SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Adaptive ODE Solvers in the Continuous-Discrete Extended Kalman Filtering Method II: Square-Root Implementation and Application to Target Tracking

M. Kulikova and G. Kulikov

Abstract
The new Accurate Continuous-Discrete Extended Kalman Filter based on the combined use of the embedded Runge-Kutta pair "NIRK4(2)" with the global error control from [1] and Mazzoni's scheme [2] is discussed in detail, here. First, its square-root variant is designed to improve accuracy and robustness for a finite-precision computer arithmetics. Then, it is examined in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn. The latter is considered to be a challenging one for testing nonlinear filtering algorithms. Our numerical results confirm that the presented technique is flexible and robust. It treats successfully (and without any additional tuning) the target tracking problem for various initial data and for a range of sampling times.

Bibliography
[1] G. Yu. Kulikov, Cheap global error estimation in some Runge-Kutta pairs, IMA J. Numer. Anal., 33 (2013), pp. 136-163.
[2] T. Mazzoni, Computational aspects of continuous-discrete extended \symbol"4Balman filtering, Computational Statistics, 23 (2007), pp. 519-539.

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