arXiv subjects

Pramod K. Varshney

Publications and source records attributed to Pramod K. Varshney.

140 records · Page 8Linked to original sources

arXiv2013

Sensor Selection Based on Generalized Information Gain for Target Tracking in Large Sensor Networks

In this paper, sensor selection problems for target tracking in large sensor networks with linear equality or inequality constraints are considered. First, we derive an equivalent Kalman filter for sensor selection, i.e., generalized information filter. Then, under a regularity condition, we prove that the multistage look-ahead policy that minimizes either the final or the average estimation error covariances of next multiple time steps is equivalent to a myopic sensor selection policy that maximizes the trace of the generalized information gain at each time step. Moreover, when the measurement noises are uncorrelated between sensors, the optimal solution can be obtained analytically for sensor selection when constraints are temporally separable. When constraints are temporally inseparable, sensor selections can be obtained by approximately solving a linear programming problem so that the sensor selection problem for a large sensor network can be dealt with quickly. Although there is no guarantee that the gap between the performance of the chosen subset and the performance bound is always small, numerical examples suggest that the algorithm is near-optimal in many cases. Finally, when the measurement noises are correlated between sensors, the sensor selection problem with temporally inseparable constraints can be relaxed to a Boolean quadratic programming problem which can be efficiently solved by a Gaussian randomization procedure along with solving a semi-definite programming problem. Numerical examples show that the proposed method is much better than the method that ignores dependence of noises.

math.OC↗

arXiv2013

Update-Efficient Regenerating Codes with Minimum Per-Node Storage

Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the communication overhead for regeneration (called MBR). In this work, we propose a new encoding scheme for [n,d] error- correcting MSR codes that generalizes our earlier work on error-correcting regenerating codes. We show that by choosing a suitable diagonal matrix, any generator matrix of the [n,α] Reed-Solomon (RS) code can be integrated into the encoding matrix. Hence, MSR codes with the least update complexity can be found. An efficient decoding scheme is also proposed that utilizes the [n,α] RS code to perform data reconstruction. The proposed decoding scheme has better error correction capability and incurs the least number of node accesses when errors are present.

cs.IT↗

arXiv2012

Asymptotic Properties of Likelihood Based Linear Modulation Classification Systems

The problem of linear modulation classification using likelihood based methods is considered. Asymptotic properties of most commonly used classifiers in the literature are derived. These classifiers are based on hybrid likelihood ratio test (HLRT) and average likelihood ratio test (ALRT), respectively. Both a single-sensor setting and a multi-sensor setting that uses a distributed decision fusion approach are analyzed. For a modulation classification system using a single sensor, it is shown that HLRT achieves asymptotically vanishing probability of error (Pe) whereas the same result cannot be proven for ALRT. In a multi-sensor setting using soft decision fusion, conditions are derived under which Pe vanishes asymptotically. Furthermore, the asymptotic analysis of the fusion rule that assumes independent sensor decisions is carried out.

cs.IT↗

arXiv2012

Cooperative Sparsity Pattern Recovery in Distributed Networks Via Distributed-OMP

In this paper, we consider the problem of collaboratively estimating the sparsity pattern of a sparse signal with multiple measurement data in distributed networks. We assume that each node makes Compressive Sensing (CS) based measurements via random projections regarding the same sparse signal. We propose a distributed greedy algorithm based on Orthogonal Matching Pursuit (OMP), in which the sparse support is estimated iteratively while fusing indices estimated at distributed nodes. In the proposed distributed framework, each node has to perform less number of iterations of OMP compared to the sparsity index of the sparse signal. Thus, with each node having a very small number of compressive measurements, a significant performance gain in support recovery is achieved via the proposed collaborative scheme compared to the case where each node estimates the sparsity pattern independently and then fusion is performed to get a global estimate. We further extend the algorithm to estimate the sparsity pattern in a binary hypothesis testing framework, where the algorithm first detects the presence of a sparse signal collaborating among nodes with a fewer number of iterations of OMP and then increases the number of iterations to estimate the sparsity pattern only if the signal is detected.

cs.IT↗

arXiv2012

Controlled Collaboration for Linear Coherent Estimation in Wireless Sensor Networks

