Observation Quality in DSM-Assisted Aerial Localization: A Benchmark and Base-Anchored Uncertainty Calibration
Authors: Pengyu Yin, Junxiang Tan, Jie Pan, Mengqi Fu, Kun Cheng, Yifan Liu
Organizations: Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China · School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China
Aerial map matching provides position observations for navigation, but a position error alone does not determine how an observation should be weighted. We define five benchmark tasks: position availability and agreement, grouped error structure, predictive uncertainty, controlled updates, and temporal accumulation. A case study in digital-surface-model-assisted localization evaluates base-anchored uncertainty calibration within this framework. The method combines propagated image and map sensitivities with the second moment of a compact configuration subset relative to the reported position. The reported position remains unchanged, and scale is fitted using separate position references without local surface-height ground truth. Thirteen covariance models are evaluated on two held-out query sets from locations represented in the calibration data. Relative to a constant full-matrix baseline, the method reduces equal-location normalized position-update risk by 7.70% on 728 conditions and 5.46% on a separate 142 conditions under an independent prior, with all localization failures included. On the primary set, equal-location negative log likelihood improves by 2.571 nat. These results show improved reference-based weighting at seen locations. Exploratory base-quality and conditional-addition controls leave the incremental update benefit of configuration disagreement unresolved. Navigation benefit and real temporal accumulation remain untested.
Figures & tables
Fig. 1: Benchmark and method overview; all small plots are schematic. (a) Five tasks characterize position observations and their use. (b) Geometric sensitivity G and base-relative moment A predict error matrix R while preserving position z0 . Solid arrows carry inference data; the dashed arrow supplies parameters estimated from separate calibration data and fixed during evaluation. Task labels indicate which tasks are evaluated on real data. F-C is the constant full-matrix baseline; F-GA combines geometry and anchoring. Real-data evaluation excludes temporal accumulation and cross-frame group moments.
Fig. 2: Synthetic counterexamples with known reference positions. (a) Equal sample count and MSE, different group structure; each observation is a group. (b) Fixed residual, prior and ellipse area, different update error after rotating the ellipse. (c) Reordering the same errors preserves single-frame RMSE but changes window-mean error.
Tail rate, 5 m reference-agreement rate, capped mean loss
1, 1, m
MSE, RMSE
Mean squared error and its square root
m 2 , m
OSM, BGM, WGM
Overall squared mean, between-group and within-group moments
m 2
RMSEμ , RMSEmac
Micro and macro RMSE
m
TABLE I: Metric glossary. Units refer to per-observation values or the stated aggregate. MV and SM are vector and matrix diagnostics, not scalar rankings. The five benchmark tasks specify evaluation samples, failure treatment and aggregation.
Fig. 3: Synthetic operator examples on identical metre-scale axes. Cross: reference (0,0) ; square: fixed base; rings: minimum-diameter subset ( k=3 ); dashed segments: base-relative offsets. Traces of all-member scatter D , subset scatter CS (Cs), and anchored moment A are computed from the displayed configurations. (a) Deviating variants inflate D . (b) A retains an isolated base’s offset from a compact subset. (c) Shared displacement remains invisible. Matrices describe raw configuration dispersion rather than calibrated error covariances. The reference is shown for interpretation and is excluded from subset selection and scatter calculations.
Model
V
α
β
γ
Converged/starts
Iteration range
F-G
—
0
2.252799
—
3/3
7–11
F-D
D
0.018637
—
11.790664
3/3
15–20
F-A
A
0.025794
—
3.250298
3/3
14–17
F-GD
D
0.008367
0.289716
5.900141
4/4
22–33
F-GA
A
0.013870
0.203725
2.403562
4/4
21–26
F-GS
S
0.006267
0.442200
2.484152
4/4
19–26
TABLE II: Fitted model coefficients and convergence. All 25 starts converged within the 500-iteration limit; the solution with the lowest calibration objective was retained. Values are rounded for display.
Study
Calibration data
Evaluation data
Interpretation
Ranking diagnostic
246 outputs, 3 locations
247 outputs, same 3 locations
Within-location development analysis; overall update risk unavailable
Method development
300 opportunities, 24 locations
258 opportunities, disjoint locations
F-GD failure analysis motivating anchoring
Main comparison
Original 300; 248 complete-feature outputs
728 validation and 142 inPlace; 24 and 3 represented locations
Held-out queries; thirteen models fixed before reference labels were accessed
Base-quality control
Original 248 complete-feature outputs
Same 728/142, previously evaluated
Exploratory H-Q comparison with no extra localizer runs
Conditional addition
Nested location holdout over original 300; calibration-only fitting
300 source OOF plus previously evaluated 728/142
Exploratory H-QA/H-QI comparison within the same domain
TABLE III: Experiment stages and evaluation data. Counts denote opportunities unless explicitly marked as outputs. Later exploratory studies reuse the earlier data.
