Despite the advances in mobile robotics, the introduction of autonomous robots in human-populated environments is rather slow. One of the fundamental reasons is the acceptance of robots by people directly affected by a robot's presence. Understanding human behavior and dynamics is essential for planning when and how robots should traverse busy environments without disrupting people's natural motion and causing irritation. Research has exploited various techniques to build spatio-temporal representations of people's presence and flows and compared their applicability to plan optimal paths in the future. Many comparisons of how dynamic map-building techniques show how one method compares on a dataset versus another, but without consistent datasets and high-quality comparison metrics, it is difficult to assess how these various methods compare as a whole and in specific tasks. This article proposes a methodology for creating high-quality criteria with interpretable results for comparing long-term spatio-temporal representations for human-aware path planning and human-aware navigation scheduling. Two criteria derived from the methodology are then applied to compare the representations built by the techniques found in the literature. The approaches are compared on a real-world, long-term dataset, and the conception is validated in a field experiment on a robotic platform deployed in a human-populated environment. Our results indicate that continuous spatio-temporal methods independently modeling spatial and temporal phenomena outperformed other modeling approaches. Our results provide a baseline for future work to compare a wide range of methods employed for long-term navigation and provide researchers with an understanding of how these various methods compare in various scenarios.

CIAD UMR 7533 Univ Bourgogne Franche Comté UTBM Montbéliard France

Laboratory of Chronorobotics Artificial Intelligence Center Department of Computer Science Faculty of Electrical Engineering Czech Technical University Prague Prague Czech Republic

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Ak Ç., Ergönül Ö., Şencan İ., Torunoğlu M. A., Gönen M. (2018). Spatiotemporal Prediction of Infectious Diseases Using Structured Gaussian Processes with Application to Crimean-Congo Hemorrhagic Fever. PLoS Negl. Trop. Dis. 12, e0006737. 10.1371/journal.pntd.0006737 PubMed DOI PMC

Bayisa F. L., Ådahl M., Rydén P., Cronie O. (2020). Large-scale Modelling and Forecasting of Ambulance Calls in Northern sweden Using Spatio-Temporal Log-Gaussian Cox Processes. Spat. Stat. 39, 100471. 10.1016/j.spasta.2020.100471 DOI

Blaha J. (2020). Inferring Temporal Models of People Presence from Environment Structrure. Praha: České vysoké učení technické v Praze. Vypočetní a informační centrum. B.S. thesis.

Blanke U., Schiele B. (2009). “Daily Routine Recognition through Activity Spotting,” in International Symposium on Location-and Context-Awareness, 192–206. 10.1007/978-3-642-01721-6_12 DOI

Bravais A. (1844). Analyse mathématique sur les probabilités des erreurs de situation d’un point (Impr. Royale).

Cadena C., Carlone L., Carrillo H., Latif Y., Scaramuzza D., Neira J. (2016). Past, Present, and Future of Simultaneous Localization and Mapping: Toward the Robust-Perception Age. IEEE Trans. robotics 32, 1309–1332. 10.1109/tro.2016.2624754 DOI

Calderita L., Vega A., Bustos P., Núñez P. (2021). A New Human-Aware Robot Navigation Framework Based on Time-dependent Social Interaction Spaces: An Application to Assistive Robots in Caregiving Centers. Robotics Aut. Syst. 145, 103873. 10.1016/j.robot.2021.103873 DOI

Chinellato E., Mardia K. V., Hogg D. C., Cohn A. G. (2017). “An incremental von mises mixture framework for modelling human activity streaming data,” in Proceedings ITISE 2017.

Cliff A. D., Ord J. K. (1975). Model Building and the Analysis of Spatial Pattern in Human Geography. J. R. Stat. Soc. Ser. B Methodol. 37, 297–348. 10.1111/j.2517-6161.1975.tb01548.x DOI

Coşar S., Fernandez-Carmona M., Agrigoroaie R., Pages J., Ferland F., Zhao F., et al. (2020). Enrichme: Perception and Interaction of an Assistive Robot for the Elderly at Home. Int. J. Soc. Robotics 12, 779–805.

Dempster A. P., Laird N. M., Rubin D. B. (1977). Maximum Likelihood from Incomplete Data via the Em Algorithm. J. R. Stat. Soc. Ser. B Methodol. 39, 1–22. 10.1111/j.2517-6161.1977.tb01600.x DOI

Dodge Y. (2008). The Concise Encyclopedia of Statistics. Springer Science & Business Media. chap. Chi-Square Distance.

