuss the insight that sensing
capacity provides for the problem of sensor selection.Comment: Submitted to IEEE Transactions on Information Theory, November 200
Decentralized Random-Field Estimation for Sensor Networks Using Quantized Spatially Correlated Data and Fusion-Center Feedback
In large-scale wireless sensor networks, sensor-processor elements (nodes) are densely deployed to monitor the environment; consequently, their observations form a random field that is highly correlated in space. We consider a fusion sensor-network architecture where, due to the bandwidth and energy constraints, the nodes transmit quantized data to a fusion center. The fusion center provides feedback by broadcasting summary information to the nodes. In addition to saving energy, this feedback ensures reliability and robustness to node and fusion-center failures. We assume that the sensor observations follow a linear-regression model with known spatial covariances between any two locations within a region of interest. We propose a Bayesian framework for adaptive quantization, fusion-center feedback, and estimation of the random field and its parameters. We also derive a simple suboptimal scheme for estimating the unknown parameters, apply our estimation approach to the no-feedback scenario, discuss field prediction at arbitrary locations within the region of interest, and present numerical examples demonstrating the performance of the proposed methods
Towards Optimally Efficient Field Estimation with Threshold-Based Pruning in Real Robotic Sensor Networks
The efficiency of distributed sensor networks depends on an optimal trade-off between the usage of resources and data quality. The work in this paper addresses the problem of optimizing this trade-off in a self-configured distributed robotic sensor network, with respect to a user-defined objective function. We investigate a quadtree network topology and implement a fully distributed threshold-based field estimation algorithm. Simulations with field data as well as real robot experiments are performed, validating our distributed control strategy and evaluating the threshold-based formula for real world scenarios. We propose a theoretical analysis that predicts the system’s behavior in real world case studies. The experiments and this prediction show very good correspondence, enabling the accurate employment of the objective function, optimizing the trade-off based on user needs