Fig. 4: Real inputs and the uncertainty attached to an unchanged position. Rows show the cases with median F-GA-minus-F-C NLL change among all 629 validation outputs and among the 33 cases with increased NLL, respectively; ties are resolved by query ID. Query images, paired maps and DSM heights are from OrthoLoC. Heights share a color scale and represent the surface, not DSM error; blank map areas are retained. The right column shows dataset-local XY coordinates relative to the reference position. The dot is the shared prediction; both 90% regions share this center. Linked insets share limits and a 0.5 m scale bar. Tighter regions contain the reference in (a) but miss it in (b), despite lower NR25 in both. The examples illustrate individual outcomes alongside the complete-cohort results.
Fig. 5: Calibration, controlled updates and comparison with base-only quality. (a,b) Coverage minus nominal level; zero is ideal. Markers are offset horizontally for legibility. (c,d) Thirteen covariance models relative to F-C: NLL difference and percentage NR25 change. Arrows connect F-C to F-GA; negative values on both axes indicate improvement in both metrics. (e,f) Exploratory comparisons with H-Q on the same evaluation sets: F-GA minus H-Q, with descriptive 95% paired-location bootstrap intervals (10,000 resamples, seed 20261009). Negative favors F-GA; both validation intervals cross zero and inPlace NR25 slightly favors H-Q. All panels use equal-location means: 24 validation and three inPlace locations. PC/NLL include 629/136 outputs with fallbacks; NR25 includes all 728/142 eligible queries with no-output risk one, under P=25I2 m 2 . Positions and states are unchanged. The intervals describe these locations rather than a broader geographic population.
Cohort
MSE mac
Mean ∥bg∥2
Mean Wg
Val
1.5649
0.0430
1.5218
InPlace
0.3809
0.0284
0.3525
TABLE IV: Equal-location averages of position-error moments (m 2 ) among successful outputs. bg is the location’s mean residual and Wg=meani∈g∥di−bg∥2 . Mean ∥bg∥2 summarizes local offsets, not global OSM. Global BGM also requires a verified common orientation across locations. All thirteen models use the same positions.
Validation
inPlace
Method
NLL ↓
PC90
EA90
NR25 ↓
NLL ↓
PC90
EA90
NR25 ↓
(nat)
target 0.90
(m 2 )
(nat)
target 0.90
(m 2 )
Constant and configuration-only baselines
F-I
2.6583
0.9763
16.6503
0.1549
2.1439
0.9744
16.6503
0.0410
F-C
2.7420
0.9739
14.8253
0.1552
2.1251
0.9744
14.8253
0.0415
Config
0.4404
0.9549
29.8456
0.1501
-0.0748
0.9744
3.1150
0.0399
TABLE V: Comparison of thirteen covariance models using equal-location means, identical position estimates and identical failure states. NLL, PC90 and EA90 use successful outputs; NR25 includes every eligible query, with risk one for missing outputs. Bold cells mark minimum NLL/NR25 or PC90 closest to 0.90, based on unrounded values. EA90 describes region size and is interpreted alongside coverage. † denotes an NR25 tie after rounding only.
Fig. 6: Paired location differences, F-GA minus F-C (squares) or F-GD (triangles). Blue negative values indicate improvement; red positive values indicate regression. The 27 cohort–location entries share a fixed order; dashed lines separate validation (V) and inPlace (I). Right: means and descriptive 95% paired-location bootstrap intervals for each cohort and comparator. Resampling is by location rather than query; inPlace has only three locations. The right panels use different x-axis limits from the left panels; scales are shared within each panel. NLL uses outputs with valid covariance estimates; NR25 uses all eligible queries (risk 1 for cases without an output). Position predictions are unchanged.
Fig. 7: Coverage and update risk across prior settings. (a,b) Coverage at nominal 50%, 90%, and 95%; diagonals denote ideal coverage. (c,d) All thirteen models under P=pI2 , p∈{4,25,100}m2 (outlined: primary p=25 ). Cells show 100[NRm(p)/NRF−C(p)−1]% ; negative values indicate lower risk. Heatmaps share a symmetric scale. Equal-location means use 24 validation and three inPlace locations. Coverage uses 629/136 successful outputs; NR includes all 728/142 eligible cases, with no-output risk one. Performance ordering varies with the prior.
Cohort
Model
NLL (nat)
PC90 (%)
EA90 (m 2 )
NR25
Val
F-C
2.7420
97.39
14.825
0.155248
Val
H-Q
0.2722
93.14
6.996
0.143556
Val
F-GA
0.1712
92.84
7.126
0.143292
InPlace
F-C
2.1251
97.44
14.825
0.041488
InPlace
H-Q
-0.4146
88.76
2.776
0.039049
InPlace
F-GA
-0.6941
98.21
1.858
0.039224
TABLE VI: Exploratory comparison with base-only calibration on the same evaluation sets. Equal-location PC90 and EA90 use all outputs including fallbacks; NR25 retains all eligible queries. Results are reported separately for validation and inPlace; the latter contains only three locations.
