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Systematic and Stochastic Uncertainty Analysis in GNSS/IMU-Integrated Airborne Photogrammetry
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Computer and Geospatial Sciences, Geospatial Sciences.ORCID iD: 0000-0003-0192-1533
2026 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Integration of global navigation satellite systems (GNSS), inertial measurement units (IMU), and high-resolution digital cameras in airborne mobile mapping systems, such as those used in airborne photogrammetry, has revolutionized three-dimensional (3D) geospatial data acquisition. In general, 3D mapping using airborne photogrammetry consists of several steps: data collection, determination of EOPs, aerial triangulation (AT), and finally, the generation of products such as true orthophotos, planimetric and topographic maps, digital surface models (DSMs), and digital elevation models (DEMs). Yet significant challenges in system integration, data processing strategies, and quality assessment must be addressed to ensure the accuracy and reliability of the resulting mapping products. This thesis investigates systematic and stochastic error sources affecting exterior orientation parameters (EOPs) in GNSS/IMU-integrated airborne photogrammetry, addressing critical aspects of data processing and analysis. In addition, this thesis focuses on the integration of data from GNSS and IMU and the challenges that arise from this process.

Using strip-wise and block-wise approaches, the first study evaluated the impact of different a priori observation uncertainties (which set the observation weights for GNSS positions and IMU orientations) on AT results. Through analysis of checkpoint residuals, statistical evaluations, and Light Detection and Ranging (LiDAR) data comparisons, this study demonstrates that blockwise GNSS shift correction yields superior results compared with strip-wise methods, with an average accuracy improvement of 6 cm. These findings emphasize the importance of appropriate a priori observation uncertainty assignment in AT to enhance accuracy.

The second study investigates direct georeferencing (DG) in photogrammetry, focusing on systematic errors arising from inconsistencies between geodetic reference systems. It examines the effects of the deflection of the vertical (DOV) on DG in aerial mobile mapping systems. This study quantified the effect of the DOV on horizontal and vertical coordinates at different flight altitudes and camera fields of view using high-resolution geoid models for Sweden. The results confirm that the influence of the anomalous gravity field on DG using GNSS/IMU integration is not negligible, reaching up to 8–39 cm horizontally and 25 cm vertically depending on flight altitude and camera field of view. Moreover, the DOV components calculated using the EGM2008 global geopotential model are sufficiently accurate for aerial mapping in Sweden, except in mountainous areas where the topographic signal is not modelled correctly. The study further provides insights into minimizing DOV effects through optimal flight planning and highlights the importance of accounting for DOV in high-accuracy DG applications.

The third study investigated the effects of GNSS signal outages on EOPs estimation using tightly coupled GNSS/IMU integration, based on a simulated case study in Sweden. EOPs solutions were analysed for outage durations of up to 180 s using both single and network GNSS stations and the post-processed kinematic (PPK) method. The results demonstrate that the smoothing algorithm enhances positioning uncertainty (root mean square error, RMSE) for north, east, and height components by approximately 17–43%, and reduces orientation uncertainty by approximately 60% for roll, pitch, and heading compared with forward Kalman filtering (KF). Notably, post-processed smoothing reduced position uncertainty by up to 95% and orientation uncertainty by 60% during simulated signal outages.

The fourth study analyses the precision of lever arm (LA) measurements between GNSS and IMU and their impact on EOPs estimation in GNSS/IMUintegration. Using calibration data from a TerrainMapper 2 system, the research revealed that LA uncertainties have minimal influence on attitude determination and negligible impacts on positioning accuracy, provided measurements are made at centimetre-level precision. The study also examined the relationship between virtual reference station–rover baseline length, GNSS dilution of precision (DOP), and LA uncertainty on positioning accuracy.

The findings demonstrate that tightly coupled GNSS/IMU integration, particularly when combined with post-processing smoothing and a network of GNSS reference stations such as SWEPOS, substantially improves the resilience of EOPs during GNSS signal disruptions. Taken together, these four studies advance the accuracy and reliability of EOPs in GNSS/IMU-integrated airborne photogrammetry, providing quantitative guidance for observation weighting, geodetic correction, signal-outage mitigation, and sensor calibration in operational mapping applications such as topographic mapping, urban planning, and environmental monitoring.