Dunning T. (2012). Natural Experiments in the Social Sciences: A Design-Based Approach. Cambridge University Press.

Elfes A. (1989). Using Occupancy Grids for Mobile Robot Perception and Navigation. Computer 22, 46–57. 10.1109/2.30720 DOI

Fentanes J. P., Lacerda B., Krajník T., Hawes N., Hanheide M. (2015). “Now or Later? Predicting and Maximising Success of Navigation Actions from Long-Term Experience,” in 2015 IEEE international conference on robotics and automation (ICRA) (IEEE) (IEEE; ), 1112–1117.

Garrido Mejía S. H. (2018). Predicting Crime in Bogota Using Kernel Warping. Uniandes. Master’s thesis.

Gilardi A., Borgoni R., Mateu J. (2021). A Spatio-Temporal Model for Events on Road Networks: an Application to Ambulance Interventions in Milan. Pref. XIX 1 Plenary Sess., 702. 10.48550/arXiv.2106.00457 DOI

Guizilini V. C., Ramos F. T. (2015). A Nonparametric Online Model for Air Quality Prediction. Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence. 651–657.

Hanheide M., Hebesberger D., Krajník T. (2017). “The when, where, and How: An Adaptive Robotic Info-Terminal for Care Home Residents,” in Proceedings of the 2017 ACM/IEEE International Conference on Human-Robot Interaction (ACM), 341–349.

Hanley J. A., McNeil B. J. (1982). The Meaning and Use of the Area under a Receiver Operating Characteristic (Roc) Curve. Radiology 143, 29–36. 10.1148/radiology.143.1.7063747 PubMed DOI

Hawes N., Burbridge C., Jovan F., Kunze L., Lacerda B., Mudrova L., et al. (2017). The Strands Project: Long-Term Autonomy in Everyday Environments. IEEE Robotics Automation Mag. 24, 146–156. 10.1109/mra.2016.2636359 DOI

Hebesberger D., Koertner T., Gisinger C., Pripfl J. (2017). A Long-Term Autonomous Robot at a Care Hospital: A Mixed Methods Study on Social Acceptance and Experiences of Staff and Older Adults. Int. J. Soc. Robotics 9, 417–429. 10.1007/s12369-016-0391-6 DOI

Hernandez Bennetts V., Kamarudin K., Wiedemann T., Kucner T. P., Somisetty S. L., Lilienthal A. J. (2019). Multi-domain Airflow Modeling and Ventilation Characterization Using Mobile Robots, Stationary Sensors and Machine Learning. Sensors (Basel) 19. 10.3390/s19051119 PubMed DOI PMC

Jovan F., Wyatt J., Hawes N., Krajník T. (2016). “A Poisson-Spectral Model for Modelling Temporal Patterns in Human Data Observed by a Robot,” in 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE; ), 4013–4018. 10.1109/iros.2016.7759591 DOI

Ko I., Kim B., Park F. C. (2014). Randomized Path Planning on Vector Fields. Int. J. Robotics Res. 33, 1664–1682. 10.1177/0278364914545812 DOI

Kollmitz M., Hsiao K., Gaa J., Burgard W. (2015). “Time Dependent Planning on a Layered Social Cost Map for Human-Aware Robot Navigation,” in 2015 European Conference on Mobile Robots (ECMR) (IEEE; ), 1–6. 10.1109/ecmr.2015.7324184 DOI

Kostavelis I., Kargakos A., Giakoumis D., Tzovaras D. (2017). “Robot’s Workspace Enhancement with Dynamic Human Presence for Socially-Aware Navigation,” in international conference on computer vision systems (Springer; ), 279–288. 10.1007/978-3-319-68345-4_25 DOI

Krajnik T., Fentanes J. P., Cielniak G., Dondrup C., Duckett T. (2014b). “Spectral Analysis for Long-Term Robotic Mapping,” in 2014 IEEE International Conference on Robotics and Automation (ICRA) (IEEE; ), 3706–3711. 10.1109/icra.2014.6907396 DOI

