Protection levels (PLs) bound position errors under specified fault hypotheses and risk budgets, but advanced receiver autonomous integrity monitoring (ARAIM) is formulated for snapshot GNSS estimation rather than the correlated posterior of tightly coupled GNSS/IMU factor graph optimization (FGO). This paper formulates ARAIM solution separation and PL computation on the FGO posterior. Because current-epoch pseudorange factors enter only the current-state block of the fixed-lag information matrix, the fault-excluded position covariance, solution separation, and nominal-bias propagation follow exactly from the linearized current-state marginal, which re-tains correlations with velocity, IMU-bias, and clock states and with historical information. Woodbury updates with selected-output evaluation compute these quantities for fault-free, single-satellite, constellation-wide, and second-order hypotheses with-out repeated full-state inversion or graph reoptimization. Surrounding monitoring layers screen measurements, handle post-fit outliers, and determine PL validity and availability. In two road experiments, both nominal sequences achieve 100% horizontal and vertical empirical bounding over PL-valid epochs, with a maximum error-to-PL ratio of 0.96. Normalized errors show that the posterior covariance alone does not capture slowly varying ranging biases: a covariance-only bound computed from the same posteriors retains no resolvable margin, and strong temporal correlation limits the empirical evidence to consistency checks rather than validation of the integrity budget. On identical Experiment A posteriors, the proposed method reduces fault-hypothesis evaluation and PL solving time by 65.2% relative to direct full-state inversion with matching integrity decisions, and controlled fault injections demonstrate fail-safe PL invalidation while navigation continues.
Reliable positioning in dense urban environments remains challenging due to frequent GNSS signal blockage, multipath, and rapidly varying satellite geometry. While factor graph optimization (FGO)-based GNSS-IMU fusion has demonstrated strong robustness and accuracy, most formulations remain offline. In this work, we present a real-time tightly coupled GNSS-IMU FGO method that enables causal state estimation via incremental optimization with fixed-lag marginalization, and we evaluate its performance in a highly urbanized GNSS-degraded environment using the UrbanNav dataset.
Radu-Andrei Cioaca, Paul Irofti, Cristian Rusu +3
University Politehnica of Bucharest, Romania · Three Tensors S.R.L., Romania · University of Bucharest, Romania +2
Accurate positioning, navigation, and timing (PNT) is fundamental to the operation of modern technologies and a key enabler of autonomous systems. A very important component of PNT is the Global Navigation Satellite System (GNSS) which ensures outdoor positioning. Modern research directions have pushed the performance of GNSS localization to new heights by fusing GNSS measurements with other sensory information, mainly measurements from Inertial Measurement Units (IMU). In this paper, we propose a loosely coupled architecture to integrate GNSS and IMU measurements using a Factor Graph Optimization (FGO) framework. Because the FGO method can be computationally challenging and often used as a post-processing method, our focus is on assessing its localization accuracy and service availability while operating in real-time in challenging environments (urban canyons). Experimental results on the UrbanNav-HK-MediumUrban-1 dataset show that the proposed approach achieves real-time operation and increased service availability compared to batch FGO methods. While this improvement comes at the cost of reduced positioning accuracy, the paper provides a detailed analysis of the trade-offs between accuracy, availability, and computational efficiency that characterize real-time FGO-based GNSS/IMU fusion.
Radu-Andrei Cioaca, Cristian Rusu, Paul Irofti +3
Three Tensors S.R.L., Romania · Navigation Systems Definition Section (TEC-SEN), European Space Agency · Romanian InSpace Engineering S.R.L. (RISE), Romania
In Global Navigation Satellite System (GNSS)-degraded environments, pseudolites (PLs) provide additional signal sources to enhance positioning performance, but their integration in optimization-based frameworks remains limited. This paper presents a loosely coupled factor graph optimization (FGO) framework that fuses the GNSS/PL least-squares (LS) solutions with inertial measurement unit (IMU) data. The evaluation considers low GNSS visibility scenarios with four high-elevation GNSS satellites and up to two PL transmitters over an 80~s window. FGO achieves a 22.8% to 41.3% reduction in mean 3D error compared to standard LS methods. Compared to a GNSS-IMU baseline, incorporating PL transmitters further improves positioning accuracy, with performance depending on geometry.