Abstract [sv]

Integrationen av globala navigationssatellitsystem (GNSS), tröghetsmätningssystem (IMU) och högupplösta digitala kameror i luftburna mobila karteringssystem, såsom de som används inom flygfotogrammetri, har revolutionerat insamlingen av tredimensionell (3D) geospatial data. Trots detta kvarstår betydande utmaningar inom systemintegration, databearbetningsstrategier och kvalitetsbedömning, vilka måste hanteras för att säkerställa noggrannheten och tillförlitligheten hos de slutliga karteringsprodukterna. Denna avhandling undersöker systematiska och stokastiska felkällor som påverkar yttre orienteringsparametrar (EOPs) i GNSS/IMU-integrerad flygfotogrammetri, med fokus på kritiska aspekter av databearbetning och analys. Flygfotogrammetrisk 3D-kartering omfattar flera sammanlänkade processer: datainsamling under flygningen, bestämning av yttre orienteringsparametrar, flygfototriangulering (AT) samt generering av slutprodukter såsom sanna ortofoton, planimetriska och topografiska kartor, digitala ytmodeller (DSM) och digitala höjdmodeller (DEM). Avhandlingen fokuserar specifikt på integrationen av GNSS- och IMU-data samt de utmaningar som uppstår vid denna process.

Den första studien utvärderade hur olika a priori-observationsosäkerheter, vilka styr observationsvikterna för GNSS-positioner och IMU-orientering, påverkar resultaten från flygfototriangulering, genom jämförelse av strip-wise och blockvis bearbetning. Analys av kontrollpunktsresidua, statistiska utvärderingar och jämförelser med LiDAR-data visar att blockvis GNSS-skiftkorrigering ger överlägsna resultat jämfört med strip-wise-metoder, med en genomsnittlig noggrannhetsförbättring på 6 cm. Resultaten understryker vikten av ändamålsenlig tilldelning av a priori-observationsosäkerheter i flygfototrianguleringför att förbättra kartläggningsnoggrannheten.

Den andra studien undersöker direkt georeferering (DG) inom fotogrammetri, med fokus på systematiska fel som uppstår till följd av skillnader mellan geodetiska referenssystem. Studien undersökte effekterna av lodavvikelser (DOV) på direkt georeferering i luftburna mobila karteringssystem och kvantifierade DOV:s inverkan på horisontella och vertikala koordinater vid olika flyghöjder och synfältsvinklar, med hjälp av högupplösta geoidmodeller för Sverige. Resultaten bekräftar att gravitationsfältets anomalier inte är försumbara vid direkt georeferering med GNSS/IMU-integration, och kan uppgå till 8–39 cm horisontellt och 25 cm vertikalt beroende på flyghöjd och kamerans synfält. Vidare visar resultaten att DOV-komponenter beräknade med EGM2008-modellen är tillräckligt noggranna för flygkartering i Sverige, med undantag för bergsområden där den topografiska signalen inte modelleras korrekt. Studien ger praktisk vägledning för hur lodavvikelsernas effekter kan minimeras genom optimal flygplanering och betonar deras betydelse i högprecisionsapplikationerför direkt georeferering.

Den tredje studien undersökte effekterna av GNSS-signalavbrott på bestämning av EOPs med hjälp av tätkopplad GNSS/IMU-integration, baserat på en simulerad fallstudie i Sverige. EOPs-lösningar analyserades för avbrott av varierande längd, upp till 180 sekunder, med både enstaka och nätverksbaserade GNSS-stationer samt efterbearbetad kinematisk (PPK) metod. Resultaten visar att utslätningsalgoritmer förbättrar positionsosäkerheten (RMSE) för nord-, öst- och höjdkomponenter med cirka 17–43% och minskar orienteringsosäkerheten med cirka 60% för roll, pitch och kurs jämfört med framåtriktad Kalmanfiltrering. Dessa förbättringar är särskilt framträdande under simulerade GNSS-signalavbrott, där efterbearbetad utslätning reducerade positionsosäkerheten med upp till 95% och orienteringsosäkerheten med 60%.

Den fjärde studien analyserar precisionen hos hävarmsmätningar (LA) mellan GNSS-antenn och IMU samt deras inverkan på bestämning av EOPs vid GNSS/IMU-integration. Med kalibreringsdata från ett TerrainMapper 2-system visar forskningen att hävarmsosäkerheter har minimal påverkan på attitydbestämning och försumbar inverkan på positionsnoggrannheten, förutsatt att mätningarna utförs med centimetersnoggrannhet. Studien undersökte också sambandet mellan baslinjelängden för virtuell referensstation–rover, GNSS DOP (Dilution of Precision) och hävarmsosäkerhetens inverkan på positionsnoggrannheten.

