Method and system for propagating the state of an object and its uncertainty

摘要

Embodiments of the present invention are directed to reducing the computational cost of propagating the uncertainty in the state of an object, which requires the numerical solution of an initial value problem (IVP) ensemble, by means of a computer. The present invention uses an implicit-Runge-Kutta-based (IRK) method that exploits the proximity of the initial conditions within the IVP ensemble. More specifically, one of the IVPs can be solved over a given time span consisting of one or more time steps with an IRK method, and the resulting trajectory can be recorded. The system of equations that arises on each time step of the IRK method can be solved using various iterative methods. The remaining IVPs can be solved over the same timespan using the same IRK method and time steps, together with the recorded trajectory from the first propagation.

主权项

1. A method for propagating the state of an object and an uncertainty associated with the state of the object, the method comprising:
receiving, by a computer system, an interval of time over which the uncertainty is to be propagated, as well as an ensemble of initial conditions that characterize the initial uncertainty associated with the state of an object and an ordinary differential equation (ODE) describing dynamics of the state of the object, which together define an initial value problem (IVP) ensemble, for the object, the IVP ensemble comprising a plurality of IVPs; solving, by the computer system, the IVPs in the IVP ensemble wherein the solution of one or more of the IVPs in the IVP ensemble depends upon the solution of one or more of the other IVPs in the IVP ensemble; characterizing, by the computer system, the uncertainty associated with the state of the object at the end of the time interval based on solving the IVPs in the IVP ensemble.