Analysis of Target Localization With Ideal Binary Detectors via Likelihood Function Smoothing

Abstract

This letter deals with noncooperative localization of a single target using censored binary observations acquired by spatially distributed sensors. An ideal, noise-free setting is considered whereby each sensor can perfectly detect if the target is in its close proximity or not. Only those detecting sensors communicate their decisions and locations to a fusion center (FC), which subsequently forms the desired location estimator based on censored observations. Because a maximum-likelihood estimator (MLE) does not exist in this setting, current approaches have relied on heuristic, centrality-based geometric estimators such as the center of a minimum enclosing circle (CMEC). A smooth surrogate to the likelihood function is proposed here, whose maximizer is shown to approach the CMEC asymptotically as the likelihood approximation error vanishes. This provides rigorous analytical justification as to why the CMEC estimator outperforms other heuristics for this problem, as empirically observed in prior studies. Since the Cramer-Rao Bound does not exist either, an upshot of the results in this letter is that the CMEC performance can be adopted as a benchmark in this ideal setting and also for comparison with other more pragmatic binary localization methods in the presence of uncertainty.