Neural Ranging Correction (NeRC)

Updated 9 July 2026

NeRC is a framework that employs neural networks to learn and correct biases in radio-based distance estimates affected by multipath and non-line-of-sight interference.
It integrates advanced signal representations, such as Channel Impulse Response and signal strength features, to predict corrections or confidence weights that improve localization accuracy.
Empirical results demonstrate significant error reductions (e.g., in RMSE and MAE) across LTE, UWB, and GNSS settings, showcasing NeRC’s robustness and deployability.

Searching arXiv for the specified NeRC and related neural ranging correction papers to ground the article in current literature. Neural Ranging Correction (NeRC) denotes the use of neural networks to learn complex, environment-dependent biases and errors in radio-based ranging, particularly those imposed by multipath and non-line-of-sight (NLOS) propagation. In the literature, the term covers direct range estimation from Channel Impulse Response (CIR), learned mitigation of biased Ultra-Wideband (UWB) measurements, self-supervised correction of UWB ranges without ground-truth labels, and end-to-end pseudorange correction for Global Navigation Satellite System (GNSS) using differentiable Moving Horizon Estimation (MHE) (Lee et al., 2020, Coppens et al., 2024, Weng et al., 20 Aug 2025). Across these variants, the central object is a learned correction or weighting mechanism that improves downstream localization when analytic error models, Gaussian assumptions, or explicit ranging-error annotations are inadequate.

1. Problem formulation and conceptual scope

NeRC methods are organized around the fact that the observed range is typically a biased proxy for physical distance. One explicit formulation writes the UWB observation as $\hat{d} = d + \Delta d$ , where $d$ is the true physical distance and $\Delta d$ is the range error; a neural regressor estimates $\hat{y}$ for $\Delta d$ so that $\hat{d} - \hat{y} \approx d$ (Angarano et al., 2022). In LTE indoor ranging, the model produces an estimate $\hat{r}_i$ for the true range $r_i$ at each sample, and performance is evaluated by the root mean squared error (RMSE), maximum error, and standard deviation (Lee et al., 2020). In smartphone GNSS, the corrected pseudorange is formed by subtracting a predicted bias, $\rho_{c_k}^{(n)} - \hat{\mu}_k^{(n)}$ , before invoking a classical localization engine (Weng et al., 2023).

Within this scope, neural correction does not always mean direct regression of a scalar error. In low-cost UWB localization, the network may instead output the probability that a ranging measurement is LOS, and that probability is then used as the weight $\beta_i$ in Weighted Least Squares (WLS) (Shalihan et al., 2022). In self-supervised UWB correction, the network outputs a continuous correction action bounded in $d$ 0 mm and is trained through a reinforcement-learning reward rather than a supervised target (Coppens et al., 2024). In end-to-end GNSS NeRC, an upstream MultiLayer Perceptron (MLP) predicts per-satellite pseudorange errors over a horizon, and a downstream differentiable MHE converts those corrections into a trajectory estimate used for training (Weng et al., 20 Aug 2025).

This suggests that NeRC is best understood as a methodological family rather than a single model class: the learned component may estimate range directly, regress a correction, infer a confidence weight, or interact with a model-based estimator through a differentiable objective.

2. Measurement representations and learned observables

A defining property of NeRC systems is their reliance on measurement representations richer than scalar range alone. In LTE indoor localization, a software-defined radio extracts the CIR from the Cell-specific Reference Signal of the LTE downlink after synchronization using PSS and SSS signals and removal of guard bands; the magnitude of the CIR is then fed to the neural network as a temporal sequence (Lee et al., 2020). For UWB range error mitigation on microcontrollers, the sole input is the CIR vector $d$ 1, with $d$ 2 studied for $d$ 3 (Angarano et al., 2022). In the self-supervised reinforcement-learning formulation, the raw complex CIR is converted to real-valued samples by

$d$ 4

cropped to a fixed window of 150 samples around the detected first path, and min-max normalized to define the state $d$ 5 (Coppens et al., 2024).

