Fusion of In-Situ Network and Auxiliary Information: A Probabilistic Approach

PhD Thesis Defense Presentation

Gabriel Oduori

University College Dublin

Tuesday, 21 April, 2026

Overview

Setting the Scene

Contributions

Closing

Problem
Space

1

2

Gaps

Research
Questions

3

4

Data
Sources

Modelling
Approach

5

6

RQ0
Systematic Review

RQ1
FusionGP

7

8

RQ2
GAM‑SSM

RQ3
Transfer Learning

9

10

RQ4
Uncertainty Quantification

Conclusions

11

12

Future
Work

This is the roadmap for today’s presentation. I have structured it into three parts. First, Setting the Scene — stops 1 through 5 — where I will cover the problem space, the gaps in the state of the art, the research questions that emerged from those gaps, the data sources I used, and the modelling approach underpinning the work. Second, the Contributions — stops 6 through 10 — where I will walk through each of the four research papers: a systematic review, data fusion with Gaussian Processes, temporal modelling with GAM-SSM, transfer learning, and uncertainty communication. Finally, Closing — stops 11 and 12 — where I will draw conclusions and outline future directions. I will keep this tight — the thesis has the detail, this presentation tells the story.

Problem Space

Urban air quality monitoring requires the integration of large, heterogeneous datasets — yet existing data fusion methods have a restricted capacity to process such diverse inputs while simultaneously providing robust uncertainty quantification.

🕸️

Spatial & Temporal Dependencies

Jointly represent complex dependencies across space and time

🔍

Interpretable Structure

Model outputs must be explainable to scientists and policymakers

📊

Rigorous Uncertainty Quantification

Propagate and communicate uncertainty end-to-end

⚙️

Computational Tractability

Scalable and deployable in real urban settings

This thesis proposes a probabilistic approach to address all four requirements simultaneously

This slide comes directly from the thesis. The problem is not just that air quality data is heterogeneous — it’s that existing fusion methods can only partially address the challenge. They might handle multiple data sources but ignore uncertainty, or quantify uncertainty but fail to scale. What’s needed is a framework that satisfies all four requirements at once: it must capture spatial and temporal structure, be interpretable enough for policy use, propagate uncertainty rigorously, and remain computationally tractable at urban scale. The probabilistic approach proposed in this thesis — using Gaussian Processes and State Space Models — is specifically designed to meet all four.

Gaps in the State of the Art

Gap 1: Probabilistic fusion is rare

Most methods produce point estimates. Uncertainty either ignored or treated as an afterthought. Limited probabilistic framework within multiple heterogeneous fusion.

→ RQ1

Gap 2: Temporal dynamics overlooked

Most models are static spatial snapshots. Time-varying pollutant behaviour — diurnal cycles, traffic peaks, seasonal trends — is rarely modelled explicitly.

→ RQ2

Gap 3: Models do not transfer

Models are trained and validated in a single city. Transferability to new cities or sparse-sensor environments is rarely tested or reported.

→ RQ3

Gap 4: Uncertainty never reaches the decision-maker

Even where uncertainty is estimated, it is rarely communicated in formats that support policy or public health decisions.

→ RQ4

This is the core motivation for the thesis. The systematic review — which is itself RQ0 — mapped 80+ data fusion studies singled out air quaklity as the most prominent with the same four gaps recurring across the literature. Gap 1: fusion is done but rarely probabilistically — you get a map but no sense of how confident the model is. Gap 2: the time dimension is almost always collapsed — models are fitted to annual averages or daily means, not the hour-by-hour dynamics that matter most for exposure. Gap 3: models are local by design — nobody tests whether they generalise. Gap 4: even the studies that do estimate uncertainty leave it in the supplementary material — it never reaches the planner or the regulator. And cutting across all four is a fifth concern — computational tractability. Fully probabilistic models are often dismissed precisely because they are seen as too expensive to run at urban scale. A key design constraint throughout this thesis was ensuring the methods remain tractable — not just theoretically elegant, but deployable in practice. Each gap maps directly to one research question.

