Sparsity-Promoting Sensor Selection for Non-linear Measurement Models (1310.5251v2)

Abstract: Sensor selection is an important design problem in large-scale sensor networks. Sensor selection can be interpreted as the problem of selecting the best subset of sensors that guarantees a certain estimation performance. We focus on observations that are related to a general non-linear model. The proposed framework is valid as long as the observations are independent, and its likelihood satisfies the regularity conditions. We use several functions of the Cram\'er-Rao bound (CRB) as a performance measure. We formulate the sensor selection problem as the design of a selection vector, which in its original form is a nonconvex l0-(quasi) norm optimization problem. We present relaxed sensor selection solvers that can be efficiently solved in polynomial time. We also propose a projected subgradient algorithm that is attractive for large-scale problems and also show how the algorithm can be easily distributed. The proposed framework is illustrated with a number of examples related to sensor placement design for localization.

• The paper introduces a framework that optimizes sensor selection in nonlinear models by relaxing the ℓ0-norm minimization into a tractable convex problem.
• It employs sparsity-enhancing techniques, including a concave surrogate to the ℓ1-norm, to iteratively refine sensor choices and reduce resource consumption.
• The projected subgradient algorithm allows for scalable, distributed implementations, as demonstrated by simulations in localization tasks.

Sensor Selection for Non-linear Measurement Models: A Structured Approach

The paper under examination presents a comprehensive framework for addressing the critical problem of sensor selection in large-scale sensor networks characterized by non-linear measurement models. Authored by Sundeep Prabhakar Chepuri and Geert Leus, this work approaches the sensor selection task with a focus on optimizing estimation performance while balancing the constraints of computational complexity and practicability.

Problem Statement

Sensor selection in expansive networks poses a challenge primarily due to the substantial volume of data generated by numerous sensors. The paper conceptualizes sensor selection as the problem of determining the most informative subset of sensors that guarantees a certain estimation accuracy—measured in terms of the Cramér-Rao bound (CRB). This selection problem is crucial for reducing resource consumption in terms of power, storage, and computation.

Methodology Overview

The crux of the methodology revolves around formulating the sensor selection problem as an optimization issue with the aim of minimizing a non-convex $\ell_0$-(quasi) norm. The paper employs several innovative strategies to relax and solve this challenging problem:

1. Convex Relaxation: The paper skillfully relaxes the integer constraint problem, rendering it tractable by approximating it with a convex problem using an $\ell_1$-norm heuristic. This transformation allows for leveraging well-established convex optimization techniques to obtain efficient solutions.
2. Sparsity-Enhancing Algorithms: A notable contribution is the use of sparsity-promoting techniques, including a concave surrogate to the $\ell_1$-norm. This method iteratively refines the solution to enhance sparsity, which is particularly beneficial in cases of multiple near-identical measurements.
3. Projected Subgradient Algorithm: For scalability, the authors present a projected subgradient algorithm suitable for distributed implementation. This first-order method is particularly advantageous for handling large-scale problems due to its reduced per-iteration complexity.

Numerical Results and Implications

The numerical simulations presented include sensor placement for localization tasks. These simulations meticulously illustrate the efficiency and efficacy of the proposed approaches by demonstrating significant reductions in sensor deployment while maintaining estimation performance within defined accuracy thresholds. Key takeaways involve:

• Demonstration of how the minimum eigenvalue constraint can offer a more computationally efficient alternative to trace constraints, despite its potentially tighter feasible set.
• Successful application of the methodology across various measurement models, including range, RSS, and bearing, attests to the framework’s versatility.

Theoretical and Practical Implications

From a theoretical standpoint, this research enriches the field of sensor network design by presenting a robust analytical framework accommodating non-linear statistical models. The use of CRB as a performance measure not only grounds the problem in established statistical methods but also assures practical applicability in real-world systems where sensor resources are constrained and accurate estimation is crucial.

Practically, the proposed framework can significantly influence the deployment and operational strategies of sensor networks such as those used in environmental monitoring, industrial process control, or surveillance.

Future Directions

The pathways for future exploration, as suggested by the research, can involve enhancing the algorithmic efficiency for even larger networks and exploring extensions to dynamic or adaptive sensor networks where non-stationary conditions necessitate more frequent recalibrations of the selection set. Increasing integration with machine learning techniques for better context-awareness and decision-making could also amplify the impact of this research.

Overall, the paper stands as a foundational piece for advancing the optimization of sensor networks with non-linear models, offering both breadth and depth in methods applicable across academia and industry.