Particle filtering with observations in a manifold

This paper describes the application of particle filtering to the solution of the problem of filtering with observations in a manifold. Mathematically, this is based on an original use of so-called connector maps. It is shown that well-chosen connector maps can be used to transform successive samples from a continuous time observation process, evolving on a manifold, into a discrete sequence of random vectors, which are asymptotically independent and normally distributed, in the limit where the sampling interval goes to zero. Roughly speaking, this “innovation sequence” can be used as the input of a sequential Monte Carlo algorithm. As a concrete application, numerical simulation results are presented, for the problem of estimating the angular velocity of a rigid body from noisy observations of its attitude.