An ADMM approach for elliptic positioning in non-line-of-sight environments

Elliptic positioning (EP) has recently emerged as a prevailing subject within localization research, holding significant relevance for a variety of multistatic systems including distributed multiple-input multiple-output radar, sonar, and wireless sensor networks. Mathematically, EP refers to estimating the location of a signal-reflecting/relaying target from the bistatic range (BR) measurements acquired by employing multiple spatially separated transmitters and receivers. BRs, as a specific type of range-based sensor observations, will however be positively biased when non-line-of-sight (NLOS) signal propagation occurs. Such a phenomenon is widespread across various localization scenarios, which can seriously degrade the positioning accuracy if not properly addressed. Through the alternating direction method of multipliers, this contribution introduces a computationally efficient iterative algorithm designed for error-mitigated EP in NLOS environments. In addition to target position coordinates, we incorporate a non-negatively bounded balancing parameter into the formulation and perform joint estimation, thereby achieving NLOS bias error reduction in a simple yet impactful manner. Numerical simulations are conducted to validate the functionality of the presented EP approach in NLOS situations.