ITF project: Safety-certified multi-source fusion positioning (HK$1.18M ITF project)

ITF project: Safety-certified multi-source fusion positioning (HK$1.18M ITF project)

• Motivation
  • The widespread deployment of autonomous vehicles (AVs) in dense urban environments (like Hong Kong’s “Urban Canyons”) is hindered by severe “long-tail” safety risks such as signal occlusion, Non-Line-of-Sight (NLOS) reception, and multipath effects.
  • Traditional GNSS filters rely on Gaussian error assumptions that fail to capture the heavy-tailed, non-Gaussian errors typical of urban canyons, leading to underestimated position uncertainty.
  • Existing commercial positioning solutions focus primarily on accuracy and lack real-time integrity monitoring (such as quantifying a Protection Level), creating a dangerous “blind trust” hazard for AV navigation stacks.
• Method Developed The project developed a safety-certified multi-source fusion positioning system consisting of two core innovative algorithms:
  1. Fault Diagnosis Module: This front-end algorithm autonomously identifies and excludes faulty measurements using multiple modalities. It uses a fisheye camera-aided Vision Transformer (ViT) for sky segmentation to directly detect and exclude NLOS satellites. It also features a loosely-coupled LiDAR/Inertial Factor Graph Optimization (FGO) module to provide an initial high-frequency positioning guess. Finally, it employs Adaptive Incremental Pseudorange Error Modeling (AIPEM) using Gaussian Mixture Models (GMM) to dynamically capture heavy-tailed measurement errors and perform statistical Adaptive Fault Detection and Exclusion (AdaptiveFDE).
  2. Simultaneous Positioning and Safety Certification: This back-end Risk-aware FGO (IM-FGO) fuses the remaining “basically healthy” GNSS measurements with the multi-sensor initial state. Instead of hard-excluding slightly contaminated measurements, it uses “switch variables” to dynamically reweight them. By applying stringent safety constraints—including a residual-based Chi-square test and a Multiple Hypothesis Solution Separation (MHSS) integrity risk constraint—the system outputs both high-precision positioning and a real-time Horizontal Protection Level (HPL).
• Experiments Conducted
  • Hardware Setup: The algorithms were deployed on a surveying vehicle equipped with a commercial u-blox Zed F9P GNSS receiver, Xsens/Bynav IMUs, Velodyne/RoboSense LiDARs, and a sky-pointing fisheye camera. A tactical-grade NovAtel SPAN-CPT RTK/INS system was used to provide centimeter-level ground truth.
  • Test Scenarios: Extensive field validation was conducted across six distinct high-density urban scenarios in Hong Kong, including Kowloon Tong, Hong Kong Science Park, West Kowloon Cultural District, Sha Tin Center, East Tsim Sha Tsui, and Nathan Road.
• Result Analysis The proposed system successfully met or exceeded all of the project’s stringent Key Performance Indicators (KPIs) and comprehensively outperformed the commercial u-blox F9P NMEA solution baseline:
  • Fault Detection Rate (FDR): The system consistently achieved an FDR above 90% across all scenes (ranging from 91.79% in West Kowloon up to 100% in Sha Tin Center).
  • Horizontal Positioning Error (HPE): The maximum horizontal positioning error remained tightly controlled within the 0.4-meter target, with mean HPEs ranging from just 0.132m to 0.234m depending on the scenario.
  • Horizontal Protection Level (HPL): The system consistently produced a reliable safety bound, keeping the maximum HPL strictly below the 1.5-meter automotive Alert Limit requirement (averaging around 1.37m) across all tested urban canyons.
  • Computational Efficiency: The total average processing time for executing both complex algorithms (including image processing and FGO) ranged from 31.30 ms to 33.26 ms per epoch, easily satisfying the strict < 0.05 seconds real-time operational requirement.

