Quality-Aware Denoising of Ultra-Short TDoA Measurements for 5G-NR UAV Localization Zexin Fang∗ , Bin Han∗ , Anjie Qiu∗ , Zhuojun Tian† and Hans D. Schotten∗‡ ∗ RPTU University Kaiserslautern-Landau, Germany; † KTH Royal Institute of Technology, Sweden
arXiv:2604.08734v1 [eess.SP] 9 Apr 2026
‡ German Research Center for Artificial Intelligence (DFKI), Germany.
Abstract—Reliable positioning is essential for Uncrewed Aerial Vehicles (UAVs) in safety-critical urban operations, yet achieving sub-meter accuracy under stringent latency constraints remains challenging. While 3rd Generation Partnership Project (3GPP) specifies repeated Positioning Reference Signals (PRS) transmissions for accurate Time Difference of Arrival (TDoA) measurements, denoising techniques specifically tailored for extremely limited measurement sequences within 3GPP frameworks remain underexplored. We propose Adaptive Gain Exponential Smoother (AGES), a lightweight filter combining exponentially weighted averaging with adaptive gains informed by 3GPP measurement quality reports. Simulations demonstrate AGES achieves 30 − 40% reduction in positioning error with only 3 − 5 repeated measurements while maintaining Fifth Generation New Radio (5G-NR) infrastructure compatibility. Index Terms—UAV; TDoA; 3GPP; 5G-NR
I. I NTRODUCTION With the advancement of Low Altitude Economy (LAE), Uncrewed Aerial Vehicles (UAVs) are increasingly deployed for safety-critical civil services such as emergency medical supply delivery, search and rescue operations, and infrastructure inspection in urban areas. As regulatory frameworks worldwide open airspace for commercial UAV operations, demand for robust positioning systems has intensified. While Global Navigation Satellite System (GNSS) remains the primary positioning method, its vulnerability to signal degradation in urban canyons and multipath interference poses significant challenges for autonomous navigation. Research and standardization efforts have shifted toward terrestrial infrastructure-supported localization, with 3rd Generation Partnership Project (3GPP) progressively enhancing positioning capabilities: Release 16 introduced Fifth Generation New Radio (5G-NR) positioning features including Downlink Observed Time Difference of Arrival (DL-OTDOA) and Uplink Observed Time Difference of Arrival (UL-OTDOA) with submeter accuracy targets, while Releases 17 and 18 targeted decimeter-level accuracy for industrial Internet of Things (IoT) and Vehicle-to-Everything (V2X) applications [1], [2], [3]. Commercial deployments are underway globally, including China Mobile and China Unicom in major cities, Verizon and AT&T pilots in the United States, and Deutsche Telekom and Vodafone trials in Europe. Despite these advances, achieving reliable sub-meter accuracy in challenging propagation environments remains an open challenge for aerial platforms in dense urban settings.
To enhance localization accuracy in DL-OTDOA positioning, Positioning Reference Signals (PRS) signals are transmitted periodically, enabling the User Equipment (UE) to obtain multiple Time Difference of Arrival (TDoA) measurements over consecutive PRS occasions. These measurements, along with quality reports, are forwarded to the Localization Management Function (LMF) for temporal smoothing and position estimation. Emerging 5G-NR positioning targets emphasize both low latency and high accuracy: Rel-17 defines a commercial positioning latency target of ≤ 100 ms endto-end, with desirable latencies of 10 ms for industrial IoT use cases, alongside sub-meter accuracy requirements. However, meeting these dual objectives simultaneously presents a fundamental challenge: achieving the required latency necessitates processing measurements over ultra-short observation windows. Consequently, ultra-short measurement sequences are prevalent in practical 5G-NR positioning for UAVs and industrial IoT devices. In dense urban environments, the UE may only receive 3 − 7 consecutive PRS measurements before reporting to the LMF to satisfy real-time constraints. Standard smoothing and Kalman filtering methods typically assume longer measurement sequences. Applying conventional filters over short sequences either underperforms due to insufficient data for velocity modeling, or introduces delays that violate latency targets. As the result, there is a critical need to investigate lightweight denoising techniques specifically tailored to ultra-short sequences that: i) improve measurement reliability without extensive historical data, ii) maintain low computational complexity suitable for UE or LMF processing, iii) respect end-to-end latency constraints, iv) and provide robust performance with 3 − 7 samples. To the best of our knowledge, lightweight measurementlevel filtering for ultra-short sequences in dynamic UAV scenarios remains largely unexplored. Several studies have investigated denoising techniques for limited observation windows. Palivonaite et al. propose algebraic short-term forecasting with mixed smoothing, demonstrating meaningful noise reduction with very short sequences [4]. Exponential smoothing methods have been widely studied for short-term smoothing and forecasting, emphasizing recent observations while requiring minimal historical data and computational complexity [5], [6]. In acoustic source localization, Kalman filtering and recursive smoothing of TDoA measurements have demonstrated effectiveness by directly processing noisy measurements [7], [8]. Inspired by these studies and tailored for 5G-NR, we
Positioning Preparation
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gNBs Positioning Request Request Accepted Config. Instruction
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Fig. 1: 5G-NR DL-OTDOA localization procedure showing signaling flow between network entities.