From Gaps to Research Questions

Central Research Question

How can probabilistic models be designed to fuse heterogeneous air quality data (in-situ sensors, satellite observations, and spatial covariates) for accurate and uncertainty-aware estimation of pollutant concentrations?

RQ1: How can probabilistic models fuse satellite and spatial data for accurate NO₂ mapping?

RQ2: How can LUR be embedded in a State Space Model to capture temporal dynamics?

RQ3: How transferable are probabilistic air quality models across cities and deployments?

RQ4: How can uncertainty quantification improve estimation reliability and support decision-making?

The central question drives everything in this thesis. Each sub-question tackles a specific dimension of the problem: how to fuse data probabilistically (RQ1), how to handle the time dimension (RQ2), how to generalise across cities (RQ3), and how to communicate uncertainty honestly to decision-makers (RQ4). Each maps directly to a paper. The gaps on the previous slide motivated each of these questions — the monitoring gap → RQ1, the temporal limitation → RQ2, scalability → RQ3, policy decisions → RQ4.

Methodology — Data Sources

🏭

In-Situ Networks

High accuracy
Low density

🛰️

Satellite (TROPOMI)

Global coverage
Coarse resolution

🚗

Traffic Volume

Primary NO₂
emission proxy

🗺️

OSM Geodata

Land use
spatial structure

Approach	Uncertainty	Multi-source	Temporal	Transferable
LUR	✗	Partial	✗	Limited
Kriging	Partial	✗	✗	✗
Deep Learning	✗	✓	✓	Limited
This thesis	✓	✓	✓	✓

Four data sources feed into this thesis, each with complementary strengths and limitations. In-situ networks are the gold standard — accurate but there are only 9 in Dublin. TROPOMI satellite retrievals cover the entire globe daily but at 3.5 × 5.5 km resolution — far too coarse for urban street-level analysis. Traffic volume is the primary proxy for NO₂ emission in cities. OSM geodata provides the spatial structure for land use regression. The table below shows why no existing approach ticks all four boxes simultaneously. This thesis does.

Methodology — Probabilistic Modelling

Gaussian Processes

• Non-parametric Bayesian framework
• Principled uncertainty quantification
• Flexible kernel design for spatial correlation
• Treats each source as a noisy observation of a latent field

State Space Models

• Dynamic latent state representation
• Kalman filter / smoother for inference
• Natural for temporal evolution of pollution fields
• Embeds Land Use Regression as the spatial observation model

Why probabilistic? Every data source in this thesis is a noisy, incomplete observation of the same underlying truth — the actual NO₂ concentration field. Only a probabilistic framework propagates that uncertainty honestly end-to-end.

GPs are ideal for spatial modelling — they give smooth, continuous predictions with principled uncertainty. State Space Models handle the temporal dimension — they track how pollution evolves over time and allow the model to update as new observations arrive. Land Use Regression provides the spatial backbone: road density, green space, elevation, and building footprints as covariates. The key insight is that embedding LUR inside a State Space Model turns a static spatial tool into a dynamic spatio-temporal model. The callout captures the fundamental motivation: every sensor reading is noisy, every satellite retrieval has error, every spatial covariate is a proxy. A probabilistic model is the only scientifically honest way to work with this data.

Contributions Overview

Principal contributions to probabilistic air quality modelling:

Methodological

1. A probabilistic GP fusion framework integrating satellite, spatial, and in-situ data (RQ1)
2. A hybrid GAM–State Space model embedding LUR for spatio-temporal NO₂ prediction (RQ2)

Applied

3. A transfer learning approach for generalising probabilistic models across cities and sensor deployments (RQ3)
4. An UQ framework propagating estimation uncertainty through the full fusion pipeline (RQ4)

These four contributions form a coherent end-to-end pipeline: from data fusion → temporal dynamics → transferability → uncertainty communication. Each builds on the previous. Each is a paper.

This thesis has four principal contributions — two methodological, two applied. Together they form a pipeline. FusionGP establishes how to fuse heterogeneous sources probabilistically. The Hybrid GAM-SSM extends this to the temporal dimension. Transfer learning addresses scalability across cities. Uncertainty quantification closes the loop by formalising how to communicate what the model doesn’t know. No prior approach addresses all four simultaneously — and doing so is the unifying contribution of this thesis.

