Two stage GNSS outlier detection for factor graph optimization based GNSS-RTK/INS/odometer fusion

TL;DR

This work tackles the challenge of GNSS outliers in complex environments by introducing a two-stage outlier mitigation that combines GNSS-only Doppler-based checks with IMU/odometer-aided predictions within a factor graph framework. The first stage uses Doppler to generate a coarse, GNSS-only screening, while the second stage leverages pre-integrated IMU and odometer data to produce physically grounded predictions of double-difference ranges for refined outlier rejection. Integrated into a tightly coupled GNSS-RTK/INS/odometer fusion via a factor graph, the approach delivers improved robustness and centimeter-level accuracy in open-sky and highly degraded urban canyon scenarios, as demonstrated by significant RMSE reductions (e.g., from $0.52$ m to $0.30$ m in deep urban canyons). The practical impact lies in more reliable outdoor navigation for autonomous ground vehicles in GPS-challenged environments, with potential extensions to multi-constellation GNSS and additional sensors for further resilience.

Abstract

Reliable GNSS positioning in complex environments remains a critical challenge due to non-line-of-sight (NLOS) propagation, multipath effects, and frequent signal blockages. These effects can easily introduce large outliers into the raw pseudo-range measurements, which significantly degrade the performance of global navigation satellite system (GNSS) real-time kinematic (RTK) positioning and limit the effectiveness of tightly coupled GNSS-based integrated navigation system. To address this issue, we propose a two-stage outlier detection method and apply the method in a tightly coupled GNSS-RTK, inertial navigation system (INS), and odometer integration based on factor graph optimization (FGO). In the first stage, Doppler measurements are employed to detect pseudo-range outliers in a GNSS-only manner, since Doppler is less sensitive to multipath and NLOS effects compared with pseudo-range, making it a more stable reference for detecting sudden inconsistencies. In the second stage, pre-integrated inertial measurement units (IMU) and odometer constraints are used to generate predicted double-difference pseudo-range measurements, which enable a more refined identification and rejection of remaining outliers. By combining these two complementary stages, the system achieves improved robustness against both gross pseudo-range errors and degraded satellite measuring quality. The experimental results demonstrate that the two-stage detection framework significantly reduces the impact of pseudo-range outliers, and leads to improved positioning accuracy and consistency compared with representative baseline approaches. In the deep urban canyon test, the outlier mitigation method has limits the RMSE of GNSS-RTK/INS/odometer fusion from 0.52 m to 0.30 m, with 42.3% improvement.

Figures (10)

• Figure 1: Basic principal of the proposed GNSS outlier detection method, where real red shape and line denote the receiver position estimated using pseudo-range measurements and the pseudo-range affected by multi-path signal, the dashed blue shape and line denotes the predicted position and the predicted range measurement using Doppler or IMU/odometer measurements.
• Figure 2: GNSS/INS/odometer integrated factor graph structure overview, including state nodes and factor edges composed by marginalization, double differenced pseudo-range, double differenced carrier-phase, Doppler, IMU integral and odometer integral measurements.
• Figure 3: Application of the outlier detection method in an FGO-based GNSS-RTK/INS/odoemter fusion system, including four parts: measurement input (grey boxes), the proposed two-stage GNSS outlier detection (pink boxes), factor formulation (blue boxes), optimization and ambiguity resolution (yellow boxes). The pink boxes denote the main contributions of this work.
• Figure 4: The open-sky scene view
• Figure 5: satellite number and PDOP overview, while the average satellite number is 16.78 and the average PDOP is 1.34