propose a Kalman-inspired filter using exponentially weighted averaging combined with Kalman-style gain-based updates and measurement quality reports defined in the 3GPP framework, detailed in Alg. 1. The rest of this paper is organized as follows: In Sec.II, we introduce the relevant 3GPP framework and Air to Ground (A2G) channel model. In Sec.III, we present the TDoA measurement system model and proposed denoising techniques. In Sec.IV, we evaluate these techniques. Finally, we conclude in Sec.V. II. P RELIMINARY A. 3GPP 5G-NR framework We introduce a 5G-NR localization system following the 3GPP architecture for Observed Time Difference of Arrival (OTDOA)-based UE positioning. The LMF serves as the central positioning entity, coordinating localization procedures, computing UE positions from reported measurements, and managing inter-cell synchronization for accurate multilateration. The Access and Mobility Management Function (AMF) handles connection and mobility management, tunneling LTE Positioning Protocol (LPP) messages between the LMF and UE. The Next Generation Node Bs (gNBs) transmit PRS and maintain precise time synchronization for TDoA-based positioning. The positioning procedure relies on three key protocols: 1) LPP facilitates signaling between the LMF and UE [9]. The LMF sends measurement configuration specifying the Positioning Reference Configuration (PRC), instructing the UE on which PRS to measure. The UE performs TDoA measurements and returns detailed reports to the LMF for position computation. 2) NG-RAN Positioning Protocol A (NRPPa) enables the LMF to coordinate PRS transmission across gNBs [10], specifying transmission timing, duration, frequency resources, and beam configuration for coordinated network deployment.
3) PRS are downlink reference signals transmitted by gNBs according to the configured PRC. The UE measures TDoA between signals from different gNBs and reports measurements with Quality report (QR) indicators. PRS can be time-multiplexed (avoiding inter-cell interference) or frequency-multiplexed (enabling simultaneous transmissions for reduced latency in mobile UAV scenarios). We employ DL-OTDOA, where the UE passively measures TDoA and reports to the LMF for position computation (Fig. 1). This centralized approach minimizes signaling overhead and computational burden on UEs while enabling sophisticated positioning algorithms. Specifically, we consider frequency-multiplexed PRS-enabled DL-OTDOA as specified in Release 17 for high-accuracy, low-latency applications [2]. B. A2G channel model The A2G propagation characteristics have been comprehensively analyzed by 3GPP, with corresponding models documented in [11]. For the Urban Micro–Aerial Vehicle (UMiAV) scenario, Line of Sight (LOS) probability is expressed as 1, d2D ≤ d1 , (1) Plos = 1 − d1 exp −d2D + d1 , d2D > d1 , d2D p1 d2D where d2D represents the horizontal distance between the aerial vehicle and the terrestrial base station. The UAV altitude h influences the model through parameters d1 and p1 , defined as d1 = max 294.05 log10 (h) − 432.94, 18 , (2) p1 = 233.98 log10 (h) − 0.95. Combining LOS and Non-Line-of-Sight (NLOS) conditions, the average path-loss exponent η (in dB), as defined in [11], is given by η = 4.32 − 0.76 log10 (h) (1 − Plos ) (3) + 2.225 − 0.05 log10 (h) Plos .
These expressions reveal that channel quality generally improves with increasing altitude due to higher LOS probability, while degrading with increasing horizontal distance as NLOS conditions become more prevalent. III. M ETHODOLOGY A. System model First, TDoA measurements are derived through correlation of PRSs, which exhibit short pulse characteristics with desirable autocorrelation properties. Research in [12], [13] demonstrates that dense multipath propagation fundamentally constrains TDoA measurement accuracy via the Cramér-Rao lower bound σd2 ≥ JT−1 , where the Fisher information matrix JT for TDoA estimation is expressed as: JT = 2c−1 4π 2 SINRγβ 2 sin2 (ϕ).