Not all NeRC-relevant methods depend on CIR. Because low-cost UWB devices do not provide Channel Impulse Response data, one neural NLOS-mitigation method uses only signal-strength-derived features: RxRssi, FpRssi, RSSD, and STD computed within a 0.5-second window (Shalihan et al., 2022). The reported correlation structure is asymmetric: RxRssi and FpRssi have a negative correlation with ranging error, whereas RSSD and STD have a positive correlation with ranging error (Shalihan et al., 2022). GNSS pseudorange correction likewise uses higher-level measurement and context features rather than waveform data: $d$ 6, elevation, PRN, position estimates, geometry vectors, and smartphone heading are assembled into 16 per-satellite inputs in PrNet, while end-to-end NeRC augments satellite-wise signal-quality and geometry features with pseudorange residuals and their root-sum-squares over a time horizon (Weng et al., 2023, Weng et al., 20 Aug 2025).

A broader signal-modeling variant appears in dual-radar tracking, where coordinate measurement errors are normalized and encoded using Poisson spike trains, then processed by an Izhikevich spiking neural network whose firing rate represents the error compensation amount (Gao et al., 29 Dec 2025). This broadens the NeRC-related landscape from continuous waveform features to event-based neural encodings of measurement error.

3. Architectural families

The architectural spectrum associated with neural ranging correction is notably heterogeneous. A recurrent formulation for LTE CIR ranging uses an embedding layer with output dimension 128, one LSTM layer with hidden size 128, and two dense layers with ReLU activations; the baseline is a shallow model with two dense layers and no sequential processing (Lee et al., 2020). For low-cost UWB NLOS mitigation, the selected classifier is a fully connected neural network with 10 hidden layers, 300 neurons per layer, ReLU hidden activations, and a Sigmoid output producing the LOS probability (Shalihan et al., 2022). REMNet for UWB range error mitigation adopts a modified 1D CNN with an initial convolutional layer, a stack of $d$ 7 Residual Reduction Modules, Flatten, Dropout, and a single linear output neuron; self-attention blocks present in the original REMNet were removed to maximize microcontroller compatibility (Angarano et al., 2022).

Self-supervised UWB NeRC uses an actor-critic construction under Deep Deterministic Policy Gradient. Both actor and critic employ convolutional feature extraction for CIR followed by dense layers; the actor outputs a scalar correction through a final tanh activation scaled to the assumed error bound, and the critic receives CIR plus action to estimate a Q value (Coppens et al., 2024). Smartphone GNSS pseudorange correction in PrNet uses a satellite-wise MLP with 20 hidden layers and 40 units per layer, processing all visible satellites in parallel with zero-padding for non-visible satellites and a visible-satellite mask post-prediction (Weng et al., 2023). The end-to-end GNSS NeRC framework also uses an MLP upstream, but its distinguishing architectural feature is the downstream differentiable MHE that backpropagates localization gradients through the estimator (Weng et al., 20 Aug 2025).

A different branch fuses ranging with inertial sensing. Neural Ranging Inertial Odometry introduces a graph attention UWB network and a recurrent neural inertial network; the IMU branch uses 1D Convolution + 2-layer GRU + MLP, while the UWB branch uses MLP + 4-layer Graph Attention Network and incorporates least-squares priors and a nominal frame (Wang et al., 11 Dec 2025). In radar guidance, the Izhikevich neuron model with spike-timing-dependent plasticity (STDP) implements online error compensation with biologically inspired spiking dynamics rather than conventional dense or recurrent layers (Gao et al., 29 Dec 2025).

This suggests that the unifying feature of NeRC is not a canonical network topology but the placement of a neural module at the ranging-error interface.

4. Supervision, objectives, and label formation

The supervision strategy is a major axis of differentiation. In LTE CIR ranging, training uses RMSE as the loss function and the Adam optimizer with learning rate $d$ 8 in TensorFlow, with a 60%/20%/20% train-validation-test split over 5,000 samples (Lee et al., 2020). In low-cost UWB NLOS mitigation, the network is trained as a LOS/NLOS classifier and the selected configuration yields 93.29% accuracy and 0.9321 precision (Shalihan et al., 2022). REMNet is trained as a regressor of $d$ 9 on both LOS and NLOS samples simultaneously, without explicit LOS/NLOS classification, and is later quantized to int8 for deployment (Angarano et al., 2022).