We consider a wireless sensor network consisting of multiple nodes that are coordinated by a fusion center (FC) in order to estimate a common signal of interest. In addition to being coordinated, the sensors are also able to collaborate, i.e., share observations with other neighboring nodes, prior to transmission. In an earlier work, we derived the energy-optimal collaboration strategy for the single-snapshot framework, where the inference has to be made based on observations collected at one particular instant. In this paper, we make two important contributions. Firstly, for the single-snapshot framework, we gain further insights into partially connected collaboration networks (nearest-neighbor and random geometric graphs for example) through the analysis of a family of topologies with regular structure. Secondly, we explore the estimation problem by adding the dimension of time, where the goal is to estimate a time-varying signal in a power-constrained network. To model the time dynamics, we consider the stationary Gaussian process with exponential covariance (sometimes referred to as Ornstein-Uhlenbeck process) as our representative signal. For such a signal, we show that it is always beneficial to sample as frequently as possible, despite the fact that the samples get increasingly noisy due to the power-constrained nature of the problem. Simulation results are presented to corroborate our analytical results.

cs.IT↗

arXiv2012

Distributed Bayesian Detection Under Unknown Observation Statistics

In this paper, distributed Bayesian detection problems with unknown prior probabilities of hypotheses are considered. The sensors obtain observations which are conditionally dependent across sensors and their probability density functions (pdf) are not exactly known. The observations are quantized and are sent to the fusion center. The fusion center fuses the current quantized observations and makes a final decision. It also designs (updated) quantizers to be used at the sensors and the fusion rule based on all previous quantized observations. Information regarding updated quantizers is sent back to the sensors for use at the next time. In this paper, the conditional joint pdf is represented in a parametric form by using the copula framework. The unknown parameters include dependence parameters and marginal parameters. Maximum likelihood estimation (MLE) with feedback based on quantized data is proposed to estimate the unknown parameters. These estimates are iteratively used to refine the quantizers and the fusion rule to improve distributed detection performance by using feedback. Numerical examples show that the new detection method based on MLE with feedback is much better than the usual detection method based on the assumption of conditionally independent observations.

cs.IT↗

arXiv2012

Linear Coherent Estimation with Spatial Collaboration

A power constrained sensor network that consists of multiple sensor nodes and a fusion center (FC) is considered, where the goal is to estimate a random parameter of interest. In contrast to the distributed framework, the sensor nodes may be partially connected, where individual nodes can update their observations by (linearly) combining observations from other adjacent nodes. The updated observations are communicated to the FC by transmitting through a coherent multiple access channel. The optimal collaborative strategy is obtained by minimizing the expected mean-square-error subject to power constraints at the sensor nodes. Each sensor can utilize its available power for both collaboration with other nodes and transmission to the FC. Two kinds of constraints, namely the cumulative and individual power constraints are considered. The effects due to imperfect information about observation and channel gains are also investigated. The resulting performance improvement is illustrated analytically through the example of a homogeneous network with equicorrelated parameters. Assuming random geometric graph topology for collaboration, numerical results demonstrate a significant reduction in distortion even for a moderately connected network, particularly in the low local-SNR regime.

cs.IT↗

arXiv2012

Cramér-Rao Bounds for Polynomial Signal Estimation using Sensors with AR(1) Drift

We seek to characterize the estimation performance of a sensor network where the individual sensors exhibit the phenomenon of drift, i.e., a gradual change of the bias. Though estimation in the presence of random errors has been extensively studied in the literature, the loss of estimation performance due to systematic errors like drift have rarely been looked into. In this paper, we derive closed-form Fisher Information matrix and subsequently Cramér-Rao bounds (upto reasonable approximation) for the estimation accuracy of drift-corrupted signals. We assume a polynomial time-series as the representative signal and an autoregressive process model for the drift. When the Markov parameter for drift ρ<1, we show that the first-order effect of drift is asymptotically equivalent to scaling the measurement noise by an appropriate factor. For ρ=1, i.e., when the drift is non-stationary, we show that the constant part of a signal can only be estimated inconsistently (non-zero asymptotic variance). Practical usage of the results are demonstrated through the analysis of 1) networks with multiple sensors and 2) bandwidth limited networks communicating only quantized observations.

cs.IT↗

arXiv2012

Spatial Whitening Framework for Distributed Estimation

Designing resource allocation strategies for power constrained sensor network in the presence of correlated data often gives rise to intractable problem formulations. In such situations, applying well-known strategies derived from conditional-independence assumption may turn out to be fairly suboptimal. In this paper, we address this issue by proposing an adjacency-based spatial whitening scheme, where each sensor exchanges its observation with their neighbors prior to encoding their own private information and transmitting it to the fusion center. We comment on the computational limitations for obtaining the optimal whitening transformation, and propose an iterative optimization scheme to achieve the same for large networks. We demonstrate the efficacy of the whitening framework by considering the example of bit-allocation for distributed estimation.

