GNSS/UWB/IMU Fusion Framework

• GNSS/UWB/IMU Fusion Framework is a comprehensive approach that integrates satellite fixes, UWB ranging, and inertial dead-reckoning to achieve robust localization.
• Fusion architectures employ diverse methods like Grid filters, ESKF, FGO, and Particle Filters to mitigate sensor limitations such as multipath, drift, and NLOS errors.
• Real-world experiments show sub-meter mean error in static conditions and ~1.6 m error in dynamic urban vehicular trials, demonstrating the framework's practical accuracy.

Global Navigation Satellite Systems (GNSS), Ultra-Wideband (UWB), and Inertial Measurement Units (IMU) represent three complementary modalities for robust localization in outdoor and indoor environments. GNSS/UWB/IMU fusion frameworks tightly combine these diverse sensor data streams to mitigate individual weaknesses such as GNSS multipath and blockage, UWB signal degradation, and IMU drift, enabling continuous, accurate pose estimation for vehicles and pedestrians even across challenging transitions between environments. Fusion architectures vary in estimator structure, state-space formulation, measurement models, and strategies for handling nonlinearity, asynchrony, and map constraints.

1. System Architecture and State Representation

A unified GNSS/UWB/IMU fusion framework comprises several sensor front-ends and a probabilistic back-end. The canonical state vector encompasses position, velocity, and orientation. For vehicles, a discrete grid-based state $x_i = [x_i, y_i, z_i]^T$ is often used; in pedestrian systems, the state can be parameterized as $x_k = [p_k; v_k; q_k]$ with $p_k \in \mathbb{R}^3$, $v_k \in \mathbb{R}^3$, and $q_k \in \mathrm{SO}(3)$. In planar pedestrian fusion, a reduced state $T_k = [x_k, y_k, \psi_k]^T$ suffices (Schwarzbach et al., 2023, Zhang et al., 11 Dec 2025).

The IMU provides inertial dead-reckoning increments; UWB delivers absolute or relative ranging to known anchors; GNSS yields position fixes or raw pseudoranges. Seamlessly fusing these asynchronous, multi-rate sources requires state estimation paradigms capable of integrating both tightly-coupled geometric observations and loosely coupled absolute fixes, while managing multi-modal posteriors in NLOS conditions and enforcing map-based feasibility constraints.

2. Sensor Models and Measurement Updates

IMU/Odometry Motion Model

Discrete motion increments are produced from wheel odometry or pedestrian dead-reckoning (PDR) via step detection and a calibrated Weinberg-style step-length estimator. Propagation of the state follows

$$p_{k+1} = p_k + \Delta p_k, \quad \psi_{k+1} = \psi_k + \Delta \psi_k$$

for planar PDR, with propagation noise incorporated via Gaussian process models (Zhang et al., 11 Dec 2025).

GNSS Measurement Model

For tight integration, frameworks employ raw pseudorange or pseudorange-difference (BSSD) likelihoods, incorporating multi-path/NLOS effects via Gaussian mixture models (GMM). In hybrid particle/grid filters:

$$L_i^{\rm GNSS} = \sum_{c=1}^{C} \omega_c \prod_{s_1 \neq s_2} \mathcal{N}(y_i^{s_1 s_2}; \mu_c, \Sigma_c)$$

where $y_i^{s_1 s_2}$ is the innovation between measured and predicted between-satellite single differences at grid cell $i$ (Schwarzbach et al., 2023). Alternatively, loosely-coupled approaches treat each GNSS fix as a direct observation:

$$z^{\rm GNSS}_k = H_G x_k + v_k, \qquad v_k \sim \mathcal{N}(0, R_G)$$

with $H_G$ a selection matrix (Zhang et al., 11 Dec 2025).

UWB Measurement Model

UWB anchor-based two-way ranging yields

$$z^{\rm UWB}_{k,i} = \| p_k - p_A^{(i)} \| + \eta_{k,i}, \qquad \eta_{k,i} \sim \mathcal{N}(0, \sigma_r^2)$$

Measurement noise is modeled as a mixture to capture LOS/NLOS:

$$L_i^{\rm UWB} = \phi \mathcal{N}(y_i^n; 0, \sigma_{\rm LOS}^2) + (1-\phi) \mathcal{N}(y_i^n; \mu_{\rm NLOS}, \sigma_{\rm NLOS}^2)$$

with empirical parameters obtained from real-world deployment (Schwarzbach et al., 2023, Zhang et al., 11 Dec 2025).

3. Fusion Algorithms: Grids, Kalman, Graphs, and Particles

Three principal back-end algorithmic paradigms are employed for GNSS/UWB/IMU fusion, each with distinct statistical and computational properties (Zhang et al., 11 Dec 2025, Schwarzbach et al., 2023):

Grid (Recursive Bayes) Filter

• State space discretized into a 2D/3D grid; each cell maintains posterior probability $p_i^k$.
• Prediction: Convolve $p_i^{k-1}$ with a motion model kernel parameterized by velocity and heading.
• Measurement update: Multiply predicted probabilities by likelihoods from all geometric measurements (GNSS BSSD, UWB ranges).
• Normalization and extraction: Posterior is normalized, MAP cell extracted, and optionally a local weighted mean is computed.
• Tight coupling is realized by integrating raw measurements via shared likelihoods over the grid and by triggering predict/update on arrival of any sensor packet (multi-rate, time-synchronized).
• Superior for handling nonlinearities, multi-modal posteriors, and non-Gaussian errors in urban canyons.
• Demonstrated mean L2 error of $0.64$ m (static), $1.62$ m (dynamic) in urban vehicular trials (Schwarzbach et al., 2023).

