Distributed Parameter Estimation Problem Research Articles

Online distributed detection of sensor networks with delayed information

Distributed decision on sensor network is affected by the bandwidth, network congestion, and computation capability of sensors, which cause the communication delays and feedback delays during the signal processing process. In this paper, the effects of state constraints, directed graph, communication delays and feedback delays on the online distributed parameter estimation problem for multi-sensor networks are considered comprehensively. To this end, we first propose an Online Decentralized Gradient Descent Algorithm (ODGDA) to overcome the effects of these factors and give the regret upper bounds for convex loss function and strongly convex loss function, respectively. Further, considering that the loss function may not be fully disclosed in the complex environment, we extend ODGDA to the scenario of bandit feedback and propose an Online Decentralized Bandit Feedback Algorithm (ODBFA), which is updated using historical state information stored by sensors. The analysis shows that, compared with the ODGDA which can directly use the gradient information for state update, the ODBFA utilizing two-point bandit feedback information does not lead to regret degradation in the order sense. Finally, the effectiveness of the proposed algorithm is verified by the multi-sensor network.

Event-Triggered Distributed State Estimation Under Unknown Parameters and Sensor Saturations Over Wireless Sensor Networks

In this brief, the distributed state and parameter estimation problem is addressed for a class of discrete-time nonlinear systems subject to sensor saturations over wireless sensor networks. In this regard, a novel estimation design is proposed that involves identification of an unknown parameter under event-triggering mechanism. A sufficient condition for exponential uniform ultimate boundedness of estimation error is established using Lyapunov stability theory. The estimator gains to ensure boundedness of error are linked to the solution of inequality constraints. Finally, the effectiveness of proposed estimator is demonstrated using a simulation example.

An adaptive gain based approach for event-triggered state estimation with unknown parameters and sensor nonlinearities over wireless sensor networks

The distributed state and parameter estimation problem is investigated in this paper for discrete-time nonlinear systems subject to sensor nonlinearities and stochastic disturbances over a wireless sensor network. A novel architecture for distributed state estimator is introduced that incorporates adaptive coupling gains to govern the information exchange between the sensor nodes under event-triggering mechanism. The aim of this paper is to provide a scalable structure for unknown parameter identification independent of sensor networks’ complexity. The boundedness of estimation error is ensured in the framework of uniformly ultimately bounded stability by developing an algebraic connectivity based criterion. The estimator gains including proposed coupling gains are then presented as solution to matrix inequalities. Finally, two simulation examples are presented to demonstrate the effectiveness of proposed estimation architecture.

Convergence Analysis of Weighted SPSA-based Consensus Algorithm in Distributed Parameter Estimation Problem

Abstract In this paper, we study a distributed parameter estimation problem in a large-scale network of communication sensors. The goal of the sensors is to find a global estimate of an unknown parameter minimizing, which minimizes some aggregate cost function. Each sensor can communicated to a few “neighbors”, furthermore, the communication channels have limited capacities. To solve the resulting optimization problem, we use a weighted modification of the distributed consensus-based SPSA algorithm whose main advantage over the alternative method is its ability to work in presence of arbitrary unknown-but-bounded noises whose statistical characteristics can be unknown. We provide a convergence analysis of the weighted SPSA-based consensus algorithm and show its efficiency via numerical simulations.

On Rate Requirements for Achieving the Centralized Performance in Distributed Estimation

We consider a distributed parameter estimation problem, in which multiple terminals send messages related to their local observations using limited rates to a fusion center which obtains an estimate of a parameter related to the observations of all terminals. It is well known that if the transmission rates are in the Slepian–Wolf region, the fusion center can fully recover all observations and hence can construct an estimator having the same performance as that of the centralized case. One natural question is whether Slepian–Wolf rates are necessary to achieve the same estimation performance as that of the centralized case. In this paper, we show that the answer to this question is negative. We establish our result by explicitly constructing an asymptotically minimum variance unbiased estimator that has the same performance as that of the optimal estimator in the centralized case while using information rates less than the conditions required in the Slepian–Wolf rate region. The key idea is that, instead of aiming to recover the observations at the fusion center, we design universal schemes enabling the fusion center to compute a sufficient statistic using rates outside of the Selpian–Wolf region.