Jackknife ARAIM: Efficient GNSS Integrity Monitoring for Simultaneous Faults under Non-Gaussian Errors

• Motivation: Mainstream fault detection methods in navigation rely on Gaussian assumptions for nominal errors. Current non-Gaussian alternatives lack rigorous statistical properties or are computationally expensive, hindering reliability in real-world environments. Advanced Receiver Autonomous Integrity Monitoring (ARAIM) usually assumes Gaussian nominal errors, which causes overly conservative protection levels in non-Gaussian reality. Existing multi-hypothesis algorithms that solve this are computationally exhausting when handling multiple simultaneous faults.
• Method: Develops a “jackknife detector” tailored for linearized pseudorange-based systems. It leverages the cross-validation jackknife technique to derive a test statistic (a linear combination of measurement errors) without restrictive distribution assumptions. Proposes a “Jackknife ARAIM” adopting a hybrid strategy: it uses fast scalar jackknife residual tests for single-fault modes, and triple-axis (East/North/Up) combinations of jackknife residuals for multi-fault modes. Incorporates non-Gaussian overbounding to safely model heavy tails.
• Experiments 1: Evaluated via worldwide simulations (MAAST), a DGNSS setup using CORS data from Minneapolis with artificially injected bias, and a real-world evaluation using single-frequency SPP to detect the actual GPS PRN-1 satellite clock anomaly.
• Result Analysis 1: Outperformed multiple hypothesis solution separation (MHSS) in detection rate under non-Gaussian noises (e.g., detecting small 3m-6m faults significantly better). For the real-world satellite anomaly, the JT detector identified the fault 8 minutes earlier than MHSS.
• Experiments 2: Worldwide simulations targeting LPV-200 precision approach requirements using both single (GPS) and dual constellations (GPS-Galileo). Nominal measurement errors were bounded using authentic experimental data profiles.
• Result Analysis 2: Achieved theoretically equivalent monitoring performance to standard Solution Separation (SS) ARAIM but proved significantly more computationally efficient for single-fault modes. It reduced the 99.5 percentile Vertical Protection Level (VPL) below 45m (compared to 50m for Gaussian algorithms).

2. Credible Uncertainty Quantification under Noise and System Model Mismatch

• Motivation: State estimators provide self-assessed uncertainties (e.g., covariances) that are often misleading due to Noise Model Mismatch (NMM) or System Model Mismatch (SMM). Standard metrics like NEES or NCI cannot independently separate system biases from pure optimism/pessimism.
• Method: Proposes a unified multi-metric credibility framework. It uses an Empirical Location Test (ELT) based on energy distance to first detect SMM (bias). If SMM exists, it centers the residuals and applies “directional probing” (artificially scaling the covariance) using the asymmetric sensitivities of Negative Log-Likelihood (NLL) and Energy Score (ES) to pinpoint optimism or pessimism.
• Experiments: Validated via Monte Carlo simulations evaluating 2D to 100D state estimations across six distinct credibility scenarios. Further validated on a real-world ultra-wideband (UWB) positioning dataset (STAR-loc).
• Result Analysis: Achieved 80%–100% diagnosis accuracy in simulations, significantly outperforming single-metric baselines. In real UWB data, it successfully untangled the nuances of the data, accurately diagnosing the coexistence of both pessimism and SMM that traditional NEES missed.

3. Fault Detection Algorithm for Gaussian Mixture Noises: An Application in Lidar/IMU Integrated Localization Systems

• Motivation: Conventional chi-squared fault detection methods assume Gaussian noise distributions, limiting their effectiveness for real-world lidar-based localization systems where noise exhibits heavy-tailed or non-Gaussian behaviors.
• Method: Models non-Gaussian noises as a Gaussian Mixture Model (GMM). It rigorously propagates this error through an Extended Kalman Filter (EKF) to establish the GMM relationship with the measurement residual. The residual is then transformed to approximate a standard multivariate normal distribution, enabling a reliable chi-squared test statistic.
• Experiments: Applied to a 2D Lidar/IMU integrated localization system in a simulated urban environment constructed in the CARLA 3D simulator, where step failures (faults) were artificially injected into the measurements.
• Result Analysis: The proposed total Gaussian-GMM method outperformed conventional Gaussian methods, exhibiting a 30% improvement in the fault detection rate and a 17%–23% reduction in detection delay during failures.