A more intricate supervised scheme appears in PrNet. Because true pseudorange bias is not directly observable, the target value is derived by combining ground-truth location with a Rauch-Tung-Striebel (RTS) smoother:

$\Delta d$ 0

The loss explicitly incorporates the estimation residuals of smartphone clock bias,

$\Delta d$ 1

aligning the learned pseudorange corrections with the structure of GNSS state estimation (Weng et al., 2023).

Two later developments reduce dependence on explicit ranging-error labels. Self-supervised UWB NeRC defines the state as the pre-processed CIR, the action as the predicted correction, and the reward as

$\Delta d$ 2

where $\Delta d$ 3 is a smoothed estimate of the true range obtained from trajectory predictability, filtering, and smoothing rather than from ground-truth labels (Coppens et al., 2024). End-to-end GNSS NeRC replaces ranging-error supervision with localization-related training objectives. It supports supervised 3D loss, supervised 2D loss, and Euclidean Distance Field (EDF) loss for map-derived supervision:

$\Delta d$ 4

with gradients propagated through differentiable MHE (Weng et al., 20 Aug 2025).

A recurrent theme is the practical difficulty of obtaining reliable ranging-error labels. The literature therefore moves from explicit labels, to derived intermediate labels, to self-supervised or task-level supervision.

5. Coupling with localization and estimation engines

NeRC modules are frequently embedded within larger estimation pipelines rather than used in isolation. In low-cost UWB localization, the neural output is the LOS probability and the position estimate is computed through WLS:

$\Delta d$ 5

where $\Delta d$ 6 is set to the LOS probability output by the NN; the minimization is solved with the Trust Region Reflective algorithm (Shalihan et al., 2022). PrNet follows the same philosophy at GNSS scale: predicted pseudorange biases are subtracted from raw pseudoranges and the corrected measurements are then fed into WLS, MHE, EKF, or an RTS smoother (Weng et al., 2023).

End-to-end GNSS NeRC makes this coupling differentiable. The upstream MLP predicts pseudorange errors over a horizon,

$\Delta d$ 7

and the downstream MHE solves a nonlinear least-squares problem involving prior cost, state-transition costs, and measurement costs. The chain rule is then used to backpropagate the position loss through the estimator to the neural module (Weng et al., 20 Aug 2025). This design keeps GNSS physics, state dynamics, and clock models inside the optimization loop rather than replacing them with a black-box trajectory regressor.

The same hybridization appears in UWB-inertial fusion. Neural Ranging Inertial Odometry uses a classical least-squares model as a direct position prior, concatenates that prior with graph-node features, and predicts a bias-corrected 6-DoF pose in a nominal frame (Wang et al., 11 Dec 2025). In self-supervised UWB NeRC, Kalman filtering and smoothing are not auxiliary post-processing but part of the reward-generation mechanism that defines the self-supervised signal (Coppens et al., 2024).

A persistent misconception is that neural correction must replace classical estimation wholesale. The reported systems instead show repeated use of WLS, EKF, RTS smoothing, least squares, or MHE as structural components around the neural corrector.

6. Empirical results, deployment, and operating regimes

The empirical record spans LTE, UWB, GNSS, radar, and fused inertial settings. Representative results reported in the literature are summarized below.

Setting	Neural mechanism	Reported result
LTE indoor ranging	RNN-LSTM on LTE CIR magnitude	RMSE reduced from 13.11 m to 9.02 m; maximum error reduced from 55.68 m to 27.40 m (Lee et al., 2020)
UWB NLOS mitigation	LOS-probability NN + WLS	Lobby: 2.79 m to 2.32 m; Corridor: 3.41 m to 2.45 m; Office: 2.02 m to 1.14 m (Shalihan et al., 2022)
UWB range error mitigation	REMNet on CIR	Initial MAE 0.1242 m; corrected MAE 0.0687 m with $\Delta d$ 8 (Angarano et al., 2022)
Self-supervised UWB NeRC	DDPG on CIR	MAE all: 155 mm to 106 mm; MAE NLOS: 181 mm to 118 mm (Coppens et al., 2024)
Smartphone GNSS urban	End-to-end NeRC with differentiable MHE	GSDC21U horizontal position error 19.3 m vs. 54.7 m for MHE and 38.1 m for PrNet (Weng et al., 20 Aug 2025)
UWB-inertial odometry	IR-ULSG	Outdoor 3D: 1.06 m to 0.19 m; Tunnel 3D: 1.35 m to 0.34 m (Wang et al., 11 Dec 2025)

