Pith. sign in

REVIEW 4 major objections 6 minor 46 references

Sensor Fusion for Track Geometry Monitoring: Integrating On-Board Condition Monitoring and Degradation Models via Kalman Filtering

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper shows that fusing frequent noisy on-board sensor data with rare accurate track-recording-car inspections through a Kalman filter reduces track-geometry prediction uncertainty by up to 80–90% at six months.

desk verdict A genuinely new integration of degradation models and on-board sensor data, clearly written, but the empirical support for the headline reductions is thin and needs a proper out-of-sample validation. read the letter →

arxiv 2506.08028 v2 pith:3L4N5YNU submitted 2025-06-02 eess.SY cs.SYstat.AP

Huy Truong-Ba , Jacky Chin , Michael E. Cholette , Pietro Borghesani This is my paper
classification eess.SYcs.SYstat.AP
keywords trackgeometrydegradationon-boardconditionmonitoringsensorfusionKalmanfiltercredibleintervalmultivariateWienerprocessrecordingcarmaintenanceplanning
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Railway track geometry is normally inspected by Track Recording Cars (TRCs), which are accurate but expensive and infrequent, so forecasts made from TRC records alone have wide credible intervals that grow with the prediction horizon. This paper tries to establish that adding frequent, noisy measurements from low-cost sensors mounted on trains can keep those intervals narrow, if the two data sources are fused through a Kalman filter wrapped around a multivariate Wiener degradation model. In an experiment where the sensor system rode on a TRC itself for a year, weekly sensor updates reduced the six-month credible-interval width by up to 80–90% for the Top indicator and 40–60% for Alignment under fast degradation relative to TRC-only predictions. The same simulation-based frequency analysis shows that even measurements every four weeks cut long-horizon uncertainty by more than 40% in many cases, and that the credibility zone stabilizes after roughly two months. The practical attraction, if this holds, is that rail operators could monitor track deterioration and plan tamping with far fewer TRC runs.

What carries the argument

The load-bearing object is a Kalman filter applied in log-space to two coupled Gaussian models: the state transition $\boldsymbol{Z}_k \mid \boldsymbol{Z}_{k-1} \sim N(\boldsymbol{\mu}_k, \mathbf{Q}_k)$ from a multivariate Wiener degradation model (with drift $\boldsymbol{\mu}$, diffusion $\boldsymbol{\Sigma}$, and a tamping reset $\boldsymbol{z}^+$, $\boldsymbol{\Sigma}_{z^+}$), and the observation model $\boldsymbol{Y}_k \mid \boldsymbol{Z}_k = \boldsymbol{z}_k \sim N(\mathbf{H}\boldsymbol{z}_k + \mathbf{b}, \mathbf{R})$, where $\mathbf{H}$ and $\mathbf{b}$ are fitted by multivariate regression of concurrent on-board and TRC data and $\mathbf{R}$ is the residual covariance. The filter propagates the state mean and covariance between accurately measured TRC times, absorbs each noisy on-board update through the Kalman gain, and is re-initialized with $\mathbf{P}_0 = 0$ whenever a TRC record becomes available. The predicted credible-interval width is evaluated as $W_k = |\mathbf{P}_{k|k}|^{1/n}$, the determinant-based measure from Eqs. (13)–(14), averaged over MCMC samples of the degradation parameters.

What would settle it

Take TRC campaigns that were not used to fit $\mathbf{H}$, $\mathbf{b}$, and $\mathbf{R}$, feed the filter with on-board readings collected on a service train running at a different speed, and compare the filtered predictions with the held-out TRC records; if the credible-interval reduction over the no-on-board baseline largely disappears, or the filtered predictions are systematically biased, the paper's uncertainty-reduction claim is only an in-sample artifact.

