Discrete recursive Bayesian filtering on intervals and the unit circle

Various applications necessitate the estimation of quantities defined on intervals or the unit circle, which can also be parameterized as an interval. These applications include estimation of joint angles that are either limited to a certain range or that are 360-degree-periodic. For this purpose, we consider two approaches based on discretizing the state space that use fundamentally different density representations. We show how prediction and measurement update for systems with nonlinear dynamics and nonlinear measurement models can be performed in each representation. In particular, we discuss the choices that go into designing discrete filters, which are sometimes taken for granted. A thorough comparison and a numerical evaluation of both approaches show the advantages and disadvantages of each method.