Integration of Vehicle Dynamic Model and System Identification Model for Extending the Navigation Service Under Sensor Failures

• Motivation: Autonomous Vehicles (AVs) rely heavily on active/passive sensors (LiDAR, GNSS) which are vulnerable to spoofing, weather, or signal outages. Vehicle Dynamic Models (VDM) provide an environmentally independent backup, but their accuracy degrades quickly due to inaccurate system dynamics modeling.
• Method: Proposes a sensor-free localization method (VDM-SI). It integrates System Identification (SI) using low-order process models (e.g., pseudo-random binary sequence inputs) to learn the real-time response of the AV’s powertrain and steering. These responses are fed as control inputs into the VDM to estimate vehicular positioning during outages.
• Experiments: Conducted in a half-simulated environment using Gazebo. Tested the AV driving along a 90-degree bend and an S-curve. Also simulated a scenario where sensors fail entirely and then recover, requiring the VDM to provide an initial guess for re-localization.
• Result Analysis: VDM-SI reduced the mean absolute translation error by roughly 70% compared to a conventional VDM. It significantly improved fusion stability under high noise and safely extended the acceptable sensor outage time window for successful re-localization.

Investigation of performance improvement in GNSS PPP-RTK ambiguity resolution via Gaussian overbounding for heavy-tailed error modeling

• Motivation: In precise point positioning-real time kinematic (PPP-RTK) systems, unmodeled heavy-tailed noise degrades ambiguity resolution (AR), leading to incorrectly fixed ambiguities and safety hazards.
• Method: Evaluates a single-epoch Weighted Least Squares (WLS) PPP-RTK estimator utilizing Gaussian Cumulative Distribution Function (CDF) overbounding instead of traditional Gaussian fitting to create a conservative stochastic model for pseudorange and carrier phase errors.
• Experiments: Conducted dual-frequency simulation experiments generating specific heavy-tailed noises (via GMMs and real-data sampling) alongside real-world static tests using a dataset from a reference station in Hong Kong.
• Result Analysis: The overbounding method heavily suppresses the miss detection rate (incorrectly fixed ambiguities) compared to traditional fitting, trading a slight amount of fix-rate availability for massive reliability gains. On the real dataset, it reduced the 3D RMSE of fixed solutions by an average of 18.34%.

Learning Credible Weightings based on Differential Factor Graph Optimization for Urban GNSS Navigation

• Motivation: Learning-based Differentiable Factor Graph Optimization (DFGO) typically trains purely on point-estimation geometric accuracy (MAE). This causes “covariance collapse,” where the estimator outputs confident but heavily biased uncalibrated covariances in urban canyons under severe Non-Line-of-Sight (NLOS) conditions.
• Method: Proposes CredibleDFGO (CDFGO). By supervising the end-to-end network with strictly proper scoring rules (Negative Log-Likelihood and Energy Score) instead of pure geometric loss, it forces the network to learn measurement weighting policies that output heteroscedastic, statistically calibrated posterior covariances.
• Experiments: Tested on the UrbanNav dataset in Hong Kong across varying complexities (Medium, Deep, and Harsh urban canyons) using commercial hardware (u-blox ZED-F9P) and high-grade SPAN-CPT ground truth.
• Result Analysis: Greatly improved probabilistic calibration without sacrificing accuracy. In the Harsh Urban sequence, it reduced the mean horizontal error by 15.2% and slashed the dangerous $3\sigma$ confidence exceedance rate from a failing 44.72% down to 10%, generating realistic map-level uncertainty envelopes.