cs.IT↗

arXiv2012

Accurate Estimation of Gaseous Strength using Transient Data

Information about the strength of gas sources in buildings has a number of applications in the area of building automation and control, including temperature and ventilation control, fire detection and security systems. Here, we consider the problem of estimating the strength of a gas source in an enclosure when some of the parameters of the gas transport process are unknown. Traditionally, these problems are either solved by the Maximum-Likelihood (ML) method which is accurate but computationally intense, or by Recursive Least Squares (RLS, also Kalman) filtering which is simpler but less accurate. In this paper, we suggest a different statistical estimation procedure based on the concept of Method of Moments. We outline techniques that make this procedure computationally efficient and amenable for recursive implementation. We provide a comparative analysis of our proposed method based on experimental results as well as Monte-Carlo simulations. When used with the building control systems, these algorithms can estimate the gaseous strength in a room both quickly and accurately, and can potentially provide improved indoor air quality in an efficient manner.

eess.SY↗

arXiv2012

Optimal Identical Binary Quantizer Design for Distributed Estimation

We consider the design of identical one-bit probabilistic quantizers for distributed estimation in sensor networks. We assume the parameter-range to be finite and known and use the maximum Cramér-Rao Lower Bound (CRB) over the parameter-range as our performance metric. We restrict our theoretical analysis to the class of antisymmetric quantizers and determine a set of conditions for which the probabilistic quantizer function is greatly simplified. We identify a broad class of noise distributions, which includes Gaussian noise in the low-SNR regime, for which the often used threshold-quantizer is found to be minimax-optimal. Aided with theoretical results, we formulate an optimization problem to obtain the optimum minimax-CRB quantizer. For a wide range of noise distributions, we demonstrate the superior performance of the new quantizer - particularly in the moderate to high-SNR regime.

cs.IT↗

arXiv2012

On Linear Coherent Estimation with Spatial Collaboration

We consider a power-constrained sensor network, consisting of multiple sensor nodes and a fusion center (FC), that is deployed for the purpose of estimating a common random parameter of interest. In contrast to the distributed framework, the sensor nodes are allowed to update their individual observations by (linearly) combining observations from neighboring nodes. The updated observations are communicated to the FC using an analog amplify-and-forward modulation scheme and through a coherent multiple access channel. The optimal collaborative strategy is obtained by minimizing the cumulative transmission power subject to a maximum distortion constraint. For the distributed scenario (i.e., with no observation sharing), the solution reduces to the power-allocation problem considered by [Xiao, TSP08]. Collaboration among neighbors significantly improves power efficiency of the network in the low local-SNR regime, as demonstrated through an insightful example and numerical simulations.

cs.IT↗

arXiv2011

Dynamic Bit Allocation for Object Tracking in Bandwidth Limited Sensor Networks

In this paper, we study the target tracking problem in wireless sensor networks (WSNs) using quantized sensor measurements under limited bandwidth availability. At each time step of tracking, the available bandwidth $R$ needs to be distributed among the $N$ sensors in the WSN for the next time step. The optimal solution for the bandwidth allocation problem can be obtained by using a combinatorial search which may become computationally prohibitive for large $N$ and $R$. Therefore, we develop two new computationally efficient suboptimal bandwidth distribution algorithms which are based on convex relaxation and approximate dynamic programming (A-DP). We compare the mean squared error (MSE) and computational complexity performances of convex relaxation and A-DP with other existing suboptimal bandwidth distribution schemes based on generalized Breiman, Friedman, Olshen, and Stone (GBFOS) algorithm and greedy search. Simulation results show that, A-DP, convex optimization and GBFOS yield similar MSE performance, which is very close to that based on the optimal exhaustive search approach and they outperform greedy search and nearest neighbor based bandwidth allocation approaches significantly. Computationally, A-DP is more efficient than the bandwidth allocation schemes based on convex relaxation and GBFOS, especially for a large sensor network.

stat.AP↗

arXiv2009

Approximation of Average Run Length of Moving Sum Algorithms Using Multivariate Probabilities

Among the various procedures used to detect potential changes in a stochastic process the moving sum algorithms are very popular due to their intuitive appeal and good statistical performance. One of the important design parameters of a change detection algorithm is the expected interval between false positives, also known as the average run length (ARL). Computation of the ARL usually involves numerical procedures but in some cases it can be approximated using a series involving multivariate probabilities. In this paper, we present an analysis of this series approach by providing sufficient conditions for convergence and derive an error bound. Using simulation studies, we show that the series approach is applicable to moving average and filtered derivative algorithms. For moving average algorithms, we compare our results with previously known bounds. We use two special cases to illustrate our observations.

stat.ME↗