Article information

2016 , Volume 21, ¹ 4, p.64-98

Kulikova M.V., Kulikov G.Y.

Numerical methods for nonlinear filtering of signals and measurements

This paper studies numerical methods of contemporary nonlinear Kalman filtering for estimation of unknown vector of state in stochastic continuous-time systems presented by Ito-type stochastic differential equations with discrete measurements. The elaborated methods are analysed and compared in the case of severe conditions of tackling a seventh-dimensional radar tracking problem, where an aircraft executes a coordinated horizontal turn. The latter problem is considered to be a challenging example for testing nonlinear filtering algorithms. This paper explores such effective state estimation methods as the cubature and unscented Kalman filters, including their square-root versions. Implementation particulars and performances of the mentioned techniques are studied for various values of aircraft’s turn rate and sampling time. New variants of the extended and unscented Kalman filters are also presented for treating continuousdiscrete stochastic systems. It is shown that the new methods outperform the traditional extended Kalman filter in the considered air traffic control scenario.

[full text]
Keywords: Ito-type stochastic differential equations with discrete measurements, optimal estimate of the state vector of stochastic system, extended Kalman filter, unscented Kalman filter, cubature Kalman filter

Author(s):
Kulikova Maria Vyacheslavovna
Office: CEMAT Instituto Superior Tecnico Universidade de Lisboa
Address: Portugal, Lissabone, 1049-001 Lisboa

Kulikov Gennadiy Yurievich
Dr. , Associate Professor
Position: Senior Research Scientist
Office: CEMAT, Instituto Superior Tecnico, Lissabone
Address: Portugal, Lissabone, Av. Rovisco Pais 1
Phone Office: (351) 21401 607
E-mail: gkulikov@math.ist.utl.pt
SPIN-code: 11451

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Bibliography link:
Kulikova M.V., Kulikov G.Y. Numerical methods for nonlinear filtering of signals and measurements // Computational technologies. 2016. V. 21. ¹ 4. P. 64-98
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