Krajník T., Fentanes J. P., Mozos O. M., Duckett T., Ekekrantz J., Hanheide M. (2014c). “Long-term Topological Localisation for Service Robots in Dynamic Environments Using Spectral Maps,” in 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE; ), 4537–4542. 10.1109/iros.2014.6943205 DOI

Krajník T., Fentanes J. P., Santos J. M., Duckett T. (2017). Fremen: Frequency Map Enhancement for Long-Term Mobile Robot Autonomy in Changing Environments. IEEE Trans. Robotics 33, 964–977. 10.1109/tro.2017.2665664 DOI

Krajník T., Kulich M., Mudrová L., Ambrus R., Duckett T. (2015a). “Where’s Waldo at Time T? Using Spatio-Temporal Models for Mobile Robot Search,” in 2015 IEEE International Conference on Robotics and Automation (ICRA) (IEEE) (IEEE; ), 2140–2146.

Krajník T., Santos J. M., Duckett T. (2015b). “Life-long Spatio-Temporal Exploration of Dynamic Environments,” in 2015 European Conference on Mobile Robots (ECMR) (IEEE; ), 1–8. 10.1109/ecmr.2015.7324052 DOI

Krajnik T., Santos J., Seemann B., Duckett T. (2014a). Froctomap: An Efficient Spatio-Temporal Environment Representation. Adv. Aut. Robotics Syst. 269. 10.1007/978-3-319-10401-0 DOI

Krajník T., Vintr T., Broughton G., Majer F., Rouček T., Ulrich J., et al. (2020). “Chronorobotics: Representing the Structure of Time for Service Robots,” in Proceedings of the 2020 4th International Symposium on Computer Science and Intelligent Control, 1–8.

Krajník T., Vintr T., Molina S., Fentanes J. P., Cielniak G., Mozos O. M., et al. (2019). Warped Hypertime Representations for Long-Term Autonomy of Mobile Robots. IEEE Robotics Automation Lett. 4, 3310–3317. 10.1109/lra.2019.2926682 DOI

Kubiš F. (2020). Application Of Spatiotemporal Modeling Used In Robotics For Demand Forecast. Praha: České vysoké učení technické v Praze. Vypočetní a informační centrum. B.S. thesis.

Kucner T., Magnusson M., Schaffernicht E., Hernandez Bennetts V., Lilienthal A. (2016). “Tell Me about Dynamics!: Mapping Velocity Fields from Sparse Samples with Semi-wrapped Gaussian Mixture Models,” in Robotics: Science and Systems Conference (RSS 2016), Workshop: Geometry and Beyond-Representations, Physics, and Scene Understanding for Robotics, Ann Arbor, Ml, USA, June 18-22, 2016 (Ann Arbor, MI: University of Michigan; ).

Kucner T. P., Magnusson M., Schaffernicht E., Bennetts V. H., Lilienthal A. J. (2017). Enabling Flow Awareness for Mobile Robots in Partially Observable Environments. IEEE Robotics Automation Lett. 2, 1093–1100. 10.1109/lra.2017.2660060 DOI

Kucner T., Saarinen J., Magnusson M., Lilienthal A. J. (2013). “Conditional Transition Maps: Learning Motion Patterns in Dynamic Environments,” in Intelligent Robots and Systems (IROS), 2013 IEEE/RSJ International Conference on (IEEE; ), 1196–1201. 10.1109/iros.2013.6696502 DOI

Kulich M., Krajník T., Přeučil L., Duckett T. (2016). “To Explore or to Exploit? Learning Humans’ Behaviour to Maximize Interactions with Them,” in International Workshop on Modelling and Simulation for Autonomous Systems (Springer; ), 48–63. 10.1007/978-3-319-47605-6_5 DOI

Kunze L., Hawes N., Duckett T., Hanheide M., Krajník T. (2018). Artificial Intelligence for Long-Term Robot Autonomy: A Survey. IEEE Robotics Automation Lett. 3, 4023–4030. 10.1109/lra.2018.2860628 DOI

Laboratory of Chronorobotics (2019). Kdynakoupit. Availableat: https://kdynakoupit.cz/ (Accessed 02 02, 2022).

Leonard M. (2020).

Massey E. O. (2019). Comparative Analysis of Techniques for Spatio-Temporal World Modeling. Sankt Augustin: Hochschule Bonn-Rhein-Sieg.