Avhandlingens resultat visar att tätkopplad GNSS/IMU-integration, särskilt i kombination med efterbearbetad utslätning och ett nätverk av GNSS-referensstationer såsom SWEPOS, avsevärt förbättrar EOPs robusthet vid GNSSsignalstörningar. Sammantaget bidrar dessa fyra studier till en förbättrad noggrannhet och tillförlitlighet hos EOPs i GNSS/IMU-integrerad flygfotogrammetri, och ger kvantitativ vägledning för observationsviktning, geodetisk korrigering, hantering av GNSS-signalavbrott samt sensorkalibrering inom operativa karteringstillämpningar såsom topografisk kartering, stadsplanering och miljöövervakning.

Place, publisher, year, edition, pages
Gävle: Gävle University Press , 2026. , p. 144
Series
Doctoral thesis ; 81
Keywords [en]
Aerial mobile mapping systems, photogrammetry, georeferencing, GNSS/IMU integration, geodetic reference system, geoid, error analysis, systematic and stochastic errors.
Keywords [sv]
Luftburna mobila karteringssystem, flygfotogrammetri, georeferering, GNSS/IMU-integration, geodetiskt referenssystem, geoid, felanalys, systematiska och stokastiska fel.
National Category
Earth and Related Environmental Sciences
Identifiers
URN: urn:nbn:se:hig:diva-50807ISBN: 978-91-90111-09-3 (print)ISBN: 978-91-90111-10-9 (electronic)OAI: oai:DiVA.org:hig-50807DiVA, id: diva2:2092235
Public defence
2026-10-09, Lilla Jadwigasalen, Kungsbäcksvägen 47, Gävle, 13:00 (English)
Opponent
Supervisors
Available from: 2026-09-18 Created: 2026-08-14 Last updated: 2026-09-18Bibliographically approved
List of papers
1. Comparison of the strip- and block-wise aerial triangulation using different exterior orientation parameters weights
Open this publication in new window or tab >>Comparison of the strip- and block-wise aerial triangulation using different exterior orientation parameters weights
2022 (English)In: Journal of Spatial Science, ISSN 1449-8596, Vol. 67, no 3, p. 377-394Article in journal (Refereed) Published
Abstract [en]

In this study, three different procedures: checkpoint RMS of residuals, statistical evaluation of AT results using t-test, and comparison of a photogrammetric digital surface model (DSM) and LiDAR data are used to analyse the effect of IMU and GNSS uncertainties on the final adjusted results. The outcome suggests that the method of block-wise GNSS shift correction is the better method for aerial triangulation and one should use appropriate observable weights in AT. The comparison of checkpoint RMS residuals between the two methods shows that the block-wise solution is on average 6cm more accurate than the strip-wise solution.

Place, publisher, year, edition, pages
Taylor & Francis, 2022
Keywords
Photogrammetry, Direct georeferencing, INS/GNSS Integration
National Category
Geosciences, Multidisciplinary
Identifiers
urn:nbn:se:hig:diva-35211 (URN)10.1080/14498596.2020.1871086 (DOI)000614777300001 ()2-s2.0-85100533681 (Scopus ID)
Available from: 2021-02-04 Created: 2021-02-04 Last updated: 2026-09-04Bibliographically approved
2. Deflection of Vertical Effect on Direct Georeferencing in Aerial Mobile Mapping Systems: A Case Study in Sweden
Open this publication in new window or tab >>Deflection of Vertical Effect on Direct Georeferencing in Aerial Mobile Mapping Systems: A Case Study in Sweden
2022 (English)In: Photogrammetric Record, ISSN 0031-868X, E-ISSN 1477-9730, Vol. 37, no 179, p. 285-305Article in journal (Refereed) Published
Abstract [en]

GNSS/INS applications are being developed, especially for direct georeferencing in airborne photogrammetry. Achieving accurately georeferenced products from the integration of GNSS and INS requires removing systematic errors in the mobile mapping systems. The INS sensor's uncertainty is decreasing; therefore, the influence of the deflection of verticals (DOV, the angle between the plumb line and normal to the ellipsoid) should be considered in the direct georeferencing. Otherwise, an error is imposed for calculating the exterior orientation parameters of the aerial images and aerial laser scanning. This study determines the DOV using the EGM2008 model and gravity data in Sweden. The impact of the DOVs on horizontal and vertical coordinates, considering different flight altitudes and camera field of view, is assessed. The results confirm that the calculated DOV components using the EGM2008 model are sufficiently accurate for aerial mapping system purposes except for mountainous areas because the topographic signal is not modelled correctly.

