Paired-Geometry BLE AoA Measurement

• Paired-Geometry BLE AoA Measurement is a technique that uses spatially distributed BLE receivers with calibrated antenna arrays to estimate transmitter location via angle-of-arrival fusion.
• It employs BLE 5.1 CTE-based phase sampling and rigorous calibration to calculate phase differences, ensuring minimal spatial aliasing and mitigating multipath effects.
• The method integrates 3D coordinate transformation and geometric redundancy to achieve sub-meter accuracy in controlled indoor and outdoor deployments.

Paired-geometry Bluetooth Low Energy (BLE) Angle-of-Arrival (AoA) measurement refers to the methodology in which spatially distributed BLE receivers, each equipped with calibrated antenna arrays, estimate the AoA of incoming BLE transmissions and fuse these directions through geometric pairing to determine transmitter (tag) location. This approach leverages the BLE 5.1 Direction Finding extension—specifically the Constant Tone Extension (CTE)—to enable precise carrier-phase sampling and subsequent direction estimation. The paired-geometry technique forms the architectural basis for practical BLE localization systems in GNSS-denied environments across IoT, industrial, and asset-tracking applications (Cominelli et al., 2019, Paulino et al., 2022, Alghananim et al., 15 Jan 2025, Talebian et al., 1 Feb 2026).

1. BLE AoA Measurement Architecture and Signal Model

Paired-geometry BLE AoA measurement systems rely on BLE 5.1-compliant anchors (receivers) equipped with antenna arrays. BLE Direction Finding packets extend standard BLE frames with the CTE field, structured as follows: an 8 μs reference period sampled at 1 MS/s, followed by a sequence of switch slots (2 μs) and sample slots (2 μs), mapped to individual antennas via a time-multiplexed RF switch (Cominelli et al., 2019). The I/Q samples acquired during CTE are used to compute phase differences between antenna elements.

For a linear array of two antennas with element spacing $d$ exposed to a plane wave of wavelength $\lambda$, the phase difference $\Delta\varphi$ between antennas is given by: $\Delta\varphi = \frac{2\pi}{\lambda}d\sin\theta$ Solving for the arrival angle $\theta$: $$\theta = \arcsin\left(\frac{\lambda\Delta\varphi}{2\pi d}\right), \qquad |\Delta\varphi| \leq \pi, \quad d < \frac{\lambda}{2}$$ This ensures spatial aliasing is avoided. The same principle generalizes to circular arrays, where for adjacent antenna pairs, the path difference becomes $d\cos\theta'$, supporting full $360^\circ$ coverage (Paulino et al., 2022).

2. Calibration, Switching, and Preprocessing

Accurate AoA estimation requires calibration of phase offsets across receiver chains. A calibration procedure typically involves connecting all anchor inputs to a common CW source via a splitter and measuring offset phases, which are then subtracted from subsequent Δφ readings to ensure geometric fidelity (Cominelli et al., 2019). Antenna switching is performed deterministically or pseudo-randomly to enhance tamper resistance and reduce predictability of sampling, mitigating protocol-level attacks.

Outlier screening is crucial in measurement campaigns. Robust preprocessing pipelines combine per-feature interquartile range (IQR), median absolute deviation (MAD), and multivariate minimum covariance determinant (MCD) tests to filter anomalous CTE packets, frequently reducing retained packet counts to below 10% of raw observations in cluttered indoor environments (Talebian et al., 1 Feb 2026).

3. End-to-End Positioning and Geometry Factor

After phase measurement and calibration, AoA per anchor is estimated—typically as a pair of angles (azimuth $\alpha$ and elevation $\gamma$). These are converted to unit vectors in each anchor's coordinate system: $$u_x = \cos(\alpha)\cos(90^\circ - \gamma), \quad u_y = \cos(\alpha)\sin(90^\circ - \gamma), \quad u_z = \sin(\alpha)$$ To fuse bearings from multiple anchors, coordinate frame alignment is performed via 3D rotation matrices $R(\psi, \theta, \phi)$ (Z–Y–X convention) estimated in an explicit calibration stage using tags at surveyed positions. The location $(x, y, z)$ of the tag is derived by solving the intersection (in a least-squares sense) of lines-of-bearing from transformed anchor unit vectors: $$\text{stack}\ F^{(i)}_{1,2} \rightarrow A[x, y, z]^T = B, \quad [x, y, z]^T = (A^T A)^{-1} A^T B$$ A geometry factor $G = \sqrt{\operatorname{trace}[(A^TA)^{-1}]}$ quantifies the dilution of precision (PDOP); low $G \lesssim 1.2$ yields sub-meter accuracy, while $G \gtrsim 1.8$ produces errors above 1 m (Alghananim et al., 15 Jan 2025).

