2 research outputs found
Active Target Localization using Low-Rank Matrix Completion and Unimodal Regression
The detection and localization of a target from samples of its generated
field is a problem of interest in a broad range of applications. Often, the
target field admits structural properties that enable the design of lower
sample detection strategies with good performance. This paper designs a
sampling and localization strategy which exploits separability and unimodality
in target fields and theoretically analyzes the trade-off achieved between
sampling density, noise level and convergence rate of localization. In
particular, the strategy adopts an exploration-exploitation approach to target
detection and utilizes the theory of low-rank matrix completion, coupled with
unimodal regression, on decaying and approximately separable target fields. The
assumptions on the field are fairly generic and are applicable to many decay
profiles since no specific knowledge of the field is necessary, besides its
admittance of an approximately rank-one representation. Extensive numerical
experiments and comparisons are performed to test the efficacy and robustness
of the presented approach. Numerical results suggest that the proposed strategy
outperforms algorithms based on mean-shift clustering, surface interpolation
and naive low-rank matrix completion with peak detection, under low sampling
density.Comment: 24 pages, 10 figure
Unimodality-Constrained Matrix Factorization for Non-Parametric Source Localization
Herein, the problem of simultaneous localization of multiple sources given a
number of energy samples at different locations is examined. The strategies do
not require knowledge of the signal propagation models, nor do they exploit the
spatial signatures of the source. A non-parametric source localization
framework based on a matrix observation model is developed. It is shown that
the source location can be estimated by localizing the peaks of a pair of
location signature vectors extracted from the incomplete energy observation
matrix. A robust peak localization algorithm is developed and shown to decrease
the source localization mean squared error (MSE) faster than O(1/M^1.5) with M
samples, when there is no measurement noise. To extract the source signature
vectors from a matrix with mixed energy from multiple sources, a
unimodality-constrained matrix factorization (UMF) problem is formulated, and
two rotation techniques are developed to solve the UMF efficiently. Our
numerical experiments demonstrate that the proposed scheme achieves similar
performance as the kernel regression baseline using only 1/5 energy measurement
samples in detecting a single source, and the performance gain is more
significant in the cases of detecting multiple sources