Watch

Extended reading notes

Core claim

The central claim is that a linear-Gaussian state-space model—where the hidden state is the logarithm of track geometry indicators and the observations are logarithmically transformed on-board sensor indices—makes long-horizon track geometry prediction a standard filtering problem, and that solving it with a Kalman filter yields far tighter predictions than the degradation model alone. The degradation transition is a multivariate Wiener process with drift and diffusion parameters estimated from TRC history, including a tamping reset term, while the observation equation is a linear regression of on-board indices on TRC indicators, with noise covariance obtained from concurrent recordings. The filter is restarted at each accurate TRC observation, and the reported credible intervals are mixtures of Gaussians over posterior samples of the degradation parameters. The paper argues that this fusion reduces prediction uncertainty substantially even for noisy signals, with the largest gains on fast-degrading sections, and that the resulting stable credibility zone supports more flexible TRC deployment and earlier detection of geometry deviation.

Load-bearing premise

The central assumption is that the mapping from noisy on-board readings to true track geometry, learned from the same concurrent TRC/on-board recordings used to demonstrate the filter's accuracy, remains representative for future runs, other train speeds, and different operating conditions.

Editorial extensions

If this is right

  • Under fast degradation, weekly on-board updates cut the six-month credible-interval width by 80–90% for Top and 40–60% for Alignment relative to TRC-only predictions.
  • Even four-week sensor intervals reduce long-horizon uncertainty by more than 40% in many cases, so the benefit does not require extremely dense sensor coverage.
  • With on-board data, the credibility zone stabilizes after about two months and stays nearly constant as the horizon extends, whereas the degradation-model-only zone keeps widening.
  • Operators could therefore schedule TRC inspections much less frequently while keeping prediction intervals tight, provided regulations allow the on-board system to support inspection decisions.
  • Because the on-board index vector can differ in nature from the TRC indicators, the same fusion structure can incorporate other low-cost sensor signals as they become available.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the filter is deployed on in-service trains rather than on the TRC, the regression calibration of $\mathbf{H}$, $\mathbf{b}$, and $\mathbf{R}$ would need to be repeated per vehicle class and checked for speed dependence; the paper's absorption of speed effects into $\mathbf{R}$ is a testable assumption, not a demonstrated result.
  • The framework naturally suggests a deployment optimization problem the paper does not solve: given a target credible-interval width, how many sensor-equipped service trains per line are needed, and at what measurement interval, to meet that target at minimum cost.
  • The tight intervals could feed directly into maintenance and inspection planning—for example, by triggering TRC visits only when the fused posterior crosses a threshold—turning the monitoring output into a decision rule for tamping.
  • Because the observation model allows on-board indices to differ in type from the tracked indicators, the same method could be tested with even cheaper proxies such as smartphone accelerometer features or bogie vibration spectra, provided a stable statistical relationship to TRC indicators can be calibrated.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes a Kalman-filter-based framework for fusing sparse, accurate Track Recording Car (TRC) measurements with frequent, noisy on-board sensor signals to track and predict two track geometry indicators (Top and Alignment). The state evolves according to a multivariate Wiener degradation model, with a reset mechanism at tamping events, and the on-board measurements are related to the true geometry through a linear observation model with parameters H, b, and R estimated by multivariate regression. The method is demonstrated on a single TRC instrumented with low-cost MEMS accelerometers, with data from five TRC visits over 34 weeks. The authors further use Monte Carlo simulations to study how measurement frequency affects the width of credible intervals, reporting large reductions (up to 80–90% for Top at a six-month horizon) when frequent on-board data are included.

Significance. If the empirical claims hold, the paper addresses a genuinely practical problem: reducing dependence on expensive, infrequent TRC runs while keeping track-geometry prediction uncertainty within acceptable bounds. The idea of coupling a stochastic degradation model with low-cost sensor streams in a Kalman filter is natural and potentially valuable, and the use of posterior samples of degradation parameters to build a mixture distribution is a reasonable way to propagate parameter uncertainty. However, the central quantitative claims currently rest on an unstated calibration/validation split and on simulations that reuse the fitted observation model, so the significance is conditional on a stronger out-of-sample demonstration.