4. Experimental Evaluation and Impact of Geometry

Performance strongly depends on antenna configuration and spatial geometry. In controlled outdoor and indoor trials, a two-anchor BLE 5.1 system with $d = 6$ cm spacing achieves standard angular errors $\sigma_\theta < 2^\circ$ over central angular cones (45°–135°) and sub-meter localization in 95% of estimates. Full circular arrays with $d\approx5$ cm spacing and eight elements enable unambiguous $360^\circ$ AoA estimation, exhibiting sinusoidal phase-difference profiles robust to multipath after software histogram-based filtering (Cominelli et al., 2019, Paulino et al., 2022).

Paired-geometry ensures redundancy: all adjacent pairs (in circular arrays) provide repeated information about the angle, improving confidence and allowing aggregation (e.g., through least-squares circle fit). The geometry factor $G$, anchor placement, and coverage volume are critical for ensuring bounded error—especially in kinematic mode or sparse deployments (Alghananim et al., 15 Jan 2025).

Anchor Geometry	G factor	Horizontal RMS (m)	Vertical RMS (m)
Corners (<1.3)	1.15	0.33	0.22
Edge (~1.6)	1.60	0.62	0.49
Center (>1.9)	2.15	1.14	2.12

Accuracies degrade with increased average tag-to-anchor distance and poor geometry.

5. Channel Characterization and Propagation Effects

Empirical signal statistics vary significantly between line-of-sight (LOS) and non-line-of-sight (NLOS) conditions. Rigorous paired LOS/NLOS BLE AoA datasets, collected under controlled geometry, reveal statistically significant differences across virtually all I/Q-derived features in both means and variances ($>$92% for variance).

Advanced characterization employs L-moment statistics (L-skewness $\tau_3$, L-kurtosis $\tau_4$) to distinguish regimes. NLOS yields “heavier tails” and higher skew (i.e., deeper fades, rare large peaks), best modeled by the four-parameter Kappa distribution (GoF $Z\approx0.01$–$0.0001$) and poorly by classical Rayleigh, Rice, or Normal models ($|Z| > 1.0$–$4.4$) (Talebian et al., 1 Feb 2026). This indicates that product-moment-based channel assumptions significantly underestimate the severity of NLOS-induced multipath.

Model	$Z_{\text{NLOS}}$	$D_{\text{NLOS}}$	$Z_{\text{LOS}}$	$D_{\text{LOS}}$
Kappa	0.0118	$3.2 \times 10^{-4}$	0.00018	$1.71 \times 10^{-4}$
Rayleigh	0.246	$3.06 \times 10^{-2}$	1.409	$6.39 \times 10^{-2}$
Rice	1.094	$1.47 \times 10^{-1}$	2.034	$8.77 \times 10^{-2}$

The L-moment approach also supports unsupervised LOS/NLOS detection, with clustering in $(\tau_3,\tau_4)$ space separating regimes more distinctly than clustering by product moments.

6. Security, Deployment Recommendations, and System Robustness

BLE AoA systems are vulnerable to protocol-level tampering, notably malicious transmitters injecting phase shifts during BLE CTE switch slots, thereby biasing AoA estimates. Recommended countermeasures include randomizing and secret-keeping antenna switch patterns, alternating reference antennas across packets, and augmenting CTEs with integrity checks (Cominelli et al., 2019).

Practical deployment guidelines include:

• Ensuring antenna spacing $d \leq \lambda/2$ to avoid spatial aliasing.
• Frequent RX chain calibration using a known continuous-wave source.
• Averaging AoA over $\geq 15$ BLE data channels to suppress multipath bias.
• Restricting operation to well-behaved angular cones (typically $45^\circ–135^\circ$) for stable phase-difference readings.
• Placing anchors on the convex hull of the area of interest and avoiding colinear anchor arrangements to minimize $G$.
• Keeping anchor-tag ranges below $4$ m for $\leq 0.5$ m accuracy (Alghananim et al., 15 Jan 2025).
• Using long CTE tones and maximal reference periods to enhance phase tracking.

A plausible implication is that robust AoA-based BLE systems must integrate geometry-aware anchor planning, heavy-tailed statistical channel models, and security-hardened switching protocols to achieve reliable sub-meter localization in realistic environments.

7. Implications and Future Perspectives

Paired-geometry BLE AoA measurement frameworks, combining signal-processing advances (phase-difference estimation, L-moment-based statistics), calibration and rotation estimation, and deployment-centric geometry analysis, now routinely achieve static sub-meter accuracy under controlled deployments. However, centimeter-level accuracy remains limited by physical aperture, multipath, and anchor geometry.

Key research directions include adoption of heavy-tailed channel models (e.g., Kappa), channel-state-adaptive processing, ML-based LOS/NLOS classifiers leveraging L-moment descriptors, and optimal anchor arrangement algorithms. Real-world deployments must contend with dynamic environment-induced degradation and persistently mitigate protocol- and signal-level vulnerabilities.

Together, these technical advances establish paired-geometry BLE AoA measurement as a rigorously characterized, mathematically tractable, and practically deployed location technology across diverse IoT contexts (Cominelli et al., 2019, Paulino et al., 2022, Alghananim et al., 15 Jan 2025, Talebian et al., 1 Feb 2026).