Swarnendu Kar

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 Crameŕ-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.

Accurate estimation of indoor occupancy using gas sensors

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 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.

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.

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 et. al.. 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.

Optimized Sensor Collaboration for Estimation of Temporally Correlated Parameters

In this paper, we aim to design the optimal sensor collaboration strategy for the estimation of time-varying parameters, where collaboration refers to the act of sharing measurements with neighboring sensors prior to transmission to a fusion center. We begin by addressing the sensor collaboration problem for the estimation of uncorrelated parameters. We show that the resulting collaboration problem can be transformed into a special nonconvex optimization problem, where a difference of convex functions carries all the nonconvexity. This specific problem structure enables the use of a convex-concave procedure to obtain a near-optimal solution. When the parameters of interest are temporally correlated, a penalized version of the convex-concave procedure becomes well suited for designing the optimal collaboration scheme. In order to improve computational efficiency, we further propose a fast algorithm that scales gracefully with problem size via the alternating direction method of multipliers. Numerical results are provided to demonstrate the effectiveness of our approach and the impact of parameter correlation and temporal dynamics of sensor networks on estimation performance.

On optimal sensor collaboration topologies for linear coherent estimation

In the context of distributed estimation we consider the problem of sensor collaboration, which refers to the act of sharing measurements with neighboring sensors prior to transmission to a fusion center. While incorporating the cost of sensor collaboration, we aim to find optimal sparse collaboration topologies subject to a certain information or energy constraint. To achieve this goal, we present a tractable optimization framework and propose efficient methods to solve the formulated sensor collaboration problems. The effectiveness of our approach is demonstrated by numerical examples.

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 (up to 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 nonstationary, 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.

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.

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. In this paper, 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 method, which is accurate but computationally intensive, or by recursive least squares (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.

A decentralized framework for linear coherent estimation with spatial collaboration

We study an estimation problem where a fusion center estimates a random parameter by using a partially connected network of sensor nodes. The process involves two stages. In the collaboration stage, the sensor nodes share their observations with their neighbors. In the estimation stage, all the sensor nodes form a coherent beam to the fusion center using the analog amplify-and-forward procedure. In the previous work of Kar and Varshney (2013) on this topic, a control center determines the optimum collaboration strategy that is sent to the sensor nodes prior to starting the two-stage procedure. In this paper, we develop a new framework where the collaboration strategies are computed in a decentralized manner using minimal communication with the control center. This makes the sensor network more energy efficient and reduces control channel communication requirements.