(4)
In this formulation, c denotes the speed of light, β the signal bandwidth, and SINR quantifies the signal-to-interferenceplus-noise ratio dominated by multipath effects and inter-cell interference. Given that 3GPP specifications enforce orthogonal PRS allocation across gNBs and that A2G propagation typically experiences limited multipath components, we apply the simplification SINR ≈ SNR. The parameters γ and sin2 (ϕ) characterize whitening filter efficiency and degradation from path loss uncertainty, respectively. Analysis in [14] reveals that although both terms exhibit bandwidth dependence, sin2 (ϕ) demonstrates significantly reduced sensitivity compared to γ, indicating that SNR, β, and γ constitute the primary determinants of JT . The whitening gain admits the approximation γ ∝ ln(β)β −1 [15], yielding the simplified variance bound: c . (5) σd2 ∝ 8π 2 SNRβ ln β This relationship provides a theoretical foundation for weighted positioning algorithms to improve localization robustness. Second, achieving reliable position estimates necessitates repeated TDoA measurements at the UE, the proccess of TDoA measurements from one gNB and the denoising proccess is depicted in Fig. 2. We aggregate the ground-truth TDoA observations across N base stations over K temporal instances into the measurement matrix τ : 1 τ1 τ12 · · · τ1n · · · τ1N τ21 τ22 · · · τ2n · · · τ2N .. .. .. .. .. .. . . . . . . τ = τ1 τ2 · · · τn · · · τN . k k k k . .. .. .. .. .. .. . . . . . 1 2 n N τK τK · · · τK · · · τK PRS transmissions occur at fixed periodicity ∆t . Since 3GPP specifications impose stringent synchronization requirements on gNBs, and the LMF manages synchronization errors, the inter-node timing offsets δ = [δ1 , δ2 , . . . , δN ] exhibit negligible drift over a short time span. The observed TDoA matrix is therefore modeled as: τR = τ + δ × 1K×1 + ϵD ,
(6)
Fig. 2: Illustration of measurement denoising window for ultrashort TDOA sequences where ϵD represents the measurement noise matrix. τR can be then interpreted to the distances matrix D = τR · c, where D = {d˜nk }N,K n=1,k=1 . One the distance obtained, localization can be performed by LMF. B. Denoise techniques To address the challenge of ultra-short TDoA sequences, we introduce several lightweight filtering techniques alongside our proposed approach: Exponential Smoothing: This method assigns exponentially decaying weights to historical measurements, emphasizing recent Pk observations. Pk The smoothed estimate is computed as x̂k = i=1 wi xi / i=1 wi , where wi = αk−i and α ∈ (0, 1) controls the decay rate. It requires minimal computational overhead and naturally adapts to time-varying signals. Double Exponential Smoothing: Extending simple exponential smoothing, DES incorporates trend estimation through two equations: level ℓk = αxk + (1 − α)(ℓk−1 + bk−1 ) and trend bk = β(ℓk − ℓk−1 ) + (1 − β)bk−1 . The smoothed output combines both as x̂k = ℓk + bk , enabling tracking of linear trends even with limited data. Median Filter: Computes the median value over a temporal window centered at each measurement point. This approach provides robustness against sporadic outliers by selecting the middle-ranked value within the window, though it does not account for velocity or motion trends in the data. Savitzky-Golay Filter: A polynomial-based smoothing approach that approximates the local signal behavior through least-squares polynomial fitting. By evaluating the fitted polynomial, this method attenuates measurement noise while preserving important signal characteristics such as peaks and trends. Proposed Adaptive Gain Exponential Smoother (AGES): We propose an AGES specifically designed for TDoA mea-
Input: Distances measurements d and measurement quality reports; Forgetting factor α. 2 Output: The latest distance measurement from all gNBs X . 3 Function AGES : 4 Extract Signal to Noise Ratio (SNR) from measurement reports and combine them with the bandwidths of PRS, then convert to variance matrix R using Eq. 5, where R = {rkn }N,K n=1,k=1 . 5 for n = 1 : N do 6 for k = 1 : K − 1 do 7 wk = α(K−2−k) n 8 Ppre += rkn /(K − 1) n += d˜nk wk /(K − 1) 9 Xpre 10 end n n n n ) + rK /(Ppre 11 Kgain = Ppre n n n n n ˜ ) 12 Xcur = Xpre + Kgain (dK − Xpre 13 end n 14 Output X = {Xcur | 1 ≤ n ≤ N} 15 end 1
Double Exp
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(a) Altitude: 20 m, speed: 90 km/h
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IV. E VALUATION OF M ETHODOLOGY
6 7 8 9 10 11 12 13 14 Meansurement window length
(b) Altitude: 30 m, speed: 90 km/h
Proposed Double Exp
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1.1 Normalized localization error