major comments (4)
  1. [§3.2, §4.1, Table 1] The manuscript never specifies which TRC visits (weeks 0, 11, 19, 27, 34 in Table 1) are used to fit the observation-model parameters H, b, and R in Eqs. (5)–(6) and which are held out for validation in Figure 5. Section 5 states that 'only a portion' of the TRC measurements was used for prediction and the rest for validation, but the paper does not report this split. If the week-27 and week-34 TRC records in Figure 5 are part of the regression set, the agreement shown is in-sample and does not demonstrate predictive skill. The authors should state the exact split, report per-holdout metrics such as RMSE, bias, and coverage, and ideally use a temporal split in which calibration data precede validation data.
  2. [§4.2, Steps 1–3, Table 2] The uncertainty-reduction percentages in Table 2 (e.g., 80–90% for Top at six months under fast degradation) are computed by Monte Carlo simulation that generates geometry paths and sensor observations from the same fitted degradation model and the same fitted observation model (H, b, R) that the Kalman filter later consumes. The reductions are therefore a mathematical consequence of the estimated covariance matrices, not an empirical demonstration with real sensor data in the intended deployment setting of in-service trains at varying speeds. The authors' own caveat at the end of §4.2—that a thorough empirical characterization of the measurement error is required before operational use—should be elevated: Table 2 should be explicitly labeled as a model-based sensitivity analysis, or supplemented with an out-of-sample empirical evaluation.
  3. [§4.1, Figure 5, Table 2] No quantitative validation metrics are provided for Figure 5, so the claim that the filter predictions 'align closely' with actual TRC data rests on visual inspection alone. Moreover, Table 2 reports values in the form [0.540, 1.656] without defining whether these are credible intervals for the indicators or intervals for the scalar width W_k of Eq. (14). The reduction percentages in the text cannot be independently reconstructed from the table as printed. Please define the width statistic, report its distribution (e.g., posterior quantiles), and provide numerical accuracy and coverage metrics for the filter validation.
  4. [§3.2] The observation model is calibrated from data collected with the sensor system mounted on the TRC itself, so both measurement systems operate at the same speed. The intended deployment is on in-service trains whose speeds differ. The paper states that residual speed-dependent effects are absorbed into the noise covariance R, but if speed changes H or b systematically the Kalman filter estimate will be biased and the quoted uncertainty reductions may not transfer. Because the entire uncertainty-reduction claim depends on the correctness of the observation model, this assumption should be presented as a central limitation and, if possible, tested with data collected at different speeds.
minor comments (6)
  1. [Eq. (5)] The text introducing Eq. (5) says Y is a matrix in ℝ^{N×n}, but it should be ℝ^{N×m}; the phrase 'and matrix ℝ^{N×n} of N data tuple' is also grammatically incomplete.
  2. [Eq. (8)] The subscript in 𝚺Δ𝑡𝑖𝑘 appears to be a typo; it should be 𝚺Δ𝑡𝑘 for consistency with the rest of the paper.
  3. [§4.2, Step 3] The symbol o_k is undefined; the prediction step should use the simulated observation y_k generated in Step 2.
  4. [Table 2] Please state explicitly whether the bracketed numbers are 95% credible intervals for the indicators in natural-log units, and clarify how they relate to the scalar width W_k defined in Eq. (14); the current caption says 'Widths' but the entries are intervals.
  5. [Eq. (14)] References [45,46] concern robust principal component analysis and are not an obvious source for the credible-interval width measure; please cite a standard multivariate statistics or Kalman filtering reference, or define W_k as a generalized standard deviation.
  6. [§2.2] The reset of the filter to P_0 = 0 after each TRC observation should be explicitly connected to the assumption that TRC measurements are noiseless; this assumption is central to the restart procedure and should not be implicit.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the sensor-fusion uncertainty reduction follows from the standard Kalman covariance update, the Monte Carlo frequency analysis is a model-based sensitivity study, and the authors explicitly flag the need for empirical error characterization.