RQ0: Systematic Review

Method: Systematic Review of 80+ papers across probabilistic and deterministic fusion methods

Key finding: No unified probabilistic framework exists — deterministic methods dominate, uncertainty is largely ignored

Title: Data Fusion for Low-Cost Sensors: Systematic Review

Venue: Information Fusion

🟢 Published

The systematic review is the foundation of this thesis. It maps the landscape — what methods exist, what they can and cannot do, and where the gaps are. The key finding is stark: across 80+ papers reviewed, probabilistic data fusion is rare, uncertainty quantification is almost absent, and no paper addresses all four dimensions simultaneously — multi-source, temporal, transferable, and uncertainty-aware. This review directly motivated and justified the four research questions.

RQ1: FusionGP

Method: Gaussian Process framework integrating TROPOMI satellite observations and LUR covariates with in-situ reference data

Key finding: High-resolution probabilistic NO₂ maps with calibrated uncertainty estimates at every location

Title: FusionGP: Probabilistic Data Fusion for High-Resolution Urban Air Quality Mapping

Venue: Computers, Environment and Urban Systems

🔵 Manuscript submitted and returned

FusionGP is the first and core paper. We treat NO₂ concentration as a latent Gaussian Process — a continuous spatial field we never observe directly. Satellite retrievals, land use covariates, and in-situ observations are all modelled as noisy observations of this latent field. The posterior GP gives us a spatially continuous map with calibrated uncertainty bounds everywhere — including unmonitored locations. This is the fundamental capability that deterministic LUR cannot provide.

RQ2: Hybrid GAM–SSM

Method: Hybrid Generalised Additive Model combined with State Space formulation embedding LUR

Key finding: Dynamic prediction with principled uncertainty — model updates as observations arrive. Currently revising with wind-sector based covariates.

Title: Hybrid Generalized Additive-State Space Modelling for Urban NO₂ Prediction: Integrating Spatial and Temporal Dynamics

Venue: Environmental Modelling & Software

🟡 Under revision

The second paper extends the spatial GP model by embedding LUR inside a State Space Model. The SSM gives the model memory — it doesn’t treat each day independently. The Kalman filter updates the latent state as new observations arrive. The GAM handles non-linear relationships between spatial covariates and concentrations. Currently revising with wind-sector based covariate extractions to better capture directional pollution transport — this is the main reviewer request and addresses a genuine physical mechanism we had under-modelled.

RQ3: Transfer Learning

Method: Transfer learning applied to pre-trained probabilistic fusion models across different urban deployments

Key finding: Probabilistic structure transfers well even when city morphology differs — reducing city-specific training data requirements substantially

Title: Transfer Learning for Generalizing Air Quality Models

Venue: Applied Soft Computing

🟡 Under major revision

RQ3 asks: once trained in one city, how much does a probabilistic model transfer to another? Transfer learning is the mechanism. The key finding is that the probabilistic structure — the learned spatial correlation and uncertainty representation — transfers well even when city morphology differs significantly. This is critical for scalability: we cannot build bespoke models for every city in the world, especially data-poor cities in the Global South. The major revision underway responds to reviewer requests to better characterise when and why transfer succeeds or fails — an important scientific question in its own right.

RQ4: Uncertainty Quantification

Method: Gaussian Surrogate Uncertainty Quantification Model — propagating sensor noise, retrieval error, and model uncertainty end-to-end

Key finding: Source-decomposed uncertainty enables transparent, decision-relevant communication of what the model does and does not know

Title: Uncertainty Quantification from Air Quality Fusion Models

Venue: To be confirmed

🔵 In preparation

RQ4 is the final chapter and the thread that ties everything together. Every probabilistic model produces uncertainty estimates. This paper formalises how those uncertainties propagate through the full pipeline — from raw sensor noise, through retrieval errors in satellite data, through model assumptions, to the final concentration estimate. The key output is source-decomposed uncertainty: rather than one opaque uncertainty band, the model tells us how much of the uncertainty comes from sensor noise, how much from the data, how much from the spatial structure. This is the kind of output regulators and policymakers can actually act on.

