Abstract
Time-of-Flight (ToF) estimation is a basic building block in many metrological applications. Performance criteria for these applications are the variance and the bias of the derived delay estimate. From a signal processing point of view chaotic signals exhibit properties which make them well suited for metrological applications. In this chapter we experimentally investigate the applicability of synchronized chaotic systems in a ToF measurement system. In particular, we show that the choice of the numerical solver has a significant impact on the estimation performance. We further present a new delay estimator based on Poincaré intersections and compare the resultant estimation performance with the performance of a standard correlation-based delay estimator.
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References
Abarbanel, H.: Analysis of Observed Chaotic Data. Springer (1996)
Abarbanel, H., Brown, R., Kennel, M.: Lyapunov exponents in chaotic systems: Their importance and their evaluation using observed data. International Journal of Modern Physics B 5(9), 1347–1375 (1991)
Alonge, F., Branciforte, M., Motta, F.: A novel method of distance measurement based on pulse position modulation and synchronization of chaotic signals using ultrasonic radar systems. IEEE Transactions on Instrumentation and Measurement 58(2), 318–329 (2009)
Cespedes, I., Huang, Y., Ophir, J., Spratt, S.: Methods for estimation of subsample time delays of digitized echo signals. Ultrasonic Imaging 17, 142–171 (1995)
Feldmann, U., Hasler, M., Schwarz, W.: Communication by chaotic signals: The inverse system approach. International Journal of Circuit Theory and Applications 24, 551–579 (1996)
Freedman, A.E.: Transmission channel compensation in self-synchronizing chaotic systems (1995)
Fujisaka, H., Yamada, T.: Stability theory of synchronized motion in coupled-oscillator systems. Progress of Theoretical Physics 69(1), 32–47 (1983)
Geist, K., Parlitz, U., Lauterborn, W.: Comparison of different methods for computing lyapunov exponents. Progress of Theoretical Physics 83(5), 875–893 (1990)
Parker, T.S., Chua, L.O.: Practical Numerical Algorithms for Chaotic Systems. Springer (1989)
Pecora, L.M., Carroll, T.L.: Driving systems with chaotic signals. Physical Review A 44(4), 2374–2383 (1991)
Pecora, L.M., Carroll, T.L.: Master stability functions for synchronized coupled systems. Physical Review Letters 80(10), 2109–2112 (1998)
Pecora, L.M., Carroll, T.L., Johnson, G.A., Mar, D.J., Heagy, J.F.: Fundamentals of synchronization in chaotic systems, concepts and applications. Chaos 7(4), 520–543 (1997)
Sorrentino, F., DeLellis, P.: Estimation of communication-delays through adaptive synchronization of chaos. Chaos, Solitons and Fractals 45(1), 35–46 (2012)
Sparrow, C.: The Lorenz Equations: Bifurcation, Chaos, and Strange Attractors. Springer-Verlag New York Inc., New York 10010 (1982)
Spears, B.K., Tufillario, N.B.: A chaotic lock-in amplifier. American Journal of Physics 76(3), 213–217 (2008)
Stavroulakis, P.: Chaos Applications in Telecommunications. CRC Press, Inc., Boca Raton (2005)
Wallinger, C.F., Brandner, M.: Numerical aspects of the synchronization performance of discretized dynamical systems. In: 19th IEEE Workshop on Nonlinear Dynamics of Electronic Systems (March 2011)
Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining lyapunov exponents from a time series. Physica D 16, 285–317 (1984)
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Wallinger, C.F., Brandner, M. (2013). Time-of-Flight Estimation Using Synchronized Chaotic Systems. In: Kyamakya, K., Halang, W., Mathis, W., Chedjou, J., Li, Z. (eds) Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering. Studies in Computational Intelligence, vol 459. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34560-9_4
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DOI: https://doi.org/10.1007/978-3-642-34560-9_4
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