full rationale

The derivation chain is not circular. The degradation model (Eqs. 1–2) is adopted from prior work [19] and the observation model (Eqs. 3–6) is estimated by multivariate regression from concurrent TRC and on-board data; neither is defined in terms of the target conclusion. The Kalman filter update (Eqs. 7–12) is a standard linear-Gaussian recursion, and the claim that frequent noisy observations reduce credible-interval width is a direct algebraic property of Eq. (10): each update subtracts a positive semidefinite term KSK^T from the prediction covariance. Thus the qualitative benefit of sensor fusion is a mathematical consequence of the filtering structure, not an input fitted from data. The quantitative reductions in Table 2 come from Monte Carlo simulations in Section 4.2 in which synthetic geometry paths and sensor signals are generated from the fitted degradation model and the fitted H,b,R, then filtered under the same model. That is a self-consistency/sensitivity analysis rather than an independent empirical test; the authors themselves state at the end of Section 4.2 that a thorough empirical characterization of the measurement-system performance and error is required before practical use. The real-data validation in Section 4.1 is supported by the paper's conclusion stating that only a portion of available TRC reference measurements was used, leaving the rest for validation; however, the paper does not detail whether the H,b,R regression in Section 3.2 excluded the validation records. This is a potential validation-leakage risk, not a demonstrated circularity, because the filter's state estimate is not defined by the validation TRC values themselves. The self-citations to [8] and [19] supply sensor-processing and degradation-model inputs, but neither is invoked to assume the fusion result. Overall, the paper's central claim has independent content and no significant circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities, forces, or conserved quantities. The free parameters are the fitted degradation model parameters from prior work and the fitted observation model parameters H, b, R from the current experimental campaign. The central claim depends on the unverified generalization of these calibrated parameters to in-service trains with different operating speeds and on the noiseless-TRC assumption.

free parameters (3)
  • Degradation model parameters (mu, Sigma, z_plus, Sigma_z_plus) = Not reported in this paper; inherited from the authors' prior Bayesian multivariate Wiener model [19]
    The Kalman filter covariance growth and the Monte Carlo credibility intervals depend directly on the drift vector, diffusion matrix, and post-tamping mean and covariance, which were estimated via MCMC in prior work and used as posterior samples here.
  • Observation model parameters H, b, R = Not reported; fitted by multivariate regression in Equations (5) and (6) using concurrent TRC and on-board sensor data
    The Kalman update gain and the resulting uncertainty reduction depend on the measurement sensitivity matrix, bias, and noise covariance. These are fitted to the experimental campaign data, and no numerical values are given in the paper.
  • Degradation scenario labels (fast, typical, slow) in Table 2 = Not reported
    Table 2 reports uncertainty reductions separately for fast, typical, and slow degradation, but the paper does not specify how these scenarios are selected or defined from the posterior distribution, which affects the headline reduction percentages.
assumptions (5)
  • domain assumption TRC measurements are equivalent to direct observations of the true track geometry state.
    Stated in Section 2.2: 'Following the assumption that TRC measurements are equivalent to direct observations of the track geometry, the value of Z_k becomes known when a TRC record is available.' The Kalman filter treats these observations as noiseless and resets the state covariance to zero.
  • domain assumption Degradation increments of the geometry indicators follow a multivariate normal distribution with mean and covariance given by Equation (2), including the mid-interval maintenance model.
    The state transition in the Kalman filter, Equations (7) and (8), is exactly the multivariate Wiener degradation model adapted from the authors' prior work [19]. Its validity is assumed, not demonstrated in this paper.
  • domain assumption On-board sensor indices, conditional on the true TRC indicators, are Gaussian with linear mean H z_k + b and constant covariance R.
    Equations (3) and (4) define the observation model. The paper motivates this with approximate log-normality and reduced heteroscedasticity in log-space, but the constant-covariance linear model is an assumption.
  • domain assumption The observation model parameters H, b, and R estimated from concurrent TRC and on-board sensor data remain valid for other times, track sections, and in-service train operating conditions.
    The calibration is performed on data collected with the sensor system mounted on a TRC, at the same speed as the reference measurements. The paper acknowledges that speed-dependent effects could add variability and states that a systematic investigation is future work.
  • domain assumption The logarithm of the geometry indicators is approximately normally distributed with constant covariance over time.
    The log transform is central to the Gaussian state-space formulation. Section 3.2 argues that marginal and conditional distributions support this approximation, but it remains a statistical modeling assumption.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Sensor Fusion for Track Geometry Monitoring: Integrating On-Board Condition Monitoring and Degradation Models via Kalman Filtering." pith.science (2026). https://pith.science/paper/3L4N5YNU

