Adaptive ODE solvers in extended Kalman filtering algorithms. (English) Zbl 1301.65062
Summary: This paper studies numerical methods that are used to treat ordinary differential equations arising in extended Kalman filtering algorithms. Such problems are called the moment equations and constitute an important subclass of differential equations. They all possess a number of specific properties that make the standard available software ineffective for some mathematical models in this area. For instance, we show that built-in Matlab ODE solvers are not able to cope with a number of tests considered here. In contrast, the hybrid method developed by T. Mazzoni [Comput. Stat. 23, No. 4, 514–539 (2008; Zbl 1224.62083)] exhibits much better performance on the same examples. The latter means that specially designed numerical schemes are needed for efficient solution of the moment equations instead of the standard software designed for general systems of ordinary differential equations.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 93E11 | Filtering in stochastic control theory |
Keywords:
extended Kalman filter; continuous-discrete model; moment differential equations; adaptive ODE solvers; mazzoni’s hybrid methodCitations:
Zbl 1224.62083References:
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