UMLoc: Uncertainty-Aware Map-Constrained Inertial Localization with Quantified Bounds

TL;DR

UMLoc addresses drift in GPS-denied indoor localization by jointly modeling IMU uncertainty and map constraints. It combines an LSTM-based quantile regression module that outputs velocity bounds with a cross-attention CGAN conditioned on a 2D floor plan to generate map-consistent trajectories, propagating uncertainty through to the final predictions. The approach yields calibrated prediction intervals at $68\%$, $90\%$, and $95\%$ levels and demonstrates drift resilience, achieving an average drift of about $5.9\%$ over $70\,\mathrm{m}$ and an ATE around $1.36\,\mathrm{m}$ on a new indoor dataset, while maintaining map feasibility. The results show improved robustness, generalization across buildings and competitive performance on public datasets, indicating practical viability for real-world indoor navigation without GPS.

Abstract

Inertial localization is particularly valuable in GPS-denied environments such as indoors. However, localization using only Inertial Measurement Units (IMUs) suffers from drift caused by motion-process noise and sensor biases. This paper introduces Uncertainty-aware Map-constrained Inertial Localization (UMLoc), an end-to-end framework that jointly models IMU uncertainty and map constraints to achieve drift-resilient positioning. UMLoc integrates two coupled modules: (1) a Long Short-Term Memory (LSTM) quantile regressor, which estimates the specific quantiles needed to define 68%, 90%, and 95% prediction intervals serving as a measure of localization uncertainty and (2) a Conditioned Generative Adversarial Network (CGAN) with cross-attention that fuses IMU dynamic data with distance-based floor-plan maps to generate geometrically feasible trajectories. The modules are trained jointly, allowing uncertainty estimates to propagate through the CGAN during trajectory generation. UMLoc was evaluated on three datasets, including a newly collected 2-hour indoor benchmark with time-aligned IMU data, ground-truth poses and floor-plan maps. Results show that the method achieves a mean drift ratio of 5.9% over a 70 m travel distance and an average Absolute Trajectory Error (ATE) of 1.36 m, while maintaining calibrated prediction bounds.

Figures (6)

• Figure S1: Schematic of UMLoc. IMU sequences $X_{1:t}$ feed an LSTM quantile regressor that predicts lower and upper conditional quantiles, while CNN encodes the distance map $\mathcal{M}$. Cross-attention then fuses the IMU with the map features and the decoder generates velocities $\hat{V}_{1:t}$ which are integrated to obtain the positions. The discriminator $\mathcal{D}$ uses the CNN and $2$ LSTMs encoders followed by MLP to distinguish between real and generated sequences.
• Figure S2: CDFs of ATE (left) and RTE (right) on our datasets' unseen testing split. UMLoc achieves $80\%$ cumulative probability below $2.5\,m$ error, whereas other models have it at $7.5\,m$.
• Figure S3: Selected 2D trajectory visualizations. We selected 6 trajectories from our dataset that include the map.
• Figure S4: Illustrations of $20$ trajectory samples from CGAN for $6$ testing trajectories from our dataset. High intensity represents a higher probability of pedestrian location.
• Figure S5: Drift error versus traveled distance for the map-aware model (UMLoc) and its IMU-only variant. Curves show the median drift across unseen test sequences. We computed the error over the average travel distance of $70\,m$ after aggregating all the trajectories. The shaded area denotes the drift distribution over the testing trajectories. Incorporating map information (blue) constrains maximum drift growth to $5\,m$ throughout the testing trajectories versus $13\,m$ in the IMU-only model (orange), demonstrating the map’s effectiveness in long-distance indoor localization.