Robust Matrix Completion for Elliptic Positioning in the Presence of Outliers and Missing Data

Abstract

Elliptic target positioning from the bistatic ranges (BRs), as an emerging localization scheme, has recently gained considerable traction for its diverse applications in multistatic systems such as radar, sonar, and wireless sensor networks. This contribution extends the work of previous research on the low-rank property of the BR matrix (Xiong, “Denoising of bistatic ranges for elliptic positioning,” IEEE Geosci. Remote Sens. Lett., vol. 20, pp. 1–3, 2023, Art. no. 3500503) to the brand new use case of robust elliptic positioning in the presence of missing data. Due to the structures of the outlier-inducing errors when embodied in the BR matrix, many of the off-the-shelf low-rank matrix completion (LRMC) solutions cannot be applied. We address this challenge by formulating the problem of outlier-resistant BR matrix recovery as constrained minimization of an ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> -norm based loss function, and devising an algorithm based on alternating direction method of multipliers to efficiently solve the resultant LRMC. Simulations are conducted to demonstrate the efficacy of the developed robust elliptic positioning technique in various localization scenarios.