This study presents a comprehensive mathematical framework for modeling Bluetooth Low Energy (BLE) beacon Received Signal Strength Indicator (RSSI) measurements to improve the estimation of RSSI-distance model parameters through the integration of stochastic and functional modeling. Although such approaches are well established in geodesy, they have been only sparsely applied to indoor positioning, particularly for characterizing RSSI dependencies arising from multipath propagation. Experiments were conducted using two types of BLE beacons in a controlled static outdoor environment to isolate signal behavior and facilitate reliable RSSI–distance modeling. Outliers were mitigated using a median filter based on local neighborhood comparisons. Stochastic modeling was then performed using the autocorrelation function (ACF) and partial autocorrelation function (PACF), revealing that RSSI noise exhibits short-memory, time-correlated behavior that is well represented by a second-order autoregressive AR(2) model. Measurement weights were estimated using Least Squares Variance Component Estimation (LS-VCE), followed by functional modeling for the estimation of environmental and beacon transmit-power parameters together with their uncertainties. The estimated candidate AR models were further compared using their maximized log-likelihood values, which confirmed that the AR(2) model provides the most appropriate representation of the RSSI noise process. The reconstructed RSSI achieved root mean square errors (RMSEs) of 1.12dBm and 0.50dBm for the IT002 and IT008 beacons, respectively, at a distance of 1m, increasing to 2.19dBm and 2.40dBm at 10m. These errors correspond to relative distance uncertainties of approximately 6–13% at 1m and 15–25% at 10m, demonstrating the effectiveness of the proposed framework for accurate RSSI modeling and parameter estimation.

Indoor positioning systems based on Bluetooth technology have gained significant attention with the widespread adoption of Bluetooth Low Energy (BLE). The rapid growth of BLE-enabled devices—now exceeding eight billion worldwide—has enabled the development of cost-effective, location-aware applications. The precision of BLE indoor positioning systems depends on several factors, among which the quality of received signal strength indicator (RSSI) measurements and the spatial deployment of sensors are most critical. Existing research has largely focused on improving RSSI accuracy through techniques such as multichannel measurements, outlier detection, Kalman filtering, and regression modeling. In this work, we examine two primary components that govern positioning precision: 1) the uncertainty in the RSSI-distance model parameters, including the path-loss exponent, reference power, and raw RSSI values; and 2) the geometry of sensor deployment, which directly affects estimation precision through the geometric dilution of precision (GDoP). We demonstrate that optimizing sensor placement using centroidal Voronoi tessellation (CVT) reduces GDoP and substantially improves positioning precision. Comparative experiments across two deployment scenarios, one based on CVT, confirm that CVT-based sensor configurations yield significantly higher precision in BLE RSSI-based indoor positioning.