An improved incremental least-mean-squares algorithm for distributed estimation over wireless sensor networks

Distributed parameter estimation problem has attracted much attention due to its important foundation of some applications in wireless sensor networks. In this work, we first investigate the performance tradeoff between existing incremental least-mean-squares algorithm and traditional steepest-descent algorithm from the aspects of initial convergence rate, steady-state convergence behavior, and oscillation, and present the motivations for improvements. Thereby we propose an improved incremental least-mean-squares distributed estimation algorithm that starts from the incremental least-mean-squares algorithm and works toward the objective of improvement on initial convergence rate and steady-state performance. The proposed algorithm meets the requirements of diminishing step size for wireless sensor networks without any increase in communication overhead and the mean stability condition is derived for a practical guideline. A target localization model in wireless sensor networks is used to illustrate the effect of the proposed algorithm. Simulation results confirm the performance improvement of our method, as well as the effectiveness of application in wireless sensor networks.

The Performance Analysis of Diffusion LMS Algorithm in Sensor Networks Based on Quantized Data and Random Topology

We study the performance of diffusion LMS (Least-Mean-Square) algorithm for distributed parameter estimation problem over sensor networks with quantized data and random topology, where the data are quantized before transmission and the links are interrupted at random times. To achieve unbiased estimation of the unknown parameter, we add dither (small noise) to the sensor states before quantization. We first propose a diffusion LMS algorithm with quantized data and random link failures. We further analyze the stability and convergence of the proposed algorithm and derive the closed-form expressions of the MSD (Mean-Square Deviation) and EMSE (Excess Mean-Square Errors), which characterize the steady-state performance of the proposed algorithm. We show that the convergence of the proposed algorithm is independent of quantized data and random topology. Moreover, the analytical results reveal which factors influence the network performance, and we show that the effect of quantization is the main factor in performance degradation of the proposed algorithm. We finally provide computer simulation results that illustrate the performance of the proposed algorithm and verify the results of the theoretical analysis.

An Alternating Direction Algorithm for Total Variation Reconstruction of Distributed Parameters

Augmented Lagrangian variational formulations and alternating optimization have been adopted to solve distributed parameter estimation problems. The alternating direction method of multipliers (ADMM) is one of such formulations/optimization methods. Very recently, the number of applications of the ADMM, or variants of it, to solve inverse problems in image and signal processing has increased at an exponential rate. The reason for this interest is that ADMM decomposes a difficult optimization problem into a sequence of much simpler problems. In this paper, we use the ADMM to reconstruct piecewise-smooth distributed parameters of elliptical partial differential equations from noisy and linear (blurred) observations of the underlying field. The distributed parameters are estimated by solving an inverse problem with total variation (TV) regularization. The proposed instance of the ADMM solves, in each iteration, an l(2) and a decoupled l(2) - l(1) optimization problems. An operator splitting is used to simplify the treatment of the TV regularizer, avoiding its smooth approximation and yielding a simple yet effective ADMM reconstruction method compared with previously proposed approaches. The competitiveness of the proposed method, with respect to the state-of-the-art, is illustrated in simulated 1-D and 2-D elliptical equation problems, which are representative of many real applications.

Block Least Mean Squares Algorithm over Distributed Wireless Sensor Network

In a distributed parameter estimation problem, during each sampling instant, a typical sensor node communicates its estimate either by the diffusion algorithm or by the incremental algorithm. Both these conventional distributed algorithms involve significant communication overheads and, consequently, defeat the basic purpose of wireless sensor networks. In the present paper, we therefore propose two new distributed algorithms, namely, block diffusion least mean square (BDLMS) and block incremental least mean square (BILMS) by extending the concept of block adaptive filtering techniques to the distributed adaptation scenario. The performance analysis of the proposed BDLMS and BILMS algorithms has been carried out and found to have similar performances to those offered by conventional diffusion LMS and incremental LMS algorithms, respectively. The convergence analyses of the proposed algorithms obtained from the simulation study are also found to be in agreement with the theoretical analysis. The remarkable and interesting aspect of the proposed block-based algorithms is that their communication overheads per node and latencies are less than those of the conventional algorithms by a factor as high as the block size used in the algorithms.

Nonparametric One-Bit Quantizers for Distributed Estimation

In this paper, we consider the nonparametric distributed parameter estimation problem using one-bit quantized data from peripheral sensors. Assuming that the sensor observations are bounded, nonparametric distributed estimators are proposed based on the knowledge of the first N moments of sensor noises. These estimators are shown to be either unbiased or asymptotically unbiased with bounded and known estimation variance. Further, the uniformly optimal quantizer based only on the first moment information and the optimal minimax quantizer with the knowledge of the first two moments are determined. The proposed estimators are shown to be consistent even when local sensor noises are not independent but m-dependent. The relationship between the proposed approaches and dithering in quantization is also investigated. The superiority of the proposed quantization/estimation schemes is illustrated via illustrative examples.

