Sensor placement by maximal projection on minimum eigenspace for linear inverse problems

TL;DR

This paper introduces two greedy sensor placement algorithms, MNEP and MPME, with MPME being highly efficient and outperforming existing methods in estimation accuracy for linear inverse problems, especially with limited sensors.

Contribution

The paper proposes the MPME algorithm that uses maximal projection on the minimum eigenspace for sensor placement, improving efficiency and accuracy over prior approaches.

Findings

MPME outperforms convex relaxation, SparSenSe, and FrameSense in WCEV and MSE.

MPME is computationally efficient and effective with limited sensors.

Sensor placement based on eigenspace projections enhances estimation accuracy.

Abstract

This paper presents two new greedy sensor placement algorithms, named minimum nonzero eigenvalue pursuit (MNEP) and maximal projection on minimum eigenspace (MPME), for linear inverse problems, with greater emphasis on the MPME algorithm for performance comparison with existing approaches. We select the sensing locations one-by-one. In this way, the least number of required sensors can be determined by checking whether the estimation accuracy is satisfied after each sensing location is determined. The minimum eigenspace is defined as the eigenspace associated with the minimum eigenvalue of the dual observation matrix. For each sensing location, the projection of its observation vector onto the minimum eigenspace is shown to be monotonically decreasing w.r.t. the worst case error variance (WCEV) of the estimated parameters. We select the sensing location whose observation vector has the maximum projection onto the minimum eigenspace of the current dual observation matrix. The proposed MPME is shown to be one of the most computationally efficient algorithms. Our Monte-Carlo simulations showed that MPME outperforms the convex relaxation method [1], the SparSenSe method [2], and the FrameSense method [3] in terms of WCEV and the mean square error (MSE) of the estimated parameters, especially when the number of available sensor nodes is very limited.