McCalman L., O’Callaghan S., Ramos F. (2013). “Multi-modal Estimation with Kernel Embeddings for Learning Motion Models,” in 2013 Ieee International Conference On Robotics And Automation (Icra), 2845–2852. 10.1109/icra.2013.6630971 DOI

Molina S., Cielniak G., Duckett T. (2019). “Go with the Flow: Exploration and Mapping of Pedestrian Flow Patterns from Partial Observations,” in 2019 International Conference on Robotics and Automation (ICRA) (IEEE; ), 9725–9731. 10.1109/icra.2019.8794434 DOI

Molina S., Cielniak G., Krajník T., Duckett T. (2018). “Modelling and Predicting Rhythmic Flow Patterns in Dynamic Environments,” in Annual Conference Towards Autonomous Robotic Systems (Springer; ), 135–146. 10.1007/978-3-319-96728-8_12 DOI

Nardi L., Stachniss C. (2020). “Long-term Robot Navigation in Indoor Environments Estimating Patterns in Traversability Changes,” in 2020 IEEE International Conference on Robotics and Automation (ICRA) (IEEE; ), 300–306. 10.1109/icra40945.2020.9197078 DOI

Neubert P., Sünderhauf N., Protzel P. (2013). “Appearance Change Prediction for Long-Term Navigation across Seasons,” in 2013 European Conference on Mobile Robots (IEEE; ), 198–203. 10.1109/ecmr.2013.6698842 DOI

Nilsang S., Yuangyai C. (2021). “Activity Detection for Multi-Factors of Ambulance Demand Areas: A Case Study in Bangkok,” in AIP Conference Proceedings (Sankt Augustin: Melville: AIP Publishing LLC; ), 020001. 10.1063/5.0063773 DOI

Nishio T., Niitsuma M. (2019). “Environmental Map Building to Describe Walking Dynamics for Determination of Spatial Feature of Walking Activity,” in 2019 IEEE 28th international symposium on industrial electronics (ISIE) (IEEE; ), 2315–2320. 10.1109/isie.2019.8781155 DOI

O’Callaghan S. T., Ramos F. T. (2012). Gaussian Process Occupancy Maps. Int. J. Robotics Res. 31, 42–62.

O’Callaghan S. T., Singh S. P. N., Alempijevic A., Ramos F. T. (2011). “Learning Navigational Maps by Observing Human Motion Patterns,” in 2011 Ieee International Conference On Robotics And Automation (Icra).

Okal B., Arras K. O. (2016). “Learning Socially Normative Robot Navigation Behaviors with Bayesian Inverse Reinforcement Learning,” in 2016 IEEE International Conference on Robotics and Automation (ICRA) (IEEE; ), 2889–2895. 10.1109/icra.2016.7487452 DOI

Pabón J. S. M., Rubio M. D., Castaño Y., Riascos A. J., Díaz P. R. (2020). “A Manifold Learning Data Enrichment Methodology for Homicide Prediction,” in 2020 7th International Conference on Behavioural and Social Computing (BESC) (IEEE; ), 1–4. 10.1109/besc51023.2020.9348295 DOI

Palmieri L., Andrey R., Mainprice J., Hanheide M., Alahi A., Lilienthal A., et al. (2021). Guest Editorial: Introduction to the Special Issue on Long-Term Human Motion Prediction. IEEE Robotics Automation Lett. 6, 5613–5617. 10.1109/lra.2021.3077964 DOI

Palmieri L., Kucner T. P., Magnusson M., Lilienthal A. J., Arras K. O. (2017). “Kinodynamic Motion Planning on Gaussian Mixture Fields,” in 2017 IEEE International Conference on Robotics and Automation (ICRA) (IEEE; ), 6176–6181. 10.1109/icra.2017.7989731 DOI

Quigley M., Conley K., Gerkey B. P., Faust J., Foote T., Leibs J., et al. (2009). “ROS: an Open-Source Robot Operating System,” in ICRA Workshop on Open Source Software.

Ramos F., Ott L. (2016). Hilbert Maps: Scalable Continuous Occupancy Mapping with Stochastic Gradient Descent. Int. J. Robotics Res. 35, 1717–1730. 10.1177/0278364916684382 DOI

Ravankar A., Ravankar A. A., Hoshino Y., Watanabe M., Kobayashi Y. (2020). Safe Mobile Robot Navigation in Human-Centered Environments Using a Heat Map-Based Path Planner. Artif. Life Robotics 25, 264–272. 10.1007/s10015-020-00591-w DOI

Rektoris M. (2021). Anomaly Detection In Periodic Stochastic Phenomena. B.S. thesis. Praha: České vysoké učení technické v Praze. Vypočetní a informační centrum.