Next, we proceed to evaluate the aforementioned denoising techniques. We assume that the bilateration problem is resolved by the LMF, and the UAV operates in a gNBdense urban environment. The UAV flies at approximately constant velocity within the measurement window, with minor speed fluctuations induced by mechanical dynamics and wind disturbances. The detailed simulation setup regarding TDoA measurements and deployment is listed in Tab. I. Additionally, the velocity jitter is modeled as 10% of the nominal velocity with random directional perturbations. The simulation results are consolidated in Fig. 3, with each data point averaged over 1000 Monte Carlo runs. It is worth noting that, due to latency requirements, practical PRS measurements are typically limited to only a few frames. However, we extend the measurement window beyond 10 frames to provide deeper insights into the behavior and limitations of the aforementioned denoising techniques. Subsequently, the denoised measurements combined with gNB coordinates are used to localize the UAV using the efficient gradient descent algorithm introduced in [16], [17], [18]. In Fig. 3a, the UAV cruises at relatively low altitude, where A2G channels typically exhibit degraded quality due
SavGol
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Algorithm 1: AGES
Proposed Exponential
Normalized localization error
surement denoising under ultra-short observation windows. Unlike classical Kalman filtering that requires explicit statespace models and process noise characterization, AGES integrates exponentially weighted moving averages with Kalmanstyle adaptive gain mechanism informed by measurement quality reports. AGES exploits 3GPP defined measurement reports to construct time-varying measurement covariances, enabling quality-aware filtering.
1.0 0.9 0.8 0.7 0.6 3
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(c) Altitude: 30 m, speed: 50 km/h
Fig. 3: Performance of different denoising techniques. The normalized localization error is obtained by dividing by the localization error without denoising.
Deploy.
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TABLE I: Simulation setup 1 Parameter
Value
Remark
fc K Np τmax Pt No βn σt
3.5 GHz (0.1, 3.0) 4 2e-7 s 15 dBm -91 dBm 10 Mhz 1µs
Carrier frequency Rician factors Number of multipath Maximum delay spread Transmitting power Noise floor Bandwidth Average synchronization error
hu R hn Vu ∆t N
[20, 30] m 120 m ∼ U (0, 5) m [50, 90] km/h 20 ms 8 ms
UAV altitude Node coverage Node coverage UAV velocity PRS interval Assigned gNB number
els. Our evaluation revealed that velocity-agnostic methods like median filtering fail under motion, while trend-based approaches like double exponential smoothing require more data than available. AGES addresses this through adaptive weighting that accounts for measurement recency and quality. This work provides a practical solution compatible with existing 5G-NR infrastructure, enabling reliable autonomous UAV navigation in dense urban environments. ACKNOWLEDGMENT This work is supported by the Federal Ministry of Research, Technology and Space of Germany via the project Open6GHub+ (16KIS2406). B. Han ([email protected]) is the corresponding author. R EFERENCES
to increased NLOS probability. AGES achieves the best performance for short measurement windows. The median filter demonstrates effective denoising only when the measurement window is small, as it completely disregards velocity consideration. When the window is sufficiently short, UAV displacement remains minimal, making the constant-value assumption approximately valid. However, as the measurement window expands, median filter performance deteriorates significantly due to its inability to track motion-induced trends. Similarly, AGES exhibits slightly reduced denoising effectiveness with longer windows, as it does not explicitly model velocity dynamics. The Savitzky-Golay filter shows performance degradation as the measurement window increases, though it could potentially surpass our method with substantially longer windows at the cost of prohibitive latency. Double exponential smoothing underperforms compared to AGES and simple exponential smoothing, as the limited number of measurements introduces substantial estimation error when attempting to model both level and trend components. In Fig. 3b, the UAV operates at higher altitude, where measurement quality improves substantially due to enhanced channel conditions and reduced NLOS components. Under these favorable propagation conditions, double exponential smoothing performance notably improves, as higher-quality measurements enable more reliable trend estimation with reduced noise interference. In Fig. 3c, the UAV travels at reduced velocity, significantly altering the filtering performance characteristics. The performance degradation of the median filter is substantially mitigated, as slower motion results in smaller TDoA variations across the measurement window, better aligning with its implicit stationarity assumption. Notably, the optimal measurement window length extends to approximately 9 frames, demonstrating the method’s adaptiveness to velocity changes. V. C ONCLUSION This work established that effective TDoA denoising for UAV positioning is achievable with severely constrained measurement sequences. By exploiting standardized 3GPP measurement reports, significant noise reduction is obtained without additional signaling overhead or complex motion mod-
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