Phased-array Bluetooth systems have emerged as a low-cost alternative for performing aided inertial navigation in GNSS-denied use cases such as warehouse logistics, drone landings, and autonomous docking. Basing a navigation system off of commercial-off-the-shelf components may reduce the barrier of entry for phased-array radio navigation systems, albeit at the cost of significantly noisier measurements and relatively short feasible range. In this paper, we compare robust estimation strategies for a factor graph optimisation-based estimator using experimental data collected from multirotor drone flight. We evaluate performance in loss-of-GNSS scenarios when aided by Bluetooth angular measurements, as well as range or barometric pressure.
Global navigation satellite systems (GNSS) are ubiquitous in modern-day aided inertial navigation systems (INS). However, depending on the use case, GNSS may not be available at all (e.g., when indoors) or the availability of GNSS may be severely degraded due to natural or intentional interference (e.g., multipath in a dense urban area or signal jamming or spoofing). Consequently, GNSSdenied INS are necessary in these domains with examples including systems based on LiDAR (Brossard et al., 2022), vision (Lupton and Sukkarieh, 2012), and phased-array radio systems (PARS) (Okuhara et al., 2023).
Although most PARS-based navigation systems can be categorised as industry-or military-grade, Bluetooth Low Energy (BLE) PARS has emerged as a low-cost alternative based on commercial-off-the-shelf (COTS) components for aiding of e.g., fixed-wing UAV flight (Sollie et al., 2024). By basing a navigation system on COTS BLE components, the barrier of entry for employing such phased-array radio systems can be greatly reduced, albeit at the cost of a relatively short operating range and considerably noisier measurements. Furthermore, additional time synchronisation of measurements is necessary as a result of antenna switching and less stable oscillators (Sollie et al., 2022). Consequently, it is essential to employ robust estimation techniques to handle outliers.
⋆ The work is supported by the Research Council of Norway through the project Phased-array radio systems for resilient localization and navigation of autonomous systems in GNSS-denied environments PARNAV (no. 338789). This work has been submitted to IFAC for possible publication.
In Sørensen et al. (2025), we presented an estimation scheme fusing PARS and inertial measurements based on factor graph optimisation (FGO), comparing performance against the industry-standard error-state Kalman filter (ESKF) in a simulation study. Outliers were handled with the natural test (NT), the Huber M-estimator, or the Tukey M-estimator (Gustafsson, 2010;Zhang, 1997) in the presence of simulated sensor faults. In this paper, we present the following contributions building on our previous publication:
• We apply our estimation framework on experimental data from multirotor drone flight, showcasing feasibility of BLE PARS-aided INS. • We compare the performance of our FGO-based estimator on the SE(3) matrix Lie group against a benchmark ESKF in handover scenarios where the drone goes from using Real-time kinematics (RTK)-GNSS aiding with position and compass measurements to (1) BLE PARS and RTK-GNSS range and
(2) BLE PARS and barometric pressure.
RTK-based range measurements are used as an intermediary step since it allows us to experimentally verify the methods in the face of e.g., multipath. Integration of Bluetooth LE range from channel sounding (Nordic Semiconductor, 2025) is planned.
Vectors and matrices are given in bold face, cursive lowercase v and uppercase letters A, respectively. R b a represents the rotation matrix between two coordinate frames, i.e., from frame {a} to frame {b}. In this paper, four frames are considered: local North-East-Down navigation frame {n}, the BODY-frame {b}, the inertial measurement unit (IMU) sensor frame {s}, and the Bluetooth PARS radio frame {r}. E.g., p n rb denotes the position measured in {b} relative to {r}, decomposed in {n}. Estimates are expressed with a hat, e.g., x is an estimate of x.
The SE(3) matrix Lie group is defined as the set of poses
with the corresponding Lie algebra se(3) given by the set of matrices
where ξ • is a small, local perturbation mapped to the Lie algebra using the hat operator ∧ . The exponential map of the Lie group is subsequently defined using the matrix exponential: Exp (ξ) ≜ exp (ξ ∧ ), and maps a matrix in the Lie algebra onto the Lie group itself. The reader is referred to Barfoot and Furgale (2014) for details.
The angle-of-arrival (AoA) measurements from the Bluetooth PARS receiver are obtained using direction finding. This involves appending a constant tone extension (CTE) to each advertisement packet sent from the transmitter, which is subsequently sampled by the antennae at the receiver. The raw samples are then transformed into angular measurements (azimuth Ψ and elevation α), similar to the ones found in Gryte et al. (2019):
where ε is zero-mean Gaussian noise and ρ is the horizontal range of the measured position in {r}, i.e., the Euclidean distance between the horizontal components and the origin of {r}. This is the same model we used in Sørensen et al. (2025), with the notable exclusion of the range, which is not available with direction finding. The rotation matrix R n r relating {r} to {n} needs to be estimated via rough calibration based on mounting or through some form of calibration algorithm using GNSS, as done in e.g., Okuhara et al. (2023). If the origin of {r} differs from that of {n}, the lever arm l n P ARS must also be accounted for, i.e, p n rb = R n r p r rb + l n P
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