Place, publisher, year, edition, pages
Wiley, 2022
Keywords
aerial mobile mapping systems, deflection of verticals, direct georeferencing, EGM2008, geoid, photogrammetry
National Category
Earth and Related Environmental Sciences
Identifiers
urn:nbn:se:hig:diva-39625 (URN)10.1111/phor.12421 (DOI)000829464300001 ()2-s2.0-85134685898 (Scopus ID)
Available from: 2022-07-25 Created: 2022-07-25 Last updated: 2026-09-04Bibliographically approved
3. Numerical Analysis of GNSS Signal Outage Effect on EOPs Solutions Using Tightly Coupled GNSS/IMU Integration: A Simulated Case Study in Sweden
Open this publication in new window or tab >>Numerical Analysis of GNSS Signal Outage Effect on EOPs Solutions Using Tightly Coupled GNSS/IMU Integration: A Simulated Case Study in Sweden
2023 (English)In: Sensors, E-ISSN 1424-8220, Vol. 23, no 14, article id 6361Article in journal (Refereed) Published
Abstract [en]

The absence of a reliable Global Navigation Satellite System (GNSS) signal leads to degraded position robustness in standalone receivers. To address this issue, integrating GNSS with inertial measurement units (IMUs) can improve positioning accuracy. This article analyzes the performance of tightly coupled GNSS/IMU integration, specifically the forward Kalman filter and smoothing algorithm, using both single and network GNSS stations and the post-processed kinematic (PPK) method. Additionally, the impact of simulated GNSS signal outage on exterior orientation parameters (EOPs) solutions is investigated. Results demonstrate that the smoothing algorithm enhances positioning uncertainty (RMSE) for north, east, and heading by approximately 17–43% (e.g., it improves north RMSE from 51 mm to a range of 42 mm, representing a 17% improvement). Orientation uncertainty is reduced by about 60% for roll, pitch, and heading. Moreover, the algorithm mitigates the effects of GNSS signal outage, improving position uncertainty by up to 95% and orientation uncertainty by up to 60% using the smoothing algorithm instead of the forward Kalman filter for signal outages up to 180 s.

Place, publisher, year, edition, pages
MDPI, 2023
Keywords
GNSS/INS integration; forward Kalman filter; smoothing algorithm; tightly coupled; PPK; virtual reference station; aerial photogrammetry
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:hig:diva-42795 (URN)10.3390/s23146361 (DOI)001039024700001 ()37514655 (PubMedID)2-s2.0-85166022553 (Scopus ID)
Available from: 2023-08-01 Created: 2023-08-01 Last updated: 2026-09-04Bibliographically approved
4. Lever arm measurement precision and its impact on exterior orientation parameters in GNSS/IMU integration
Open this publication in new window or tab >>Lever arm measurement precision and its impact on exterior orientation parameters in GNSS/IMU integration
2024 (English)In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 14, no 1, article id 20220179Article in journal (Refereed) Published
Abstract [en]

Airborne mobile mapping systems are crucial in various geodetic applications. A key aspect of these systems is the accurate estimation of exterior orientation parameters (EOPs), which is achieved through the integration of global navigation satellite systems (GNSSs) and inertial measurement unit (IMU) technologies. One critical component in this integration is the lever arm (LA), the vector that connects the GNSS antenna and the IMU center. The uncertainty (standard deviation) in LA measurements can introduce errors in the EOP estimation, thereby affecting the overall system performance. However, how much the EOP estimation is affected by LA measurement uncertainty is examined in this study based on calibration data (test flight) using the TerrainMapper 2 system collected by Lantmäteriet in Sweden. The findings reveal that LA uncertainties have minimal influence on attitude and negligible impacts on position in terms of standard deviation (SD) if the LA is measured with an accuracy of better than 2–3 cm. Additionally, the research explores the combined effects of virtual reference station-rover baseline length and dilution of precision on positioning accuracy and their correlation with LA uncertainty, providing further insights into the complexities of EOP estimation. By advancing GNSS/IMU integration techniques, this study contributes to the enhancement of geodetic technologies customized for airborne mobile mapping applications.

Place, publisher, year, edition, pages
de Gruyter, 2024
Keywords
lever arm; standard deviation; exterior orientation parameters; GNSS/IMU integration; airborne mobile mapping; virtual reference station
National Category
Earth and Related Environmental Sciences Other Engineering and Technologies
Identifiers
urn:nbn:se:hig:diva-46185 (URN)10.1515/jogs-2022-0179 (DOI)001365725400001 ()2-s2.0-85213061755 (Scopus ID)
Available from: 2024-12-16 Created: 2024-12-16 Last updated: 2026-09-04Bibliographically approved

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Jouybari, Arash

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123452 of 5
CiteExportLink to record
Permanent link

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  • Other style
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