Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Parallel Two-Step W-Methods with Peer Variables
SIAM Journal on Numerical Analysis
Matlab Guide
Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches
Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches
Computational aspects of continuous---discrete extended Kalman-filtering
Computational Statistics
Superconvergent explicit two-step peer methods
Journal of Computational and Applied Mathematics
Adaptive nested implicit Runge--Kutta formulas of Gauss type
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Cubature kalman filtering for continuous-discrete systems: theory and simulations
IEEE Transactions on Signal Processing
Variable-Stepsize Interpolating Explicit Parallel Peer Methods with Inherent Global Error Control
SIAM Journal on Scientific Computing
Global error estimation and control in linearly-implicit parallel two-step peer W-methods
Journal of Computational and Applied Mathematics
Square-Root Quadrature Kalman Filtering
IEEE Transactions on Signal Processing
New developments in state estimation for nonlinear systems
Automatica (Journal of IFAC)
Variable-stepsize doubly quasi-consistent parallel explicit peer methods with global error control
Applied Numerical Mathematics
Local and global error estimation and control within explicit two-step peer triples
Journal of Computational and Applied Mathematics
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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 Mazzoni (2007) 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.