@misc{pith2026250608028,
  author       = {Pith},
  title        = {Pith review of: Sensor Fusion for Track Geometry Monitoring: Integrating On-Board Condition Monitoring and Degradation Models via Kalman Filtering},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3L4N5YNU}},
  note         = {Machine review of arXiv:2506.08028}
}
read the original abstract

Track geometry monitoring is essential for maintaining the safety and efficiency of railway operations. While Track Recording Cars (TRCs) provide accurate measurements of track geometry indicators, their limited availability and high operational costs restrict frequent monitoring across large rail networks. Recent advancements in on-board sensor systems installed on in-service trains offer a cost-effective alternative by enabling high-frequency, albeit less accurate, data collection. This study proposes a method to enhance the reliability of track geometry predictions by integrating low-accuracy sensor vibration signals with degradation models through a Kalman filter framework. An experimental campaign using a low-cost sensor system mounted on a TRC evaluates the proposed approach. The results demonstrate that incorporating frequent sensor data significantly reduces prediction uncertainty, even when the data is noisy. The study also investigates how the frequency of data recording influences the size of the credible prediction interval, providing guidance on the optimal deployment of on-board sensors for effective track monitoring and maintenance planning.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

46 extracted references · 38 canonical work pages

  1. [1]

    Bridging POMDPs and Bayesian decision making for robust maintenance planning under model uncertainty: An application to railway systems

    Arcieri G, Hoelzl C, Schwery O, Straub D, Papakonstantinou KG, Chatzi E. Bridging POMDPs and Bayesian decision making for robust maintenance planning under model uncertainty: An application to railway systems. Reliability Engineering & System Safety 2023; 239:109496. https://doi.org/10.1016/j.ress.2023.109496

    work page arXiv 2023

  2. [2]

    A stochastic track maintenance scheduling model based on deep reinforcement learning approaches

    Lee JS, Yeo I -H, Bae Y . A stochastic track maintenance scheduling model based on deep reinforcement learning approaches. Reliability Engineering & System Safety 2024;241:109709. https://doi.org/10.1016/j.ress.2023.109709

    work page arXiv 2024

  3. [3]

    Identify severe track geometry defect combinations for maintenance planning

    Wu Q, Azad AK, Cole C, Spiryagin M. Identify severe track geometry defect combinations for maintenance planning. International Journal of Rail Transportation 2022;10:95–113

    work page 2022

  4. [5]

    Intelligent and adaptive asset management model for railway sections using the iPN method

    Saleh A, Remenyte-Prescott R, Prescott D, Chiachío M. Intelligent and adaptive asset management model for railway sections using the iPN method. Reliability Engineering & System Safety 2024;241:109687. https://doi.org/10.1016/j.ress.2023.109687

    work page arXiv 2024

  5. [6]

    Track geometry degradation and maintenance modelling: A review

    Soleimanmeigouni I, Ahmadi A, Kumar U. Track geometry degradation and maintenance modelling: A review. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 2018;232:73–102

    work page 2018

  6. [7]

    Position synchronization for track geometry inspection data via big-data fusion and incremental learning

    Wang Y , Wang P , Wang X, Liu X. Position synchronization for track geometry inspection data via big-data fusion and incremental learning. Transportation Research Part C: Emerging Technologies 2018;93:544–65. https://doi.org/10.1016/j.trc.2018.06.018

    work page doi:10.1016/j.trc.2018.06.018 2018

  7. [8]

    Evaluation of onboard sensors for track geometry monitoring against conventional track recording measurements

    Zhang H, Chin ZY , Borghesani P , Pitt J, Cholette ME. Evaluation of onboard sensors for track geometry monitoring against conventional track recording measurements. Measurement 2024;229:114354. https://doi.org/10.1016/j.measurement.2024.114354

    work page arXiv 2024

  8. [9]

    Peinado Gonzalo, R

    A. Peinado Gonzalo, R. Horridge, H. Steele, E. Stewart, M. Entezami. Review of Data Analytics for Condition Monitoring of Railway Track Geometry. IEEE Transactions on Intelligent Transportation Systems 2022;23:22737–54. https://doi.org/10.1109/TITS.2022.3214121

    arXiv 2022

Show all 46 references
  1. [10]

    Railway Track Geometry Degradation Modelling and Prediction for Maintenance Decision Support

    Rebello S, Cholette ME, Truong -Ba H, Reddy V, Rosser A, Watkin T. Railway Track Geometry Degradation Modelling and Prediction for Maintenance Decision Support. In: Pinto JOP , Kimpara MLM, Reis RR, Seecharan T, Upadhyaya BR, Amadi-Echendu J, editors. 15th WCEAM Proceedings, C...

