Adaptive step size approach to homotopy-based particle filtering Bayesian update

This paper describes a new approach to the numerical implementation of the Bayesian update step of the homotopy-based particle filter, by adaptively computing the step size for numerical integration of the states of the particles. The resultant flow of the particles follows the Bayesian update rule, so that, when the flow stops, the particles collectively approximate the a posteriori probability density, given an a priori probability distribution and a measurement likelihood function. The proposed approach mitigates the stiffness of the ordinary differential equation that defines the flow of particles. We will illustrate our solution concept through a simple example with a highly nonlinear measurement likelihood function so that the a posteriori probability is highly non-Gaussian.