, the k-th step get the new measurement x(t k )

, Update the one-step-ahead predictor gains ?(t k ) using algorithm (9) with L = 1 and substituting ? in the place ofc

, Computec(t k ) as (13) using the one-step-ahead predictor gains ?(t k ), Step, vol.3

. References and . Systems, Touch X specification, 2019.

S. Aranovskiy, A. Bobtsov, R. Ortega, and A. Pyrkin, Performance enhancement of parameter estimators via dynamic regressor extension and mixing, IEEE Transactions on Automatic Control, vol.62, issue.7, pp.3546-3550, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01612256

S. Aranovskiy and L. B. Freidovich, Adaptive compensation of disturbances formed as sums of sinusoidal signals with application to an active vibration control benchmark, European Journal of Control, vol.19, issue.4, pp.253-265, 2013.

S. Aranovskiy, R. Ushirobira, D. Efimov, and G. Casiez, Modeling pointing tasks in mouse-based human-computer interactions, Decision and Control (CDC), 2016 IEEE 55th Conference on. IEEE, pp.6595-6600, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01380318

S. Aranovskiy, R. Ushirobira, D. Efimov, and G. Casiez, Frequency domain forecasting approach for latency reduction in direct human-computer interaction, Conference on Decision and Control, pp.2623-2628, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01651329

K. Aström and B. Wittenmark, Adaptive Control, 1994.

F. Bérard and R. Blanch, Two touch system latency estimators: high accuracy and low overhead, Proceedings of the 2013 ACM international conference on Interactive tabletops and surfaces, pp.241-250, 2013.

G. Casiez, S. Conversy, M. Falce, S. Huot, and N. Roussel, Looking through the Eye of the Mouse : A Simple Method for Measuring End-toend Latency using an Optical Mouse, Proceedings of the 28th ACM Symposium on User Interface Software and Technology, pp.629-636, 2015.

G. Casiez, T. Pietrzak, D. Marchal, S. Poulmane, M. Falce et al., Characterizing latency in touch and button-equipped interactive systems, Proceedings of the 30th Annual ACM Symposium on User Interface Software and Technology, pp.29-39, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01586803

E. Cattan, A. Rochet-capellan, P. Perrier, and F. Bérard, Reducing latency with a continuous prediction: Effects on users' performance in direct-touch target acquisitions, Proceedings of the 2015 International Conference on Interactive Tabletops & Surfaces. ACM, pp.205-214, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01240829

J. Currie, D. I. Wilson, N. Sahinidis, and J. Pinto, Opti: Lowering the barrier between open source optimizers and the industrial matlab user. Foundations of computer-aided process operations 24, p.32, 2012.

M. A. Fischler and R. C. Bolles, Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography, Commun. ACM, vol.24, issue.6, pp.381-395, 1981.

G. C. Goodwin, S. F. Graebe, and M. E. Salgado, Control system design, 2001.

R. Jota, A. Ng, P. Dietz, and D. Wigdor, How fast is fast enough?: a study of the effects of latency in direct-touch pointing tasks, Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pp.2291-2300, 2013.

B. Kim and Y. Lim, Mobile terminal and touch coordinate predicting method thereof, p.661, 2014.

E. Lank, Y. N. Cheng, and J. Ruiz, Endpoint prediction using motion kinematics, Proceedings of the SIGCHI conference on Human factors in computing systems (CHI 07), pp.637-646, 2007.

I. S. Mackenzie and C. Ware, Lag as a determinant of human performance in interactive systems, Proceedings of the INTERACT'93 and CHI'93 conference on Human factors in computing systems, pp.488-493, 1993.

M. Mboup, C. Join, and M. Fliess, Numerical differentiation with annihilators in noisy environment, Numerical algorithms, vol.50, issue.4, pp.439-467, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00319240

F. Moussavi, Methods and apparatus for incremental prediction of input device motion, US Patent, vol.8, p.915, 2014.

A. Ng, J. Lepinski, D. Wigdor, S. Sanders, and P. Dietz, Designing for low-latency direct-touch input, Proceedings of the 25th Annual ACM Symposium on User Interface Software and Technology, pp.453-464, 2012.

A. Ng, J. Lepinski, D. Wigdor, S. Sanders, and P. Dietz, Designing for low-latency direct-touch input, Proceedings of the 25th annual ACM symposium on User interface software and technology, pp.453-464, 2012.

W. Perruquetti, T. Floquet, and E. Moulay, Finite-time observers: application to secure communication, IEEE Transactions on Automatic Control, vol.53, issue.1, pp.356-360, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00176758

. Qingkui, Curve fitting based touch trajectory smoothing method and system, CN Patent App. CN, vol.201, p.264, 2014.

J. F. Sturm, Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones, Optimization methods and software, vol.11, issue.1-4, pp.625-653, 1999.

R. Ushirobira, D. Efimov, G. Casiez, N. Roussel, and W. Perruquetti, A forecasting algorithm for latency compensation in indirect humancomputer interactions, European Control Conference (ECC). Aalborg, pp.1081-1086, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01420653

P. Varnell, M. Malisoff, and F. Zhang, Stability and robustness analysis for human pointing motions with acceleration under feedback delays, International Journal of Robust and Nonlinear Control, 2016.

J. Wu and M. Ouhyoung, On latency compensation and its effects on head-motion trajectories in virtual environments, The visual computer, vol.16, issue.2, pp.79-90, 2000.