The LTE study used an indoor test at Winston Chung Hall, UC Riverside, with a receiver trajectory of 109 meters covered in 50 seconds, T-Mobile network at 2145 MHz, and CIRs estimated for every LTE frame at 0.01 s intervals, yielding 5,000 samples (Lee et al., 2020). The self-supervised UWB NeRC experiments used 3,463 UWB ranging samples in an industrial lab with 23 anchors, a mobile robot moving at 0.1 m/s, ADS-TWR ranging, and Qualisys MOCAP for evaluation only (Coppens et al., 2024). The microcontroller-oriented REMNet experiments used the DeepUWB dataset with 55,000 samples spanning indoor and outdoor, LOS and various NLOS conditions (Angarano et al., 2022).

Deployment characteristics are equally prominent. After optimization and quantization, REMNet uses as little as ~23 kB of memory for parameters, reaches 140 Hz inference frequency on Arduino Nano 33 BLE Sense for CIR of 16, yields energy per inference below 1 mJ, and keeps total power below 53 mW in all settings (Angarano et al., 2022). End-to-end GNSS NeRC was deployed as a client-edge-server system with inference time per location of ~100 ms on an RTX 2060 GPU and end-to-end latency over WLAN of ~246 ms (Weng et al., 20 Aug 2025).

These results indicate two distinct operating regimes. One regime emphasizes embedded deployment and ultra-low-power execution; the other emphasizes task-level optimization through differentiable localization back-ends.

Several limitations recur across the literature. The low-cost UWB LOS-probability approach relies only on features available from low-cost UWB devices and therefore may not reach the very best possible NLOS discrimination obtainable with channel statistics or CIR; its accuracy also depends on the representativity of the training data (Shalihan et al., 2022). The self-supervised reinforcement-learning approach requires some degree of trajectory predictability for movement because reward shaping depends on smooth filtering, and it exhibits slightly more outliers than the supervised CNN in NLOS conditions (Coppens et al., 2024). PrNet generalizes well across phones in rural scenarios but performance decreases in urban and heterogeneous data, highlighting a domain gap (Weng et al., 2023). In the microcontroller setting, the central design trade-off is between input dimension $\Delta d$ 9, accuracy, memory, and inference speed (Angarano et al., 2022).

The literature also addresses several common misconceptions. One is that NLOS measurements should simply be discarded. In the UWB WLS formulation, the reported position is that mitigating rather than removing NLOS is preferable because excluding all NLOS readings can reduce robustness when anchor visibility is sparse (Shalihan et al., 2022). Another is that neural correction necessarily requires explicit ranging-error labels. Self-supervised UWB NeRC does not require labeled ground-truth data, and end-to-end GNSS NeRC replaces pseudorange-error labels with ground-truth locations or even EDF cost maps derived from routes (Coppens et al., 2024, Weng et al., 20 Aug 2025). A third is that NeRC always implies raw CIR access. The cited work shows both CIR-based and non-CIR-based variants (Shalihan et al., 2022, Angarano et al., 2022).

One possible source of nomenclature confusion is the acronym itself. “NeRC $\hat{y}$ 0” in point cloud compression denotes a novel point cloud compression framework leveraging implicit neural representations, with a 4D-NeRC $\hat{y}$ 1 extension for dynamic point cloud compression; it is unrelated to radio ranging correction despite the overlapping acronym (Ruan et al., 2024).

Taken together, the literature presents Neural Ranging Correction as a broad research program: learning scene-relevant compensation for biased distance-like measurements while retaining, when useful, the structure of established estimators such as WLS, least squares, EKF, RTS smoothing, and MHE. The trajectory of the field moves from direct supervised regression toward self-supervised and end-to-end task-level training, with increasing attention to deployability, calibration-free operation, and robustness under multipath, NLOS, non-Gaussian noise, sparse anchors, and urban signal obstruction.