Progress Update: January–April 2026

Published / Complete Submitted Under Revision In Preparation

January

February

March

April

Thesis

Submitted

RQ0: Systematic Review

Published — Information Fusion

RQ1: FusionGP

Finalising

Submitted — CEUS

RQ2: Hybrid GAM–SSM

Under Revision, updated methodology with — wind-sector covariates

RQ3: Transfer Learning

Major Revision — Applied Soft Computing

RQ4: Uncertainty Quantification

In Preparation

🎤 Viva — Apr 21

On this slide, I am sharing some of the activities that have progressed since January and also notincluded in the thesis. The Gantt chart shows the trajectory of all papers from January through the defense today. The thesis was submitted in March. The systematic review is fully published. FusionGP was finalised and submitted in March to CUES and for returned, which is normal in this process. RQ2 and RQ3 have just both came under active peer review revision and we are using the feedback to make revisions. — this is normal and expected in a PhD by publication. RQ4 began preparation and is being drafted. The pink line marks today — the defense.

Conclusions

Central Research Question — Answered
Probabilistic models can be designed to fuse heterogeneous air quality data — delivering accurate, uncertainty-aware, and transferable NO₂ estimates.

Research Question	Key Finding	Status
RQ0: Systematic Review	Unified probabilistic framework absent from literature	🟢 Published
RQ1: Probabilistic Fusion	FusionGP — calibrated spatial uncertainty maps	🔵 Submitted
RQ2: Spatio-temporal LUR	Hybrid GAM-SSM captures temporal evolution	🟡 In revision
RQ3: Transferability	Probabilistic structure transfers across cities	🟡 Under review
RQ4: Uncertainty	Source-decomposed uncertainty supports decisions	🔵 In prep

The thesis asked one central question and answered it through four empirical papers. FusionGP establishes that probabilistic GP fusion works for spatial NO₂ mapping. The Hybrid GAM-SSM shows that embedding LUR in a state space framework adds the temporal dimension. Transfer learning demonstrates scalability across cities. Uncertainty quantification closes the loop by formalising how to communicate what we do and don’t know. Together, these constitute the first end-to-end probabilistic pipeline for heterogeneous air quality data fusion — accurate, temporally dynamic, transferable, and uncertainty-aware.

Future Work

Near-term Extensions

• Extend FusionGP eyond NO₂
• Incorporate real-time sensor streams for online model updating

Longer-term Vision

• Replace hand-crafted LUR covariates with learned urban spatial embeddings from satellite imagery and OSM
• Pre-train probabilistically across many cities → true foundation model for air quality

🧠 Spatial Intelligence

AI systems that understand physical space — moving beyond hand-crafted covariates to learned urban representations (Fei-Fei Li's paradigm applied to environmental sensing)

🎯 Probabilistic Spatial Intelligence

Spatial Intelligence provides rich representation · Probabilistic modelling provides the inference · Together: uncertainty-aware predictions that transfer across any city

🌍 Impact

Every city deserves accurate, air quality estimates — not just those with dense reference networks. This framework.

To to a larger extent, these also reflect on some of the weaknesses of this research. The near-term extensions are straightforward given the existing framework — new pollutants and online updating. But the longer-term vision is more ambitious. The concept of Probabilistic Spatial Intelligence builds on this thesis by replacing the hand-crafted LUR covariates with learned spatial representations - embeddings that capture urban structure automatically from satellite imagery, street views, and 3D maps. When combined with the probabilistic modelling framework developed here, you get a system that generalises across cities not just by statistical similarity but by learned spatial understanding. This is the vision that connects this thesis to the broader trajectory of AI in environmental science.

Thank You

Fusion of In-Situ Network and Auxiliary Information: A Probabilistic Approach

A unified probabilistic framework for heterogeneous air quality data fusion — accurate, uncertainty-aware, and transferable across urban environments.

Gabriel Oduori · University College Dublin

gabriel.oduori@ucdconnect.ie

Supervised by Assistant Prof Chiara Cocco & Professor Francesco Pilla