Cohort
Model
NLL (nat)
PC90 (%)
EA90 (m 2 )
NR25
Source OOF
H-Q
0.8936
90.22
8.775
0.138470
Source OOF
H-QA
0.2544
94.20
13.735
0.135774
Source OOF
H-QI
0.8603
91.21
8.825
0.138469
Source OOF
F-GA
0.1427
90.76
17.020
0.135331
Val
H-Q
0.2722
93.14
6.996
0.143556
Val
H-QA
0.2166
95.33
10.431
0.141186
TABLE VII: Additive-model comparison using equal-location means. Source OOF uses nested location holdout within the calibration data; validation and inPlace reuse the earlier evaluation sets. All cohorts belong to the same domain.
We present AeroMap3D, a monocular 6-DoF UAV localization system that anchors onboard imagery to visual, geometric, and semantic map priors for GNSS-denied navigation. AeroMap3D addresses two fundamental challenges in map-referenced aerial localization: the cross-view discrepancy between UAV imagery and satellite maps, and the structural inconsistency between bare-earth digital elevation models (DEMs) and urban scenes. First, we introduce a lightweight adapter that enables a dense matcher pretrained on internet-scale generic data to perform reliable UAV-to-map registration without finetuning. By estimating the scale ratio and yaw offset between the UAV image and map tile, the adapter removes the dominant geometric misalignment induced by altitude, camera field of view, and heading before dense correspondence estimation. Second, AeroMap3D lifts 2D UAV-map correspondences onto DEM terrain while using OpenStreetMap annotations to reject semantically unreliable matches before RANSAC-PnP pose estimation, thereby reducing errors caused by unmodeled building heights and off-nadir structures. Delayed map-based pose measurements are further fused with relative-motion priors using a delayed-state EKF for continuous trajectory estimation. Without UAV-Terra3D retraining or tuning, AeroMap3D localizes all trajectories across eight Austin sites within 50 m and achieves 5.88 m mean 3D error over 55 km of flight.
Zhiyun Deng, Luis Sentis
The University of Texas at Austin · AIVE AI Systems
Aerial 6DoF localization typically relies on precise GNSS signals or radiometrically rich 3D reconstructions, limiting scalability and on-board deployment. We propose SemCityLoc, a semantic-geometric alignment system that reframes aerial pose estimation as structured surface registration between foundation-model-derived visual priors and standardized LoD-compliant 3D city models. Instead of matching sparse contours or dense texture, our method aligns semantic surfaces and monocular depth with lightweight semantic 3D building models, increasing pose discriminability in repetitive and occluded urban environments. To enable accurate evaluation, we introduce SemCityLockeD, the first real-world benchmark combining centimeter-accurate UAV poses with standardized LoD1--LoD3 semantic city models and challenging low-altitude imagery. Experiments demonstrate substantial improvements over existing map-based approaches, improving recall by up to 36% and reducing mean positional error from 9.89m to 2.62m in challenging urban canyons. Our results indicate that semantically structured geometry provides sufficient and scalable constraints for high-precision aerial localization without radiometric scene reconstructions. The code and data are available at https://albertchen98.github.io/SemCityLoc.
Jingfeng Mao, Xuyang Chen, Qilin Zhang +6
Technical University of Munich, Munich, Germany · CV4DT, University of Cambridge, Cambridge, United Kingdom · Munich Center for Machine Learning, Munich, Germany +3
Visual localization enables unmanned aerial vehicles (UAVs) to maintain absolute positioning in GNSS-denied environments. A common approach matches UAV images with geo-tagged orthographic maps and estimates camera pose using Perspective-n-Point (PnP) with elevations from Digital Surface Models (DSMs). However, accurate and up-to-date DSMs are often unavailable in practice. Orthographic-perspective geometry (OPG) enables DSM-free localization in scenes with varying elevations, yet existing methods typically estimate pose indirectly through intermediate matrix estimation and decomposition. To address this limitation, we propose Latent-Depth Variable Projection (LDVP), which treats the unknown scales along perspective viewing rays as latent depths. By analytically eliminating these depths and solving for the horizontal camera center in closed form given the rotation, LDVP reduces nonlinear estimation to a rotation-only problem, enabling direct recovery of metric horizontal position without assuming a planar scene. To improve localization robustness across different scene structures, we further introduce Structure-Adaptive Coupling (SAC), which uses relative scene structure inferred from monocular depth estimation to select LDVP when the matched points are not dominated by a single plane, and Planar-PnP otherwise. Our local observability analysis reveals how scene elevation variation affects the geometric constraints of OPG, providing a basis for this adaptive strategy. Extensive experiments show that LDVP consistently outperforms existing OPG-based DSM-free methods, while SAC further improves robustness across diverse scenes and substantially narrows the gap to DSM-based localization. Code will be released at https://github.com/UAV-AVL/LDVP-SAC.
Yibin Ye, Xichao Teng, Shuo Chen +4
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China, and Hunan Provincial Key Laboratory of Image Measurement and Vision Navigation, Changsha 410073, China. · College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China.