    2022 doi

  2. [11]

    An adaptive opportunistic maintenance model based on railway track condition prediction

    Letot C, Soleimanmeigouni I, Ahmadi A, Dehombreux P . An adaptive opportunistic maintenance model based on railway track condition prediction. IFAC -PapersOnLine 2016;49:120 –5. https://doi.org/10.1016/j.ifacol.2016.11.021

    2016 doi

  3. [12]

    Particle filter -based prognostic approach for railway track geometry

    Mishra M, Odelius J, Thaduri A, Nissen A, Rantatalo M. Particle filter -based prognostic approach for railway track geometry. Mechanical Systems and Signal Processing 2017;96:226–38

    2017

  4. [13]

    Data-driven optimization of railway maintenance for track geometry

    Sharma S, Cui Y , He Q, Mohammadi R, Li Z. Data-driven optimization of railway maintenance for track geometry. Transportation Research Part C: Emerging Technologies 2018;90:34 –58. https://doi.org/10.1016/j.trc.2018.02.019

    2018 doi

  5. [14]

    Modelling the evolution of ballasted railway track geometry by a two -level piecewise model

    Soleimanmeigouni I, Xiao X, Ahmadi A, Xie M, Nissen A, Kumar U. Modelling the evolution of ballasted railway track geometry by a two -level piecewise model. Structure and Infrastructure Engineering 2018;14:33–45. https://doi.org/10.1080/15732479.2017.1326946. 21

    2018

  6. [15]

    Lurdes S

    Vale C, M. Lurdes S. Stochastic model for the geometrical rail track degradation process in the Portuguese railway Northern Line. Reliability Engineering & System Safety 2013;116:91 –8. https://doi.org/10.1016/j.ress.2013.02.010

    2013 doi

  7. [16]

    Bivariate Gamma wear processes for track geometry modelling, with application to intervention scheduling

    Mercier S, Meier-Hirmer C, Roussignol M. Bivariate Gamma wear processes for track geometry modelling, with application to intervention scheduling. Structure and Infrastructure Engineering 2012;8:357–66

    2012

  8. [17]

    Prediction of railway track geometry defects: a case study

    Soleimanmeigouni I, Ahmadi A, Nissen A, Xiao X. Prediction of railway track geometry defects: a case study. Structure and Infrastructure Engineering 2020;16:987 –1001. https://doi.org/10.1080/15732479.2019.1679193

    2020

  9. [18]

    Principal components analysis and track quality index: A machine learning approach

    Lasisi A, Attoh-Okine N. Principal components analysis and track quality index: A machine learning approach. Transportation Research Part C: Emerging Technologies 2018;91:230 –48. https://doi.org/10.1016/j.trc.2018.04.001

    2018 doi

  10. [19]

    Bayesian multivariate track geometry degradation modeling and its use in condition -based inspection

    Truong-Ba H, Rebello S, Cholette ME, Reddy V, Borghesani P . Bayesian multivariate track geometry degradation modeling and its use in condition -based inspection. Railway Engineering Science

  11. [20]

    Estimation of railway track longitudinal irregularity using vehicle response with information compression and Bayesian deep learning

    Li C, He Q, Wang P . Estimation of railway track longitudinal irregularity using vehicle response with information compression and Bayesian deep learning. Computer -Aided Civil and Infrastructure Engineering 2022;37:1260–76. https://doi.org/10.1111/mice.12802

    2022 doi

  12. [21]

    Perspectives on railway track geometry condition monitoring from in-service railway vehicles

    Weston P , Roberts C, Yeo G, Stewart E. Perspectives on railway track geometry condition monitoring from in-service railway vehicles. Vehicle System Dynamics 2015;53:1063–91

    2015

  13. [22]

    Condition monitoring of vertical track alignment by bogie acceleration measurements on commercial high-speed vehicles

    La Paglia I, Carnevale M, Corradi R, Di Gialleonardo E, Facchinetti A, Lisi S. Condition monitoring of vertical track alignment by bogie acceleration measurements on commercial high-speed vehicles. Mechanical Systems and Signal Processing 2023;186:109869. https://doi.org/10.10...