Multiple Faults Isolation for Multiconstellation GNSS Positioning Through Incremental Expansion of Consistent Measurements

• Motivation: Deletion-based greedy search algorithms for fault detection suffer from the “swamping effect” (wrongly excluding healthy measurements). When handling multiple simultaneous faults, this aggressive exclusion reduces satellite geometry and degrades post-isolation positioning accuracy.
• Method: Proposes an incrementally expanding algorithm. It starts by constructing a minimum basic set assumed to be fault-free (based on smallest studentized residuals). It then expands this set iteratively using constellation-grouped studentized and jackknife residuals, stopping when a no-fault hypothesis test fails.
• Experiments: Worldwide simulations using 3- and 4-constellation grids injecting massive simultaneous faults (up to 15), Monte Carlo simulations testing fault magnitude stability, and real-world CORS data testing with injected biases.
• Result Analysis: Successfully reduced the mean swamping event rate by over 26% compared to deletion-based greedy searches. Because it preserved geometry by not wrongly deleting healthy satellites, it achieved a massive 75% reduction in mean post-isolation positioning error, running efficiently in under 30ms.

Principal Gaussian Overbound for Heavy-Tailed Error Bounding

• Motivation: Single-Gaussian overbounding methods for heavy-tailed GNSS errors require massive variance inflation, which leads to huge protection levels that ruin system availability.
• Method: Proposes the Principal Gaussian Overbound (PGO). It uses a Bimodal Gaussian Mixture Model (BGMM) to fit the empirical distribution, deriving a bound that tightly hugs the core while expanding appropriately for the tails. It incorporates Fast Fourier Transform (FFT) algorithms to accelerate convolution.
• Experiments: Validated using two real-world datasets: one year of open-sky DGNSS pseudorange data from the CORS network in Minneapolis, and a DGNSS dataset from a heavy-multipath, slightly urbanized seaside area in Hong Kong.
• Result Analysis: Demonstrated zero hazardously misleading information (HMI) events. For the challenging urban dataset, PGO maintained tightness and reduced the mean VPL by over 78% compared to the two-step Gaussian method, all while computing in just 0.08 seconds via FFT.

Reliable Online GNSS Multipath Detection in Non-Stationary Environments using Hazard-Rate Driven Bayesian Learning

• Motivation: Detecting GNSS multipath/NLOS in deep urban canyons is highly complex because the environment is non-stationary—signals abruptly switch between healthy and faulty regimes as the vehicle moves past buildings.
• Method: Employs Hazard-Rate Driven Bayesian Learning. It fuses two distinct signals: a weakly supervised neural network generating visual fault probability maps from fisheye sky-view images (contextual evidence), and a statistical changepoint detector tracking sudden jumps in pseudorange residual innovations (statistical evidence).
• Experiments: Conducted using a vehicle-mounted multi-sensor platform equipped with a measurement-grade NovAtel receiver and an ultra-wide fisheye camera. Tested across three dense, challenging urban datasets in Jinan, China, featuring tree-lined streets and underpasses.
• Result Analysis: The method successfully integrates visual and residual data to recursively calculate the Bayesian posterior probability of a fault online. It effectively identifies satellite faults and handles rapid environmental changes in real-world complex scenarios.

Subspace-based Adaptive GMM Error Modeling for Fault-Aware Pseudorange-based Positioning in Urban Canyons

• Motivation: Fixed static error models for GNSS positioning fail in urban canyons because the severity of multipath faults changes constantly with the environment, resulting in poor Fault Detection and Exclusion (FDE).
• Method: Proposes a subspace-based adaptive Gaussian Mixture Model (GMM) error model. It divides the measurement space into sub-bins based on satellite elevation angle and Carrier-to-Noise ratio (C/N0). Each bin dynamically updates a GMM error profile over a sliding time window, constantly feeding updated weights into the FDE and positioning solver.
• Experiments: Conducted in Hong Kong on two real-world datasets representing different complexities: the KLT dataset (slightly urbanized/low-rise) and the TST dataset (medium urbanized/high-rise), tracking GNSS signals with a U-blox receiver.
• Result Analysis: Demonstrated that the bin-specific GMMs successfully captured sudden environmental changes. This dynamic modeling outperformed conventional Gaussian FDE methods, reducing the mean positioning error by 16% in the slightly urbanized dataset and 9% in the medium urbanized dataset.