Roy A., Parui S. K., Roy U. (2012). A Mixture Model of Circular-Linear Distributions for Color Image Segmentation. Int. J. Comput. Appl. 58. 10.5120/9308-3539 DOI

Rudenko A., Palmieri L., Herman M., Kitani K. M., Gavrila D. M., Arras K. O. (2020). Human Motion Trajectory Prediction: A Survey. Int. J. Robotics Res. 39, 895–935. 10.1177/0278364920917446 DOI

Santos J. M., Krajník T., Duckett T. (2017). Spatio-temporal Exploration Strategies for Long-Term Autonomy of Mobile Robots. Robotics Aut. Syst. 88, 116–126. 10.1016/j.robot.2016.11.016 DOI

Santos J. M., Krajník T., Fentanes J. P., Duckett T. (2016). Lifelong Information-Driven Exploration to Complete and Refine 4-d Spatio-Temporal Maps. IEEE Robotics Automation Lett. 1, 684–691. 10.1109/lra.2016.2516594 DOI

Senanayake R., Hatch K. B., Zheng J., Kochenderfer M. J. (2021). 3d Radar Velocity Maps for Uncertain Dynamic Environments.

Senanayake R., Ramos F. (2017). “Bayesian Hilbert Maps for Dynamic Continuous Occupancy Mapping,” in Conference on Robot Learning, 458–471.

Senanayake R., Ramos F. (2018). “Directional Grid Maps: Modeling Multimodal Angular Uncertainty in Dynamic Environments,” in 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE; ), 3241–3248. 10.1109/iros.2018.8594041 DOI

Senanayake R., Simon Timothy O., Ramos F. (2016). Predicting Spatio-Temporal Propagation of Seasonal Influenza Using Variational Gaussian Process Regression. AAAI, 3901–3907.

Senanayake R., Toyungyernsub M., Wang M., Kochenderfer M. J., Schwager M. (2020). “Directional Primitives for Uncertainty-Aware Motion Estimation in Urban Environments,” in 2020 IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC) (IEEE; ), 1–6. 10.1109/itsc45102.2020.9294288 DOI

Shi X., Yeung D.-Y. (2018). Machine Learning for Spatiotemporal Sequence Forecasting: A Survey.

Stuede M., Schappler M. (2022). Non-parametric Modeling of Spatio-Temporal Human Activity Based on Mobile Robot Observations.

Surma F., Kucner T. P., Mansouri M. (2021). “Multiple Robots Avoid Humans to Get the Jobs Done: An Approach to Human-Aware Task Allocation,” in 2021 European Conference on Mobile Robots (ECMR) (IEEE; ), 1–6. 10.1109/ecmr50962.2021.9568843 DOI

Swaminathan C. S., Kucner T. P., Magnusson M., Palmieri L., Lilienthal A. J. (2018). Down the Cliff: Flow-Aware Trajectory Planning under Motion Pattern Uncertainty. 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 7403–7409. 10.1109/iros.2018.8593905 DOI

Talebpour Z., Navarro I., Martinoli A. (2015). “On-board Human-Aware Navigation for Indoor Resource-Constrained Robots: A Case-Study with the Ranger,” in 2015 IEEE/SICE International Symposium on System Integration (SII) (IEEE; ), 63–68. 10.1109/sii.2015.7404955 DOI

Taylor S. J., Letham B. (2018). Forecasting at Scale. Am. Statistician 72, 37–45. 10.1080/00031305.2017.1380080 DOI

Tipaldi G. D., Meyer-Delius D., Burgard W. (2013). Lifelong Localization in Changing Environments. Int. J. Robotics Res. 32, 1662–1678. 10.1177/0278364913502830 DOI

Tompkins A., Ramos F. (2018). “Fourier Feature Approximations for Periodic Kernels in Time-Series Modelling,” in AAAI Conference on Artificial Intelligence.