    2023

  14. [23]

    Condition monitoring of railway track from car-body vibration using time– frequency analysis

    Tsunashima H, Hirose R. Condition monitoring of railway track from car-body vibration using time– frequency analysis. Vehicle System Dynamics 2022;60:1170 –87. https://doi.org/10.1080/00423114.2020.1850808

    2022

  15. [24]

    Track-monitoring from the dynamic response of an operational train

    Lederman G, Chen S, Garrett J, Kovačević J, Noh HY , Bielak J. Track-monitoring from the dynamic response of an operational train. Mechanical Systems and Signal Processing 2017;87:1 –16. https://doi.org/10.1016/j.ymssp.2016.06.041

    2017 doi

  16. [25]

    Perspectives of assessing the geometric condition of railway tracks using a device for measuring the topographic profile

    Pereira P , Ribeiro F, Motta R, Neto AG, Bernucci L, Júnior EF, et al. Perspectives of assessing the geometric condition of railway tracks using a device for measuring the topographic profile. Measurement 2025;249:117020. https://doi.org/10.1016/j.measurement.2025.117020

    2025

  17. [26]

    Track geometry monitoring by an on -board computer -vision-based sensor system

    Circelli M, Kaviani N, Licciardello R, Ricci S, Rizzetto L, Arabani SS, et al. Track geometry monitoring by an on -board computer -vision-based sensor system. Transportation Research Procedia 2023;69:257–64. https://doi.org/10.1016/j.trpro.2023.02.170

    2023 doi

  18. [27]

    Olivier, F

    B. Olivier, F. Guo, Y . Qian, D. P . Connolly. A Review of Computer Vision for Railways. IEEE Transactions on Intelligent Transportation Systems 2025;26:11034 –65. https://doi.org/10.1109/TITS.2025.3552011

    2025

  19. [28]

    Estimation of lateral track irregularity through Kalman filtering techniques

    Muñoz S, Ros J, Urda P , Escalona JL. Estimation of lateral track irregularity through Kalman filtering techniques. IEEE Access 2021;9:60010–25

    2021

  20. [29]

    Experimental measurement of track irregularities using a scaled track recording vehicle and Kalman filtering techniques

    Muñoz S, Urda P , Escalona JL. Experimental measurement of track irregularities using a scaled track recording vehicle and Kalman filtering techniques. Mechanical Systems and Signal Processing 2022;169:108625

    2022

  21. [30]

    Estimation of lateral and cross alignment in a railway track based on vehicle dynamics measurements

    De Rosa A, Alfi S, Bruni S. Estimation of lateral and cross alignment in a railway track based on vehicle dynamics measurements. Mechanical Systems and Signal Processing 2019;116:606 –23. https://doi.org/10.1016/j.ymssp.2018.06.041

    2019 doi

  22. [31]

    Kinematic modeling of a track geometry using an unscented Kalman filter

    Lee JS, Choi IY , Kim S, Moon DS. Kinematic modeling of a track geometry using an unscented Kalman filter. Measurement 2016;94:707–16. 22

    2016

  23. [32]

    A Bayesian Kalman filter algorithm for quantifying estimation uncertainty of track irregularity on bridges with randomness in system parameters

    Xiao X, Xu X -Y , Zhu Q, Ren W-X. A Bayesian Kalman filter algorithm for quantifying estimation uncertainty of track irregularity on bridges with randomness in system parameters. Mechanical Systems and Signal Processing 2024;209:111097

    2024

  24. [33]

    Chapter 9 - On-board monitoring for smart assessment of railway infrastructure: A systematic review

    Hoelzl C, Dertimanis V, Landgraf M, Ancu L, Zurkirchen M, Chatzi E. Chapter 9 - On-board monitoring for smart assessment of railway infrastructure: A systematic review. In: Alavi AH, Feng MQ, Jiao P , Sharif-Khodaei Z, editors. The Rise of Smart Cities, Bu tterworth-Heinemann;...