Error-State Extended Kalman Filter (ESKF)

• Nominal state and error-state are maintained; predicts using deterministic IMU/PDR increments, corrects upon GNSS/UWB measurement arrival.
• Covariance propagation via linearized dynamics; standard KF update equations.
• Map constraints enforced by rejecting or projecting updates violating forbidden regions.
• Consistent covariance tracking, fast computation, and best median and RMSE in tested indoor/outdoor/seamless scenarios; mean horizontal errors of $0.44$–$1.73$ m (Zhang et al., 11 Dec 2025).

Sliding-Window Factor Graph Optimization (FGO)

• Maintains a moving window of poses $\{T_k\}$; defines between-factors for PDR increments and unary factors for GNSS/UWB.
• Map constraints incorporated via soft-penalty factors in the cost function.
• Solved by Gauss-Newton or Levenberg-Marquardt iterations; offers smooth trajectory refinement leveraging future information.
• Computationally heavier, particularly sensitive to window size and factor tuning, with occurrence of larger tail errors during transitions (Zhang et al., 11 Dec 2025).

Particle Filter (PF)

• Population of particles propagated by noisy motion model; weighted by absolute measurement likelihoods and enforced map feasibility.
• Well-suited to non-Gaussian, multi-modal distributions (e.g., UWB NLOS outliers, ambiguous GNSS solutions); simple map constraint via particle culling.
• Requires substantial computation and memory; accuracy lags ESKF slightly in tested implementations (mean error $0.49$–$2.28$ m) (Zhang et al., 11 Dec 2025).

4. Asynchronous Multi-Rate Fusion and Time Synchronization

Each measurement source (GNSS, UWB, IMU/PDR) operates at a different, potentially non-deterministic rate, arriving asynchronously. Efficient fusion frameworks implement a sequential, multi-rate filter:

• Each odometry/IMU increment triggers a predict-only step; GNSS or UWB arrivals trigger a full predict+update cycle.
• Sensor packets are timestamped; a common “filter clock” is maintained.
• Out-of-sequence packets can be either ignored for low rates or trigger replayed predictions and updates to accommodate late arrivals.
• This strategy eliminates the need for explicit interpolation and robustly handles the asynchronous sensor modalities inherent to wearable or vehicular systems (Schwarzbach et al., 2023, Zhang et al., 11 Dec 2025).

5. Map-Based Constraints and Environment Geometry

Environmental geometry is leveraged to constrain trajectory estimates:

• Building footprint data (e.g., OpenStreetMap polygons) defines the navigable free space $\mathcal{F} \subset \mathbb{R}^2$; interiors except instrumented areas are forbidden.
• Map constraints are integrated via:
  • Hard rejection or projection in ESKF when a state lands in forbidden space.
  • Penalty factors in FGO: $$\varphi_{\rm map}(p_k) = \lambda \cdot \max(0, -d_{\rm map}(p_k))^2$$.
  • Weight culling in PF for particles entering forbidden zones.
• Map-aided NLOS screening adjusts measurement likelihoods based on line-of-sight occlusions, enhancing robustness when GNSS signals traverse building boundaries.
• These geometric constraints limit PDR drift, reject erroneous GNSS fixes, and improve transition robustness across indoor/outdoor boundaries (Zhang et al., 11 Dec 2025, Schwarzbach et al., 2023).

6. Experimental Results and Quantitative Performance

Extensive real-world evaluations demonstrate the efficacy of GNSS/UWB/IMU fusion:

Scenario	Estimator	Mean Error (m)	Median (m)	RMSE (m)	Max (m)
Indoor (UWB+PDR)	ESKF	0.441	0.415	0.499	1.309
	PF	0.491	0.447	0.552	1.374
	FGO	0.836	0.715	0.992	3.303
Outdoor (GNSS+PDR)	ESKF	1.726	1.491	2.186	8.181
	PF	2.284	1.681	2.816	7.357
	FGO	1.995	1.946	2.389	7.619
Outdoor–Indoor Seamless	ESKF	1.085	0.997	1.248	2.631
	PF	1.292	1.017	1.653	5.108
	FGO	2.070	1.962	2.302	5.351

In urban vehicular tests, the 3DMA multi-epoch Grid Filter maintained sub-meter mean error in static settings and ~1.6 m in dynamic conditions. In all wearable pedestrian benchmarks, the ESKF achieved the lowest median and RMSE error, with factor graphs and particle filters providing additional robustness to non-Gaussian and multi-modal errors, particularly in transition and NLOS scenarios (Schwarzbach et al., 2023, Zhang et al., 11 Dec 2025).

7. Implementation and Practical Considerations

Real-world prototypes utilize modular ROS 2 architectures, timestamped sensor streams, and visualization in real time (e.g., Foxglove Studio). Sensor modules include IMU/PDR nodes (step detection, heading fusion), GNSS modules (NavSatFix—ENU conversion), UWB anchors (e.g., Decawave DWM1001), and various computational back-ends (ESKF, FGO, PF).

Quantitative ground-truthing employs motion-capture or RTK for accuracy assessment. Hardware platforms have included automotive setups (u-blox F9P, ZigPos UWB, vehicle odometry) and wearable pedestrian rigs (Raspberry Pi 5, Xsens MTi-300 IMU, u-blox ZED-F9P, Decawave UWB) (Schwarzbach et al., 2023, Zhang et al., 11 Dec 2025).

Overall, tightly integrated GNSS/UWB/IMU fusion frameworks with explicit modeling of propagation environments, geometric constraints, and sensor asynchrony yield robust, accurate, and drift-resilient localization in heterogeneous, real-world environments. The selection of estimator should be governed by computational constraints, error models, and the expected degree of environmental complexity.