Metric-Based Reliability Transition Detection in Multisensor Localization

Abstract

A two-dimensional range localization system can remain accurate over much of its operating range and then deteriorate rapidly as measurements degrade. This paper estimates the operating boundary instead of reporting only an average-error curve. Monte Carlo failure probabilities are fitted by a two-parameter logistic model whose midpoint defines the critical signal-to-noise ratio (SNR). Using the pooled fine-grid results from three independent random-seed sets, the weighted nonlinear least-squares experiment locates critical SNRs of 0.34, 2.93, and 6.05 dB for Gaussian, burst, and burst-plus-bias errors, respectively. Pairwise bootstrap tests confirm separation among the three transitions. Validation over three sensor layouts and five target positions preserves the degradation ordering while showing geometry-dependent critical-SNR ranges. A Huber estimator reduces the burst-related transition values without changing the Gaussian result materially. The contribution is an estimator-independent reliability diagnostic with explicit failure semantics, uncertainty intervals, and reproducible trial-level data; it is not a new localization optimizer.