Confidence-Aware Speed-over-Ground Estimation from Doppler Spectra via Reconstruction-Based Representation Learning

Malte Stelzer; Marvin Sach; Timo Bartels; Dinu Mihailescu-Stoica; Sören Kohnert; Florian Poprawa; Marc Zeller; Tim Fingscheidt

eess.SPOct 29, 2026

Confidence-Aware Speed-over-Ground Estimation from Doppler Spectra via Reconstruction-Based Representation Learning

Authors: Malte Stelzer, Marvin Sach, Timo Bartels, Dinu Mihailescu-Stoica, Sören Kohnert, Florian Poprawa, Marc Zeller, Tim Fingscheidt

Organizations: Technische Universität Braunschweig, Germany · Siemens Mobility GmbH, Berlin, Germany

Abstract

Reliable speed-over-ground estimation from ground-facing Doppler spectra is essential for mobile platforms such as railway systems. Classical signal-processing approaches can provide accurate estimates under favorable conditions, but often degrade in challenging conditions. We propose confidence-aware speed-over-ground estimation trained on rail-domain data that estimates speed over ground and frame-level confidence from Doppler spectra with several novel contributions: First, we transfer the idea of exploiting a reconstruction task by an autoencoder for performance estimation from previous work to Doppler RaDAR. Second, we append a speed-over-ground estimation head operating on the autoencoder's latent space features. Third, we omit the reconstruction decoder during inference but add a low-cost dedicated confidence head for frame-wise error-bound estimation. Fourth, we reveal how noise augmentation training can provide high robustness to the method. Experiments show that our approach improves speed estimation accuracy over classical baselines while providing informative confidence estimates that indicate the reliability of individual predictions, even under adverse signal conditions.

Figures & tables

Panel of Figure 1 — Figure 1: Our proposed speed-over-ground estimation with confidence estimation . Inference: Solid signal paths and blocks; training: also dashed ones.

Method	Train. noise	$\alpha$	$\mathcal{D}^{\mathrm{val}}$ clean	$\mathcal{D}^{\mathrm{val}}$ + noise	$\mathcal{D}^{\mathrm{val}}$ + -10 dB noise	$\mathcal{D}^{\mathrm{test}}$ clean	$\mathcal{D}^{\mathrm{test}}$ + noise	$\mathcal{D}^{\mathrm{test}}$ + -5 dB noise	$\mathcal{D}^{\mathrm{test}}$ + -10 dB noise	$\mathcal{D}^{\mathrm{test}}$ avg. rank $\downarrow$
PP [ 18 ]	-	-	${0.41}^{\pm 0.47}$	${0.45}^{\pm 0.06\phantom{1}}$	${1.02}^{\pm 11.24}$	${0.42}^{\pm 0.43}$	${0.45}^{\pm 0.07\phantom{1}}$	${0.60}^{\pm 6.34\phantom{1}}$	${1.17}^{\pm 12.87}$	6.00
CMA [ 19 ]	-	-	${1.04}^{\pm 1.73}$	${1.30}^{\pm 1.54\phantom{1}}$	${24.68}^{\pm 68.23}$	${0.99}^{\pm 1.51}$	${1.17}^{\pm 1.31\phantom{1}}$	${4.09}^{\pm 26.56}$	${25.07}^{\pm 69.00}$	7.00
XCA [ 19 ]	-	-	${0.36}^{\pm 1.41}$	${0.36}^{\pm 0.03\phantom{1}}$	${\underline{0.38}}^{\pm 1.52\phantom{1}}$	${0.34}^{\pm 1.31}$	${0.34}^{\pm 0.00\phantom{1}}$	${0.35}^{\pm 1.39\phantom{1}}$	${\underline{0.37}}^{\pm 1.59\phantom{1}}$	3.50
Ours	no	1.0	${\textbf{0.14}}^{\pm 0.20}$	${9.62}^{\pm 7.91\phantom{1}}$	${33.63}^{\pm 18.92}$	${\textbf{0.15}}^{\pm 0.20}$	${9.63}^{\pm 7.91\phantom{1}}$	${23.68}^{\pm 13.87}$	${33.93}^{\pm 19.28}$	6.75
	no	0.9	${\textbf{0.14}}^{\pm 0.20}$	${13.02}^{\pm 12.42}$	${37.57}^{\pm 20.08}$	${\textbf{0.15}}^{\pm 0.19}$	${13.18}^{\pm 12.54}$	${35.94}^{\pm 19.10}$	${38.17}^{\pm 20.93}$	8.25
	no	0.8	${\underline{0.15}}^{\pm 0.21}$	${11.01}^{\pm 11.99}$	${36.70}^{\pm 19.50}$	${\textbf{0.15}}^{\pm 0.22}$	${11.16}^{\pm 12.14}$	${34.40}^{\pm 18.66}$	${37.20}^{\pm 20.17}$	7.50

Table 1: MAE results on

\mathcal{D}^{\mathrm{val}}

and

\mathcal{D}^{\mathrm{test}}

: Average velocity MAE in m/s across different noise conditions. For our models, we investigated noise augmentation training and vary

\alpha

in ( 3 ). Best values are marked bold, second-best are underlined.

Panel of Figure 2 — Figure 2: Velocity MAE results on noisy $\mathcal{D}^{\mathrm{test}}$ .

Panel of Figure 3 — Figure 3: Our method: Percentage of velocity errors below error bound $\hat{\delta}_{\ell}$ and mean error bound $\hat{\delta}^{\mathrm{mean}}$ on noisy $\mathcal{D}^{\mathrm{test}}$ ; $\hat{\delta}^{\mathrm{mean}}\pm\frac{1}{2}\sigma$ are shown for visualization purposes.

Panel of Figure 4 — Figure 4: Per-frame velocity error and predicted error bound : Sequence from $\mathcal{D}^{\mathrm{test}}$ at an SNR of 5 dB, including the velocity error smoothed using an IIR and FIR filter.

Robust Estimation

Robust estimation infers reliable parameters and states despite outliers, heavy-tailed noise, data contamination, or model uncertainty.

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Untangling the Geometry and Speed for RF Sensing Spectrograms

Mert Torun, Darius Cuenca, Yasamin Mostofi

Department of Electrical and Computer Engineering, University of California, Santa Barbara

Disentangled Representation Learning Physics-Informed ML Wi-Fi Sensing

Open paper AskPDF arXiv

A fundamental challenge in RF sensing is that Doppler signatures observed by a link entangle the target's motion with the sensing geometry, resulting in limited applicability to unconstrained real-world settings. In this paper, we establish a new foundation for physically interpretable RF sensing that disentangles reflector speed from geometry, jointly recovering the speed, geometry factor, relative amplitude, and width of each dominant Doppler ridge. More specifically, we first develop a compact parametric representation of WiFi spectrograms and establish its low-dimensional structure through a systematic computer-vision analysis of a large and diverse human-activity dataset, thereby providing a tractable foundation for learning. Building on this representation, we then design a physics-informed autoencoder whose structured bottleneck and differentiable RF forward model enforce physically meaningful estimates of reflector speed and geometry. We further introduce a synthetic-to-real training framework, eliminating the need for real WiFi training data. We extensively validate the proposed framework under both known and time-varying geometries, using both independently generated synthetic test sets and 31 real WiFi experiments. The results demonstrate the superior performance in speed and geometry extraction, robustly recovering the underlying geometry, speeds, Doppler-ridge amplitudes, and ridge widths across all settings, while substantially outperforming the strongest baselines.

Abstract

Robust Estimation

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