A Fast Forward Problem Solver for the Reconstruction of Biological Maps in Magnetic Induction Tomography

The magnetic induction tomography (MIT) image reconstruction is a distributed parameter estimation problem normally solved iteratively, where each iteration engages several 3-D harmonic eddy-current problems. These calculations are the main time-consuming process in the MIT reconstruction. In this paper, an approach to accelerate the resolution of a set of similar eddy-current problems to be used in the reconstruction process is presented. Each eddy-current problem is described by a reduced magnetic vector potential eddy-current formulation using the finite integration technique (FIT) framework defined over an octree based subgridding scheme with several performance precautions. The solver accuracy is compared with analytical solutions of appropriate geometrical scenarios. A performance assessment is presented for a full set of eddy-current problems that constitutes a forward problem. The new method reduced the computing time approximately to 11% of a similar problem without performance concerns maintaining a relative mean error inferior to 1.5% relatively to analytical simulations.

Adaptive finite volume method for distributed non-smooth parameter identification

In this paper we develop a finite volume adaptive grid refinement method for the solution of distributed parameter estimation problems with almost discontinuous coefficients. We discuss discretization on locally refined grids, as well as optimization and refinement criteria. An OcTree data structure is utilized. We show that local refinement can significantly reduce the computational effort of solving the problem, and that the resulting reconstructions can significantly improve resolution, even for noisy data and diffusive forward problems.

On level set regularization for highly ill-posed distributed parameter estimation problems

The recovery of a distributed parameter function with discontinuities from inverse problems with elliptic forward PDEs is fraught with theoretical and practical difficulties. Better results are obtained for problems where the solution may take on at each point only one of two values, thus yielding a shape recovery problem. This article considers level set regularization for such problems. However, rather than explicitly integrating a time embedded PDE to steady state, which typically requires thousands of iterations, methods based on Gauss–Newton are applied more directly. One of these can be viewed as damped Gauss–Newton utilized to approximate the steady state equations which in turn are viewed as the necessary conditions of a Tikhonov-type regularization with a sharpening sub-step at each iteration. In practice this method is eclipsed, however, by a special “finite time” or Levenberg–Marquardt-type method which we call dynamic regularization applied to the output least squares formulation. Our stopping criterion for the iteration does not involve knowledge of the true solution. The regularization functional is applied to the (smooth) level set function rather than to the discontinuous function to be recovered, and the second focus of this article is on selecting this functional. Typical choices may lead to flat level sets that in turn cause ill-conditioning. We propose a new, quartic, non-local regularization term that penalizes flatness and produces a smooth level set evolution, and compare its performance to more usual choices. Two numerical test cases are considered: a potential problem and the classical EIT/DC resistivity problem.

Quasi-Newton methods for large-scale electromagnetic inverse problems

We develop quasi-Newton (QN) methods for distributed parameter estimation problems which evolve from electromagnetics, where the forward problem is governed by some form of Maxwell's equations. A Tikhonov-style regularization approach yields an optimization problem with a special structure, where the gradients are calculated using the adjoint method. In many cases, standard QN methods (such as L-BFGS) are not very effective and tend to converge slowly. Taking advantage of the special structure of the problem and the quantities that are calculated in typical gradient descent methods, we develop a class of highly effective methods for the solution of the problem. We demonstrate the merits and effectiveness of our algorithm on two realistic model problems.

Learning regularization functionals—a supervised training approach

We consider the solution of a distributed parameter estimation problem where thedata are contaminated by noise. A common approach to solve such a problem is touse Tikhonov style regularization; however, it is not always clear what type ofregularization penalty should be used for a given problem as differentregularization operators may yield very different solutions. Here we usesupervised learning techniques to determine a regularization functional givena training set of feasible solutions. Our approach leads to a constraintoptimization problem that we solve using inexact sequential quadraticprogramming type methods. We illustrate the methodology with two examples.

Sensitivity behavior analysis in distributed parameter estimation

This paper is concerned with sensitivity analysis for the distributed parameter estimation problem arising in the modeling process for fluid flow in underground porous media. An efficient algorithm was constructed using variational calculus techniques for the evaluation of sensitivity gradient curves which describe variations of system outputs resulting from variations of a spatially-varying parameter in nonlinear partial differential equations. For a test problem of estimating transmissivity of a one-dimensional ideal gas reservoir, sensitivity behavior was analyzed under various reservoir conditions, and the results were applied to devising a parameter discretization scheme which will yield improved parameter estimates.