The partial relaxation method in direction-of-arrival estimation: Design and Analysis (PRIDE)

• Applicant: Professor Dr.-Ing. Marius Pesavento
• Subject Area: Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
• Term: since 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 423747006

Direction-of-arrival estimation is fundamental in modern sensor array applications. Multi-source estimation criteria like Maximum-Likelihood Estimation, Weighted Subspace Fitting or Covariance Matching jointly estimate the parameters of multiple sources with unprecedented estimation performance, however at prohibitive complexity. Single source criteria such as Capon and spectral MUSIC only require one-dimensional search and are thus computationally efficient. These methods can be viewed as single source approximations of the multi-source criteria that are exact only for well separated sources. Recently we proposed the partial relaxation framework, where the multi-source manifold structure is partly relaxed. The idea consists in partitioning the array manifold matrix into the first steering vector, representing a source of interest, and the remaining steering vectors, modelling the set of interference sources. While the manifold structure of the first steering vector is maintained, the manifold structure of the remaining steering vectors is replaced by an arbitrary unstructured complex matrix. This partial relaxation of the array manifold applied to multi-source criteria has the benefit that it allows simple - often closed form - optimization with respect to the nuisance parameters and thus concentration of the multi-source criteria to simple spectral search criteria. The partial relaxation technique applied to the aforementioned multi-source criteria yields algorithms that exhibit excellent (threshold) performance at low complexity.In the PRIDE project we carry out fundamental research with respect to the partial relaxation approach. The first goal is to explain and to quantify from a theoretical perspective the excellent (threshold) performance achieved by the partial relaxation approach which to date has only been demonstrated numerically. Theoretical results providing conditions under which the partial relaxation approach exhibits superior threshold performance are of great interest. In this aspect we will carry out a complete statistical performance analysis of the partial relaxation estimators, both asymptotically and in threshold domain and derive statistical performance bounds, e.g., Cramer-Rao bound expressions, for the underlying partial relaxation model. The second goal is to extend the partial relaxation approach to the class of partly calibrated arrays which recently enjoyed interest in modern application areas, such as drone localization using large distributed sensor arrays. The third goal is to generalize the partial relaxation approach to source detection. This extension is promising as advanced problem specific detectors, such as the popular generalized log-likelihood ratio test, contain explicit parameter estimation as a subproblem. Given the attractive features of the partial relaxation estimators such as low computational complexity and excellent threshold performance we also expect large gains in the detection performance.

• DFG Programme: Research Grants