    2022 doi

  25. [34]

    Smartphone’s Sensing Capabilities for On -Board Railway Track Monitoring: Structural Performance and Geometrical Degradation Assessment

    Paixão A, Fortunato E, Calçada R. Smartphone’s Sensing Capabilities for On -Board Railway Track Monitoring: Structural Performance and Geometrical Degradation Assessment. Advances in Civil Engineering 2019;2019:1729153. https://doi.org/10.1155/2019/1729153

    2019 doi

  26. [35]

    Advances in Collaborative Filtering

    Koren Y , Rendle S, Bell R. Advances in Collaborative Filtering. In: Ricci F, Rokach L, Shapira B, editors. Recommender Systems Handbook, New York, NY: Springer US; 2022, p. 91 –142. https://doi.org/10.1007/978-1-0716-2197-4_3

    2022 doi

  27. [36]

    A Review on Kalman Filter Models

    Khodarahmi M, Maihami V. A Review on Kalman Filter Models. Archives of Computational Methods in Engineering 2023;30:727–47. https://doi.org/10.1007/s11831-022-09815-7

    2023 doi

  28. [37]

    Robust Kalman filtering for uncertain discrete -time systems

    Xie L, Soh YC. Robust Kalman filtering for uncertain discrete -time systems. IEEE Transactions on Automatic Control 1994;39:1310–4

    1994

  29. [38]

    Interacting multiple model estimation-based adaptive robust unscented Kalman filter

    Gao B, Gao S, Zhong Y , Hu G, Gu C. Interacting multiple model estimation-based adaptive robust unscented Kalman filter. International Journal of Control, Automation and Systems 2017;15:2013– 25

    2017

  30. [39]

    Cubature kalman filters

    Arasaratnam I, Haykin S. Cubature kalman filters. IEEE Transactions on Automatic Control 2009;54:1254–69

    2009

  31. [40]

    Probabilistic Kalman filter for moving object tracking

    Farahi F, Yazdi HS. Probabilistic Kalman filter for moving object tracking. Signal Processing: Image Communication 2020;82:115751

    2020

  32. [41]

    Nonlinear predictive controllers for continuous systems

    Lu P . Nonlinear predictive controllers for continuous systems. Journal of Guidance, Control, and Dynamics 1994;17:553–60

    1994

  33. [42]

    Robust filtering

    Calvet LE, Czellar V, Ronchetti E. Robust filtering. Journal of the American Statistical Association 2015;110:1591–606

    2015

  34. [43]

    Particle filter -based prognostics: Review, discussion and perspectives

    Jouin M, Gouriveau R, Hissel D, Péra M -C, Zerhouni N. Particle filter -based prognostics: Review, discussion and perspectives. Mechanical Systems and Signal Processing 2016;72 –73:2–31. https://doi.org/10.1016/j.ymssp.2015.11.008

    2016 doi

  35. [44]

    Gustafsson

    F. Gustafsson. Particle filter theory and practice with positioning applications. IEEE Aerospace and Electronic Systems Magazine 2010;25:53–82. https://doi.org/10.1109/MAES.2010.5546308

    2010

  36. [45]

    Principal Components Analysis Based on Multivariate MM Estimators With Fast and Robust Bootstrap

    Salibián-Barrera M, Van Aelst S, Willems G. Principal Components Analysis Based on Multivariate MM Estimators With Fast and Robust Bootstrap. Journal of the American Statistical Association 2006;101:1198–211. https://doi.org/10.1198/016214506000000096

    2006 doi

  37. [46]

    Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices

    Taskinen S, Croux C, Kankainen A, Ollila E, Oja H. Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices. Journal of Multivariate Analysis 2006;97:359–84. https://doi.org/10.1016/j.jmva.2005.03.005

    2006 doi

  38. [2025]

    https://doi.org/10.1007/s40534-025-00394-4

    doi

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.