Error Flow Filter

Particle filters have become ubiquitous in state estimation due to the relative ease of propagating a set of particles through a nonlinear dynamics model. However, incorporating information from nonlinear measurements is a perennial challenge. In particle flow, we seek to smoothly transport the particles from the prior distribution to the Bayesian posterior distribution resulting from each measurement. This work introduces a particle flow inspired by a homotopy between the prior mean and the maximizer of the posterior distribution. We derive a second homotopy that flows the set of particles along with the mean, treating them as errors on the prior distribution. We show experimental evidence that the error flow update is better able to match the shapes of non-Gaussian posterior distributions than existing flows. We also demonstrate the performance of the error flow filter in two applications, including a cislunar tracking scenario.