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Unscented Kalman Filter and Gauss-Hermite Kalman Filter for Range-Bearing Target Tracking

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Proceedings of the 6th Brazilian Technology Symposium (BTSym’20) (BTSym 2020)


Radar systems are used for estimating the position and velocity of aircraft and ships from range and bearing measurements. In this article, we consider two motion models for a civilian aircraft: a constant velocity model and a coordinated turn model. Both kinematics models are written in state-space terms, where the velocity perturbations are modeled by a white noise acceleration model. In order to estimate the aircraft states given noisy measurements obtained from sensor outputs, we follow a Bayesian statistical approach that calculates the estimators of the unknown states. In our simulation, we recreate an air traffic control scenario and implement two nonlinear filtering algorithms in order to perform target tracking of the aircraft. The nonlinear Bayesian-based filters for this target tracking problem are the unscented Kalman filter and the Gauss-Hermite Kalman filter. Finally, the performance of both nonlinear filters is evaluated with a performance metric, root mean squared error, in Monte-Carlo runs.

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  1. Bar-Shalom Y, Li XR, Kirubarajan T (2004) Estimation with applications to tracking and navigation: theory algorithms and software. Wiley, Hoboken

    Google Scholar 

  2. Särkkä S (2013) Bayesian filtering and smoothing, vol 3. Cambridge University Press, Cambridge

    Book  Google Scholar 

  3. Arasaratnam I, Haykin S (2009) Cubature Kalman filters. IEEE Trans Autom Control 54(6):1254–1269

    Article  MathSciNet  Google Scholar 

  4. Afshari HH, Gadsden SA, Habibi S (2017) Gaussian filters for parameter and state estimation: a general review of theory and recent trends. Sig Process 135:218–238

    Article  Google Scholar 

  5. Julier SJ, Uhlmann JK (2004) Unscented filtering and nonlinear estimation. Proc IEEE 92(3):401–422

    Article  Google Scholar 

  6. Wan EA, Van Der Merwe R, Haykin S (2001) The unscented Kalman filter. Kalman Filter Neural Netw 5(2007):221–280

    Article  Google Scholar 

  7. Sánchez L, Infante S, Griffin V, Rey D (2016) Spatio-temporal dynamic model and parallelized ensemble Kalman filter for precipitation data. Braz J Probab Stat 30:653–675

    Article  MathSciNet  Google Scholar 

  8. Soto J, Infante S (2019) Ensemble Kalman filter and extended Kalman filter for state-parameter dual estimation in mixed effects models defined by a stochastic differential equation. In: International conference on ‘knowledge society: technology, sustainability and educational innovation’. Springer, pp 285–300

    Google Scholar 

  9. Arasaratnam I, Haykin S, Elliott RJ (2007) Discrete-time nonlinear filtering algorithms using Gauss-Hermite quadrature. Proc IEEE 95(5):953–977

    Article  Google Scholar 

  10. Ito K, Xiong K (2000) Gaussian filters for nonlinear filtering problems. IEEE Trans Autom Control 45(5):910–927

    Article  MathSciNet  Google Scholar 

  11. Infante S, Sanchez L, Hernandez A (2020) Stochastic models to estimate population dynamics. Stat Optimiz Inf Comput 8(1):136–152

    Article  MathSciNet  Google Scholar 

  12. Barragán G (2020) State and parameter estimation in stochastic dynamical system. Bachelor’s thesis. Escuela de Ciencias Matemáticas y Computacionales, Universidad de Investigación de Tecnología Experimental Yachay, Urcuquí, Ecuador.

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Correspondence to Gabriel Barragán .

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Barragán, G., Infante, S., Hernández, A. (2021). Unscented Kalman Filter and Gauss-Hermite Kalman Filter for Range-Bearing Target Tracking. In: Iano, Y., Saotome, O., Kemper, G., Mendes de Seixas, A.C., Gomes de Oliveira, G. (eds) Proceedings of the 6th Brazilian Technology Symposium (BTSym’20). BTSym 2020. Smart Innovation, Systems and Technologies, vol 233. Springer, Cham.

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  • Print ISBN: 978-3-030-75679-6

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