Tompkins A., Ramos F. (2020). “Periodic Kernel Approximation by Index Set Fourier Series Features,” in

Triebel R., Arras K., Alami R., Beyer L., Breuers S., Chatila R., et al. (2016). “Spencer: A Socially Aware Service Robot for Passenger Guidance and Help in Busy Airports,” in Field and Service Robotics (Springer; ), 607–622. 10.1007/978-3-319-27702-8_40 DOI

Van Laerhoven K., Kilian D., Schiele B. (2008). “Using Rhythm Awareness in Long-Term Activity Recognition,” in 12th IEEE International Symposium on Wearable Computers(ISWC) (IEEE; ), 63–66. 10.1109/iswc.2008.4911586 DOI

Vintr T., Eyisoy K., Vintrová V., Yan Z., Ruichek Y., Krajník T. (2018). “Spatiotemporal Models of Human Activity for Robotic Patrolling,” in International Conference on Modelling and Simulation for Autonomous Systesm (Springer; ), 54–64.

Vintr T., Molina Mellado S., Cielniak G., Duckett T., Krajnik T. (2017). Spatiotemporal Models for Motion Planning in Human Populated Environments. lincol.ac.uk.

Vintr T., Molina S., Senanayake R., Broughton G., Yan Z., Ulrich J., et al. (2019a). “Time-varying Pedestrian Flow Models for Service Robots,” in 2019 European Conference on Mobile Robots (ECMR) (IEEE; ), 1–7. 10.1109/ecmr.2019.8870909 DOI

Vintr T., Yan Z., Duckett T., Krajník T. (2019b). “Spatio-temporal Representation for Long-Term Anticipation of Human Presence in Service Robotics,” in 2019 International Conference on Robotics and Automation (ICRA) (IEEE; ), 2620–2626. 10.1109/icra.2019.8793534 DOI

Vintr T., Yan Z., Eyisoy K., Kubiš F., Blaha J., Ulrich J., et al. (2020). “Natural Criteria for Comparison of Pedestrian Flow Forecasting Models,” in 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE; ), 11197–11204. 10.1109/iros45743.2020.9341672 DOI

Wang Z., Ambrus R., Jensfelt P., Folkesson J. (2014). “Modeling Motion Patterns of Dynamic Objectsby Iohmm,” in 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2014), Chicago, IL, 14-18 Sept. 2014 (IEEE conference proceedings; ), 1832–1838. 10.1109/iros.2014.6942803 DOI

Wang Z., Bovik A. C. (2009). Mean Squared Error: Love it or Leave it? a New Look at Signal Fidelity Measures. IEEE signal Process. Mag. 26, 98–117. 10.1109/msp.2008.930649 DOI

Yamamoto T., Terada K., Ochiai A., Saito F., Asahara Y., Murase K. (2019). Development of Human Support Robot as the Research Platform of a Domestic Mobile Manipulator. ROBOMECH J. 6. 10.1186/s40648-019-0132-3 DOI

Yan H., Zhang Z., Zou J. (2017). “An Online Spatio-Temporal Model for Inference and Predictions of Taxi Demand,” in 2017 IEEE International Conference on Big Data (Big Data) (IEEE; ), 3550–3557. 10.1109/bigdata.2017.8258345 DOI

Zhang H., Zheng Z. (2020). “Simulating Nonstationary Spatio-Temporal Poisson Processes Using the Inversion Method,” in 2020 Winter Simulation Conference (WSC) (IEEE; ), 492–503. 10.1109/wsc48552.2020.9384098 DOI

Zhi W., Senanayake R., Ott L., Ramos F. (2019). Spatiotemporal Learning of Directional Uncertainty in Urban Environments with Kernel Recurrent Mixture Density Networks. IEEE Robotics Automation Lett. 4, 4306–4313. 10.1109/lra.2019.2931262 DOI

Zhou Z., Matteson D. S. (2015). “Predicting Ambulance Demand: A Spatio-Temporal Kernel Approach,” in Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, 2297–2303.

Zhou Z., Matteson D. S. (2016). Predicting Melbourne Ambulance Demand Using Kernel Warping. Ann. Appl. Statistics 10, 1977–1996. 10.1214/16-aoas961 DOI

Zhou Z., Matteson D. S., Woodard D. B., Henderson S. G., Micheas A. C. (2015). A Spatio-Temporal Point Process Model for Ambulance Demand. J. Am. Stat. Assoc. 110, 6–15. 10.1080/01621459.2014.941466 DOI