A Novel Method for Computing State Transition Matrices due to the Unscented Transform

We present a new method for computing the state transition matrix of a nonlinear dynamical system. The proposed method does not require the implementation of complex partial derivatives or auto-differentiation of the dynamics, while removing the arbitrary choice of a perturbation step for traditional finite difference methods. We tested the new state transition matrices using three different applications: a simple two-body problem, a Mars atmospheric entry flight mechanics problem, and two future close encounters of the asteroid (101955) Bennu with the Earth. Results show that the unscented transform state transition matrices preserve symplecticity and perform just as well as the classical unscented transform. Furthermore, the new method can closely reproduce posterior distributions generated using Monte Carlo simulations, even in the presence of significant stiffness in the dynamics.